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ASReml User Guide - VSN International

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1. 58 5 5 Transforming the data IDOM A is used to form dominance covariables from a set of additive marker covariables previously declared with the MM marker map qualifier It assumes the argument A is an existing group of marker variables relating to a linkage group defined using MM which rep resents additive marker variation coded 1 0 1 representing marker states aa aA and AA respectively It is a group transformation which takes the 1 1 interval values and calculates X 0 5 2 i e 1 and 1 become one 0 becomes 1 The marker map is also copied and applied to this model term so it can be the argument in a qt1 term page 98 IDO ENDDO provides a mechanism to repeat transformations on a set of variables All tranformations except DOM and RESCALE operate once on a single field unless preceded by a DO qualifier The DO qualifier has three arguments n i i n is the number of times the following transformations are to be performed i default 1 is the increment applied to the target field i default 0 0 is the increment applied to the transformation argument The default for n is the number of variables in the current field definition ENDDO is formally equivalent to DO 1 and is implicit when another DO appears or the next field definition begins Note that when several transformations are repeated the processing order is that each is performed n times before the next is processed contrary to th
2. In the code box to the right is the ASReml win Alliance Trial 1989 command file nin89a as for a spatial analysis variety A Alphanumeric of the Nebraska Intrastate Nursery NIN field id experiment introduced Chapter 3 The lines Pid that are highlighted in bold blue type relate ane 4 to reading in the data In this chapter we use te this example to discuss reading in the data in yield detail lat long row 22 column 11 nin89aug asd skip 1 yield mu variety f mv i 2 5 2 Important rules mm 22 row AR1 904 Notice in line comment introduced by the character In the ASReml command file e all blank lines are ignored e is used to annotate the input all characters following a symbol on a line are ignored e lines beginning with followed by a blank are copied to the asr file as comments for the output e a blank is the usual separator TAB is also a separator e maximum line length is 2000 characters e a comma as the last character on the line is sometimes used to indicate that the current list is continued on the next line a comma is not needed when ASReml knows how many values to read 44 5 2 Important rules e reserved words used in specifying the linear model Table 6 1 are case sensitive they need to be typed exactly as defined they may not be abbreviated e a qualifier is a letter sequence beginning with an which sets an option some qualifiers require arguments
3. Pa HE UNIVERSITY GRDC CMM OF ADELAIDE Grano S SAG AUSTRALIA Ei aire F Development Corporation sn ASReml User Guide Release 4 1 Structural Specification A R Gilmour VSN International Hemel Hempstead United Kingdom B J Gogel University of Adelaide Australia B R Cullis Universtiy of Wollongong Australia S J Welham VSN International Hemel Hempstead United Kingdom R Thompson Rothamsted Research Harpenden United Kingdom April 8 2015 ASReml User Guide Release 4 1 Structural Specification ASReml is a statistical package that fits linear mixed models using Residual Maximum Like lihood REML It was a joint venture between the Biometrics Program of NSW Department of Primary Industries and the Biomathematics Unit of Rothamsted Research Statisticians in Britain and Australia have collaborated in its development Main authors A R Gilmour B J Gogel B R Cullis S J Welham and R Thompson Other contributors D Butler M Cherry D Collins G Dutkowski S A Harding K Haskard A Kelly S G Nielsen A Smith A P Verbyla and I M S White Author email addresses arthur gilmour Cargovale com au beverley gogel adelaide edu au bcullisQuow edu au sue welham vsni co uk robin thompson rothamsted ac uk Copyright Notice Copyright 2014 VSN International All rights reserved Except as permitted under the Copyright Act 1968 Commonwealth of Australia no part o
4. Use a SKIP qualifier after the filename to skip any heading lines Names found in the data that are not included are simply appended to the list of levels as they are discovered by ASReml An example of this would be for a genotype factor with 6 levels appearing in the data file in the order genb6 genal gena5 genb2 genb4 gena3 In this case Genotype A L genal genb2 gena3 genb4 would result in the levels of Genotype being ordered genal genb2 gena3 genb4 genb6 genad I n is required if the data is numeric defining a factor but not 1 n I must be followed by n if more than 1000 codes are present Year LI 1995 1996 AS p is required if the data field has level names in common with a previous A or I factor p and is to be coded identically for example in a plant diallel experiment Male A 22 Female AS Male integrated coding IP indicates the special case of a pedigree factor ASReml will determine whether the identifiers are integer or alphanumeric from the pedigree file qualifiers and set the levels after reading the pedigree file see Section 9 3 Animal P coded according to pedigree file A warning is printed if the nominated value for n does not agree with the actual number of levels found in the data if the nominated value is too small the correct value is used for a group of m variates or factor variables 48 5 4 Specifying and reading the data IG m 1 is used when m contiguous data fields comprise a
5. qualifiers must appear on the correct line qualifier identifiers are not case sensitive qualifier identifiers may be truncated to 3 characters 45 5 4 Specifying and reading the data 5 3 Title line The first 40 characters of the first nonblank NIN Alliance Trial 1989 text line in an ASReml command file are taken variety 1A as a title for the job Use this to document id the analysis for future reference An optional pid qualifier line see section 11 3 may precede the title line It is recognised by the presence of the qualifier prefix letter Therefore the title MUST NOT include an exclamation mark 5 4 Specifying and reading the data Typically a data record consists of all the information pertaining to an experimental unit plot animal assessment Data field definitions manage the process of converting the fields as they appear in the data file to the internal form needed by ASReml This involves mapping coding factors general transformations skipping fields and discarding unnecessary records If the necessary information is not in a single file the MERGE facility see Chapter 12 may help Variables are defined immediately after the job title These definitions indicate how each field in the data file is handled as it is read into ASReml Transformations can be used to create additional variables Users can explicity nominate how many are read with the READ qualifier described in Tabl
6. HAHAHA x xxx e ee seers art triz 2K x ls o XzxXXx 2X looL lt Do x x xXx x H ESOS smig chenn lt O lt lt LLLoo o L lt lt lt lt D DL 0 x x 1 9 378 0 38 0 50 0 65 0 77 1 00 0 77 0 65 0 50 2 0 147 0 27 0 39 0 51 0 56 0 64 0 56 0 50 0 40 3 0 05 0 11 0 19 0 28 0 35 0 42 0 40 0 35 0 30 Residuals Percentage of sigma 6 979 0 o 0 o 0 o 0 o 0 0 o 0 0 74 64 90 52 20 61 11 132 26 0 63 15 99 37 84 48 110 228 32 14 sag 30 3 37 4 23 32 44 46 109 97 83 67 o 3 6 0 2 44 16 51 25 32 120 33 10 58 417 113 2 84 19 51 45 18 30 56 9 12 53 41 7 99 123 47 87 103 81 61 81 130 94 10 55 53 55 106 15 109 153 23 43 24 90 37 23 64 130 84 122 129 126 90 38 91 133 126 218 332 174 77 19 38 29 58 63 88 4 124 49 101 129 113 352 319 253 166 152 52 28 O 97 135 67 16 9 36 96 24 356 335 183 179 189 118 124 14 52 19 7 56 81 33 63 40 352 323 288 151 56 130 188 29 78 7 12 30 39 57 89 3 I I I I I TOA paba A A Ges ag A E ts SA a 3333 ae ma gi bi sg ee g iy f Rx oF gt gt I I i I I I I I IE S a E Ia EN a IR La 3 229979 9 gt 333973773 9 T3 gt 14 gt I I I I I I I NI 313 22 2 gt gt gt gt gt gt gt gt gt 9 aa as a 2 A ata Ps a AAA gt gt gt EE 29 gt gt gt oe p le RR I I I I I wl 5 EUA AA te Pen Poe gt sk i
7. creates a factor with a new level whenever there is a level present for the factor f Levels effects are not created if the level of factor fis 0 missing or negative The size may be set in the third argument by setting the second argument to zero creates a factor with a level for every record subject to the factor level of f equalling k i e a new level is created for the factor whenever a new record is encountered whose integer truncated data value from data field fis k Thus uni site 2 would be used to create an independent error term for site 2 in a multi environment trial and is equivalent to at site 2 units The default size of this model term is the number of data records The user may specify a lower number as the third argument There is little computational penalty from the default but the s1n file may be substantially larger than needed However if the units vector is full size the effects are mapped by record number and added back to the fitted residual for creating residual plots 98 6 6 Alphabetic list of model functions Table 6 2 Alphabetic list of model functions and descriptions model function action vect v xfa f k is used in a multivariate analysis on a multivariate set of covariates v to pair them with the variates The test example included signal G 93 93 slides background G 93 dart asd ASUV signal Trait Trait vect background to fit a slide specific regression of s
8. LE oh j ee OorRPFOWRNAOAAHTOTWOODOONF OOO 8 1 32 26 85 85 36 24 00 00 80 51 12 42 42 03 35 29 35 58 85 Ad fixed by user positive definite unbounded 0 0 OO OO DO OD 0000000200 w ies gu ro mu a gt Mas lo i SS os es is ls w iS Very small components with Comp SE ratios of zero sometimes indicate poor scaling Consider rescaling the design matrix in such cases Covariance Variance Correlation Matrix US Residual 8 738 0 5849 0 2992 0 1518 0 2374 7 284 17 75 0 5067 0 2658 0 4837 0 2477 0 7052 0 1095 0 4194 0 1996 0 8168 2 038 0 2527 3 314 0 9233E 01 0 8715 2 5631 0 8205E 01 0 2088 1 543 Covariance Variance Correlation Matrix XFA xfa Trait 3 tag 1 392 0 2983 0 1874 0 2856 0 4624E 01 0 7393E 01 0 4412E 01 0 8804 O 1708 O 1022 0 5642E 01 0 4721E 01 0 6516E 01 0 3416 0 3150E 01 0 2818 0 3001E 01 0 7293E 01 0 6995 0 4765 0 1867E 01 0 7347E 02 0 2752E 02 0 1364 0 1171 0 1086E 02 0 1800 4 2190 0 2015E 01 0 1786 1 174 0 5319E 01 0 6018E 01 0 2651 0 4520E 01 0 1199 0 9429E 01 0 1166 0 4406 0 2885 Covariance Variance Correlation Matrix XFA xfa TrDam12 1 dam 1 614 1 0000 1 0000 1 465 1 330 1 0000 1 270 1 153 1 0000 Covariance Variance Correlation Matrix US TrLit1234 1it 3 847 0 6368 0 2474 1182 01 2 020 4 079 0 6455 0 4860 0 7677E 01 0 2063 0 2504E 01 0 3699 0 1183 0 8241 0 4914E 01 0 7049 5217 0000 0 000 0 000 9207E 03 8570 857
9. TrLit1234 1it TrLit1234 1it TrLit1234 1it TrLit1234 1it TrLit1234 1lit TrL1it1234 11 TrLit1234 1it TrLit1234 1lit TrL1 1234 L11t TrLit1234 1it Damv Damv Damv Damv Damv Damv phenWYG phenWYG phenWYG phenWYG phenWYG phenWYG phenD 7 phenD 8 phenD 9 phenD 10 phenF 11 phenF 12 phenF 13 phenF 14 phenF 15 Direct 23 Direct 24 Direct 25 Direct 26 Direct 27 Direct 28 Direct 29 Direct 30 Direct 31 Direct 32 Direct 33 Direct 34 Direct 35 Direct 36 Direct 37 OonRr WNP 0 0 0 0 0 0 0 0 0 0 0 0003 iS a e a 2 1583 2 2252 2 3077 16225 16827 18881E 01 15 766 11 784 24 024 43182 88424 19460 95054 1 1380 25006 4 6988 89101 2 6165 79486E 01 68664E 01 1 6644 2 3758 2 7093 6 2253 11219 11514E 01 60077E 01 23849 26281 19102091 63142 16291 53335 35085E 02 18892 13069 was 03 03 03 OO Soe Perr gs AKSONO PP PWWWNNPRPRPRP TCO an UH HS 02 b2 po 02 b2 b2 re ro 02 b2 ro 02 b2 ro OB WwW ds 33589 37368 63232 32785E 01 47001E 01 59274E 02 31286 37589 63510 33038E 01 44563E 01 55003E 02 29825 37755 37255E 01 22522 10759 14261 12431E 01 10198 51205E 01 64586 85213 1 5966 0 73359E 01 0 11109 0 14996E 01 0 44400 0 64674 0 76604E 01 0 34354 0 0 0 0 0 OO OO COO OO SS o Oo OO Oo OO Oo OOD Oo Oo 16518 27002 23889E 01 12314 65488E 01 337 0 8
10. 8 are zero 31 TrLit1234 1it 19484 effects fitted 20 are zero The REML estimates of all the variance matrices except for the dam components are positive definite Heritabilities for each trait can be calculated using the VPREDICT facility of ASReml The heritability is given by 335 16 11 Multivariate animal genetics data Sheep where o is the phenotypic variance and is given by 2 2 2 2 2 Op 0 07 0 0 recalling that i 2 2 Oo 0 s 4 A 1 2 2 2 Og 474 Om In the half sib analysis we only use the estimate of additive genetic variance from the sire variance component ASReml then carries out the VPREDICT instructions in the asr file stores the instructions in a pin file and produces the following output in a pve file ASReml 4 1 01 Dec 2014 Multivariate Sire amp Dam coopms3 pvc created 27 Mar 2015 10 12 47 786 Results from analysis of wwt ywt gfw fdm fat Residual 35200 effects 1 Residual Residual v 1 4 9 46109 0 284202 2 Residual Residual c 2 1 7 34181 0 357266 3 Residual Residual Y 22 17 6050 0 649871 4 Residual Residual G 3 0 212536 U 325222E 01 5 Residual Residual C 3 2 0 668009 0 477490E 01 6 Residual Residual V 2 B 0 141595 0 597447E 02 7 Residual Residual C 4 1 0 963017 0 333224 8 Residual Residual C 4 2 1 99771 0 548821 9 Residual Residual C 4 3 0 286984 0 564929E 01 10 Residual Residual V 4 4 3 64374 0 404860 11 Residual Residual G d 0 850282 0 100269 12 Re
11. ASReml increases to the correct value indent them to avert this message user nominated more levels than are permitted constraint parameter is probably wrongly assigned fix the argument The model term Trait was not present in the multivariate anal ysis model you may need more iterations restart to do more iterations see CONTINUE The computed LogL value is occasionally very large in magni tude but our interest is in relative changes Reporting relative to an offset ensures that differences at the units level are ap parent missing cells are normally not reported consider setting levels correctly the limit is 100 PREDICT statements because it contains errors if you really want to fit this term twice create a copy with another name gives details so you can check ASReml is doing what you intend that is these standard errors are approximate use the correct syntax the A fields will be treated as factors but are coded as they appear in the binary file use correct syntax 263 15 5 Information Warning and Error messages Table 15 2 List of warning messages and likely meaning s warning message likely meaning Warning The X Y G qualifiers are ignored There is no data to plot Warning Warning The default action with missing values in multivariate data Warning The estimation was ABORTED Warning The FOWN test of is not calculated Warning The labels fo
12. Analysis of covariance and standardisation as instances of predicton Biometrics 38 613 621 McCulloch C and Searle S R 2001 Generalized Linear and Mixed Models Wiley 346 BIBLIOGRAPHY Meuwissen and Lou 1992 Forming iniverse nrm Genetics Selection and Evolution 24 305 313 Millar R and Willis T 1999 Estimating the relative density of snapper in and around a marine reserve using a log linear mixed effects model Australian and New Zealand Journal of Statistics 41 383 394 Nelder J A 1994 The statistics of linear models back to basics Statistics and Computing 4 221 234 Patterson H D and Thompson R 1971 Recovery of interblock information when block sizes are unequal Biometrika 31 100 109 Pinheiro J C and Bates D M 2000 Mixed Effects Models in S and S PLUS Springer Verlaag Quaas R L 1976 Computing the diagonal elements and inverse of a large numerator relationship matrix Biometrics 32 949 953 Robinson G K 1991 That blup is a good thing The estimation of random effects Statistical Science 6 15 51 Rodriguez G and Goldman N 2001 Improved estimation procedures for multilevel models with binary response A case study Journal of the Royal Statistical Society A General 164 2 339 355 Sargolzaei Iwaisaki and Colleau 2005 A fast algorithm for computing inbreeding coefh cients in large populations Genetics Selection and Evolution 122 3
13. e repeated measures data multivariate analysis of variance and spline type models e un balanced designed experiments e multi environment trials and meta analysis univariate and multivariate animal breeding and genetics data involving a relationship matrix for correlated effects e regular or irregular spatial data The engine of ASReml underpins the REML procedure in GENSTAT An interface for R called ASReml R is available and runs under the same license as the ASReml program While these interfaces will be adequate for many analyses some large problems will need to use ASReml The ASReml user interface is terse Most effort has been directed towards efficiency of the engine It normally operates in a batch mode Problem size depends on the sparsity of the mixed model equations and the size of your computer However models with 500 000 effects have been fitted successfully The compu tational efficiency of ASReml arises from using the Average Information REML procedure giving quadratic convergence and sparse matrix operations ASReml has been operational since March 1996 and is updated periodically 1 3 User Interface 1 2 Installation Installation instructions are distributed with the program If you require help with installa tion or licensing please email support asreml co uk 1 3 User Interface ASReml is essentially a batch program with some optional interactive features The typical sequence of operations whe
14. extraspan p Improving the graphical labcharsize n panelcharsize n vertxlab abbrdlab n abbrxlab n If these arguments are used all prediction factors except for those specified with only one prediction level must be listed once and only once otherwise these arguments are ignored specifies the prediction factor to be plotted on the x axis specifies the prediction factors to be superimposed on the one panel specifies the conditioning factors which define the panels These should be listed in the order that they will be used specifies the page to start at for multi page predictions specifies the name of the file to save the plot to specifies the panel layout on each page specifies that the panels be arranged by columns default is by rows specifies that each page contains n blank panels This sub option can only be used in combination with the layout sub option specifies that an additional n blank panels be used every p pages These can only be used with the layout sub option appearance and readability specifies the relative size of the data points labels default 0 4 specifies the relative size of the labels used for the panels default 1 0 specifies that vertical annotation be used on the x axis default is horizontal specifies that the labels used for the data be abbreviated to n characters specifies that the labels used for the x axis annotation be appreviated to n characters 187
15. gt Q T4891 where 2 57 and N are positive definite symmetric matrices corresponding to the between traits variance matrices for sires dams and litters respectively The variance matrix for dams does not involve fibre diameter and fat depth while the variance matrix for litters does not involve fat depth The effects in each of the above vectors are ordered levels within traits Lastly we assume that the residual variance matrix is given by Ve Q L7043 Table 16 15 Wald F statistics of the fixed effects for each trait for the genetic example term wwt ywt gfw fdm fat age 331 3 67 1 52 4 26 7 5 brr 5546 73 4 149 03 13 9 sex 196 1 1233 02 2 9 0 6 age sex 103 1 7 19 5 0 329 16 11 Multivariate animal genetics data Sheep Table 16 16 presents the sequence of variance models fitted to each of the four random terms sire dam litter and error in the ASReml job IRENAME 1 ARG 1 CHANGE 1 TO 2 OR 3 FOR OTHER PARTS Multivariate Sire amp Dam DOPATH 1 tag sire 92 II dam 3561 I grp 49 sex brr 4 litter 4871 age wwt IMO MO identifies missing values ywt MO gfw MO fdm IMO fat IMO PATH 1 coop fmt PATH 2 coop fmt CONTINUE coopmsi rsv uses initial values from previous rsv file PATH 3 coop fmt CONTINUE coopms2 rsv uses initial values from previous rsv file PATH O USING SUBSET TO SET UP COMBINATIONS OF TRAITS USED IN MODEL ISUBSET TrDam123 Trait 12300 I SUBSE
16. instructs ASReml to attempt a plot of the predicted values This qualifier is only applicable in versions of ASReml linked with the Winteracter Graphics library If there is no argument ASReml produces a figure of the predicted values as best it can The user can modify the appearance by typing lt Esc gt to expose a menu or with the plot arguments listed in Table 10 2 instructs ASReml to print the predicted value even if it is not of an estimable function By default ASReml only prints predictions that are of estimable functions requests all standard errors of difference be printed Normally only an aver age value is printed Note that the default average SED is actually an SED calculated from the average variance if the predicted values and the average covariance among the predicted values rather than being the average of the individual SED values However when SED is specified the average of the individual SED values is reported requests t statistics be printed for all combinations of predicted values requests ASReml to scan the predicted values from a fitted line for possible turning points and if found report them and save them internally in a vector which can be accessed by subsequent parts of the same job using TPn This was added to facilitate location of putative QTL Gilmour 2007 185 10 3 Prediction Table 10 1 List of prediction qualifiers qualifier action TWOSTAGEWEIGHTS IVPV is inten
17. qualifier action ATSINGULARITIES BMP IBRIEF n can be specified to force a job to continue even though a singularity was detected in the Average Information AI matrix The AI matrix is used to give updates to the variance parameter estimates In release 1 if singularities were present in the AI matrix a generalized inverse was used which effectively conditioned on whichever parameters were identified as singular ASReml now aborts processing if such singularities appear unless the AISINGULARITIES qualifier is set Which particular parameter is singular is reported in the variance component table printed in the asr file The most common reason for singularities is that the user has overspeci fied the model and is likely to misinterpret the results if not fully aware of the situation Overspecification will occur in a direct product of two un constrained variance matrices see Section 2 1 15 when a random term is confounded with a fixed term and when there is no information in the data on a particular component Another common cause is when fitting an animal model and there is ex cessive sire dam variance so that heritability from a sire model would exceed 1 so that the residual variance under the animal model has ap proached zero In this case the data contradicts the assumptions of the animal model The best solution is to reform the variance model so that the ambiguity is removed or to fix one of the parameters
18. 10 3 Prediction Table 10 2 List of predict plot options option action abbrslab n specifies that the labels used for superimposed factors be abbreviated to n characters 188 10 3 Prediction 10 3 4 Associated factors ASSOCIATE factors facilitates prediction when the levels of one factor group or classify the levels of another especially when there are many levels factors is an list of factors in the model which have this hierarchical relationship Typical examples are individually named lines grouped into families usually with unequal numbers of lines per family or trials conducted at locations within regions Declaring factors as associated allows ASReml to combine the levels of the factors appropri ately For example in the preceding example when predicting a trial mean to add the effect of the location and region where the trial was conducted When identifying which levels are associated ASReml checks that the association is strictly hierarchal tree like That is each trial is associated with one location and each location is associated with only one region If a level code is missing for one component it must be missing for all Averaging of associated factors will generally give differing results depending on the order in which the averaging is performed We explore this with the following extended example Consider the mean yields from 15 trials classified by region and location in Table 10 4 Table 10
19. 11 15 Trait sire 11 15 defines 70 74 11313 33 37 F Direct Trait sire 4 defines 75 89 23 37 4 F Maternal Damv Trait 1 6 defines 90 95 54 59 23 28 F residWYG phenWYG Trait sire 1 6 defines 96 101 60 65 23 28 F residWYG phenD Trait sire 7 10 defines 102 105 66 69 29 32 F residWYG phenF Trait sire 11 15 defines 106 110 70 74 33 37 defines 96 110 60 74 23 37 H WWTh2 Direct 1 phenWYG 1 75 60 H YWTh2 Direct 3 phenWYG 3 77 62 H GFWh2 Direct 6 phenWYG 6 80 65 H FDMh2 Direct 10 phenD 4 84 69 H FATh2 Direct 15 phenF 5 89 74 R GenCor Trait sire 23 37 R MatCor Maternal 90 95 Table 16 16 Variance models fitted for each part of the ASReml job in the analysis of the genetic example term matrix PATH 1 PATH 2 PATH 3 sire x DIAG FA1 US dam Ya DIAG FA1 FA1 litter gt DIAG FA1 US error Y US US US LogL 1566 45 1488 11 1480 89 Parameters 36 48 55 The specification in Release 3 required specification of initial values for variance parameters and also through the use of CONTINUE the generation of initial values from previous analyses In Release 4 use of instead of initial values asks ASReml to estimate initial values In this example we start by fitting diagonal matrices for sire dam and litter using initial values from univariate analyses and estimate an unstructured residual matrix Unfortunately ASReml does not yet have an automatic way of ta
20. 2 1 TRR The file written by ASReml has extension own and looks like 15 2 1 0 6025860D 000 1164403D 00 This file was written by asreml for reading by your program MYOWNGDG asreml writes this file runs your program and then reads shfown gdg which it presumes has the following format The first lines should agree with the top of this file specifying the order of the matrices C 15 the number of variance parameters 2 and a control parameter you can specify 1 These are written in 315 format They are followed by the list of variance parameters written in 6D13 7 format Follow this with 3 matrices written in 6D13 7 format These are to be each of 120 elements being lower triangle row wise of the G matrix and its derivatives with respect to the parameters in turn This file contains details about what is expected in the file written by your program The filename used has the same basename as the job you are running with extension own for the file written by ASReml and gdg for the file your program writes The type of the parameters is set with the T qualifier described below The control parameter is set using the F qualifier F2 applies to OWN models With OWN the argument of F is passed to the MYOWNGDG program as an argument the program can access This is the mechanism that allows several OWN models to be fitted in a single run Ts is used to set the type of the parameters It is primarily used in conjunct
21. 2 2 1 2 2 2 gt gt FOR 2 gt gt 2 EJ gt gt 2 EJ gt The primary output follows Nfam 71 A Nfemale 26 A Nmale 37 A Clone A 860 MatOrder 914 A rep 8 A iblk 80 A prop 1 A culture 2 A treat 2 A measure 1 A CWAC6 M 9 Parsing snpData grr Clone 2 2 0 2 1 2 2 2 2 2 2 2 1 2 g Dr de Dig Dy 2 Di O59 2p Lid Lig oes 231322 132323 1 22 23271 2 Class names for factor Clone are initialized from the grr file GRR Header line begins Genotype 0 10024 01 114 0 10037 01 257 0 4854 Marker labels found Marker labels 0 10024 01 114 UMN CL98Contig1 Notice The header line indicates there are 4854 regressors in the file Notice SNP data line begins 140099 2 2 1 2 2 2 2 2 2 1 2 1 2 1 1 Notice Markers coded 9 treated as missing Marker data 0 1 2 for 923 genotypes and 4854 markers read from snpData grr 160414 missing Regressor values 3 6 replaced by column average Regressor values ranged 0 00 to 2 00 Regressor Means ranged 1 00 to 2 00 Sigma2p 1 p is 1057 12558 GIVi snpData grr 923 9 946 27 QUALIFIERS MAXIT 30 SKIP 1 DFF 1 QUALIFIER DOPART 2 is active Reading nassau_cut_v3 csv FREE FORMAT skipping 1 lines Univariate analysis of HT6 Summary of 6399 records retained of 6795 read Model term Size miss zero MinNonO Mean 1 Nfam 71 0 0 1 36 3379 2 Nfemale 26 0 0 1 12 8823 3 Nmale 37 0 0 1 15 2285 Warning More levels found in Clone than specified 4 Clone 926 0 0 1 464 676
22. 4239 91 S2 86032 666 df 0 9474 1 000 0 6596 8 LogL 4239 88 52 86169 666 df 0 9540 1 000 0 6668 9 LogL 4239 88 S2 86253 666 d 0 9571 1 000 0 6700 10 LogL 4239 88 S2 86280 666 df 0 9585 1 000 0 6714 Final parameter values 0 95918 1 0000 0 67205 Model_Term Gamma Sigma Sigma SE C variety 532 532 0 959184 82758 6 8 98 UP 296 16 7 Unreplicated early generation variety trial Wheat Variance 670 666 1 00000 86280 2 9 12 o P Residual AR AutoR 67 0 672052 0 672052 16 04 1U Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 83 6 9799 18 lt 004 3 weed 1 477 0 109 33 lt 001 The iterative sequence converged the REML estimate of the autoregressive parameter indi cating substantial within column heterogeneity The abbreviated output from the two dimensional AR1xAR1 spatial model is 1 LogL 4277 99 S2 0 12850E 06 666 df 2 LogL 4266 13 S2 0 12097E 06 666 df 3 LogL 4253 05 S2 0 10777E 06 666 df 4 LogL 4238 72 S2 83156 666 df 5 LogL 4234 53 S2 79868 666 df 6 LogL 4233 78 S2 82024 666 df 7 LogL 4233 67 S2 82725 666 df 8 LogL 4233 65 S2 82975 666 d 9 LogL 4233 65 S2 83065 666 df 10 LogL 4233 65 S2 83100 666 df Model_Term Gamma Sigma Sigma SE C variety 532 632 1 06038 838117 6 9 92 UP Variance 670 666 1 00000 83100 1 8 90 OP Residual AR AutoR 67 0 685387 0 685387 16 65 OU Residual AR AutoR 10 0 285909 0 285909 3 87 o y Wald F statistics Source of Variation NumDF Den
23. 6 10 3 Aliassing and singularities o ee ee e 106 6 10 4 Examples of alassing o co eee Ree RE es rat 107 IL Wald F SIA dc ee EEG RARE Se RGR e Ew A 107 Command file Specifying the variance structures 109 fA ip ceo a go ai ee eB ba eA eR ee Be ee ee in 109 7 1 1 Non singular variance matrices v v v vs 109 T2 Variance model specification in ASReml 0 110 7 3 A sequence of structures for the NIN data 110 7 4 Variance str ctures esparcir 117 TAL General Syke ooo cos radad oder uroka drakt 117 7 4 2 Variance header line 0 ee 119 obs R structure definition REN 120 7 4 4 G structure header and definition lines 121 7 5 Variance model description use ee a 123 7 5 1 Forming variance models from correlation models 128 vil 7 5 2 Notes on the variance models o eee ee koa GS oi Maters oe y eee e RES ROS ROSE EES 7 5 4 Notes on power models v v v vs 000 eee ee ee 7 5 5 Notes on Factor Analytic models 2 0004 7 5 6 Notes on OWN models 0 00000 pe eee 7 6 Variance structure qualifiers cis earn wk eee we ee ea Pee S fel Rules for combining variance models v v aaa 202 0000 ee 7 8 G structures involving more than one random term 7 9 Constraining variance parameters o a ee ee ee ee 7 9 1 Parameter constraints within a varia
24. 7 LogL 4225 60 as FITI 665 df 8 LogL 4225 60 S2 77786 665 df 9 LogL 4225 60 S2 77806 665 df Model_Term Gamma Sigma Sigma SE C variety 532 532 1 14370 38986 3 9 91 OP Variance 670 665 1 00000 77806 0 3 79 0 P Residual AR AutoR 67 0 671436 0 671436 15 66 OU Residual AR AutoR 10 0 266088 0 266088 253 GU Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 42 5 7073 70 lt 001 3 weed 1 457 4 91 31 lt 001 8 pol column 1 1 50 8 8 73 0 005 AR1xAR1 units pol column 1 1 LogL 4272 74 52 0 11683E 06 665 df 1 components constrained 2 LogL 4266 07 S2 50207 665 df 1 components constrained 3 LogL 4228 96 S2 76724 665 df 4 LogL 4220 63 S2 55858 665 df 5 LogL 4220 19 S2 54431 665 df 6 LogL 4220 18 S2 54732 665 df 7 LogL 4220 18 S2 54717 665 df 298 16 7 Unreplicated early generation variety trial Wheat Outer displacement Mer displacement Figure 16 7 Sample variogram of the residuals from the ARI xAR1 pol column 1 model for the Tullibigeal data 8 LogL 4220 18 S2 54715 665 df Model_Term Gamma Sigma Sigma SE C variety 532 532 1 34824 73769 0 7 08 gp units 670 670 0 556400 30443 6 off OP Variance 670 665 1 00000 54715 2 5 15 0 P Residual AR AutoR 67 0 837503 0 837503 18 67 OU Residual AR AutoR 10 0 375382 0 375382 3 26 OU Wald F statistics Source of Variation NumDF DenDF F_ine Prob 7 mu 1 13 6 4241 53 lt 001 3 weed 1 469 0 86 39 lt 001 8 p
25. A variance model can be specified but the S2 1 qualifier would then be required to fix the error variance at 1 and prevent ASReml trying to estimate two confounded parameters error variance and the parameter corresponding to the variance model specified see 3a on page 114 ASReml does not have an implicit scale parameter for G structures that are defined explic itly For this reason the model supplied when the G structure involves just one variance model must be a variance model an initial value must be supplied for this associated scale parameter this is discussed under additional_initial_values on page 121 when the G structure involves more than one variance model one must be either a homo geneous or a heterogeneous variance model and the rest should be correlation models if more than one are non correlation models then the GF qualifier should be used to avoid identifiability problems that is ASReml trying to estimate both parameters when they are confounded 7 8 G structures involving more than one random term The usual case is that a variance structure applies to a particular term in the linear model and that there is no covariance between model terms Sometimes it is appropriate to include a covariance Then it is essential that the model terms be listed together and that the variance structure defined for the first term be the structure required for both terms When the terms are of different size the terms mu
26. If the key values are the ordered sequence 1 N the key field may be omitted if NOKEY is specified If the key is not in the first field its location can be specified with KEY k If extracting a single covariate from a large set of covariates in the file the specific field to extract can be given by FIELD s in absolute terms or relative to the key field by IRFIELD r For example IMBF mbf variety 1 markers csv key 1 RFIELD 35 rename Marker35 SKIP k requests the first k lines of the file be ignored SPARSE can be used when the covariates are predominately zero Each key value is followed by as many column value pairs as required to speci fiy the non zero elements of the design for that value of key The pairs should be arranged in increasing order of column within rows The rows may be continued on subsequent lines of the file provided incomplete lines end with a COMMA This file may now be a binary format file with file extension bin indi cating 32bit real binary numbers and dbl indicating 64bit real binary values Files with these formats can be easily created in a preliminary run using the SAVE qualifier The advantage of using a binary file is that reading the file is much quicker This is important if the file has many fields and is being accessed repeatedly for example ICYCLE 1 1000 IMBF mbf Geno markers dbl key 1 RFIELD I rename M I Ir M I 1 5 8 Job control qualifiers Table 5 4 List of occasional
27. LANCER 1 NA NA 1 4 NA 4 3 15 6 13 1 LANCER 1 NA NA 1 4 NA 4 3 16 8 14 1 LANCER 1 NA NA 1 4 NA 4 3 18 15 1 buffer plots LANCER 1 NA NA 2 4 NA 17 2 7 26 4 between reps LANCER 1 NA NA 3 4 NA 25 8 22 8 19 6 LANCER 1 NA NA 4 4 NA 38 7 12 0 10 9 LANCER 1 1101 585 1 4 29 25 4 3 19 2 16 1 original data BRULE 2 1102 631 1 4 31 55 4 3 20 4 17 1 REDLAND 3 1103 701 1 4 35 05 4 3 21 6 18 1 CODY 4 1104 602 1 4 30 1 4 3 22 8 19 1 Note that e the pid raw repl and yield data for the missing plots have all been made NA one of the three missing value indicators in ASReml see Section 4 2 e variety is coded LANCER for all missing plots one of the variety names must be used but the particular choice is arbitrary 29 3 4 The ASReml command file 3 4 The ASReml command file By convention an ASReml command file has a as extension The file defines e a title line to describe the job e labels for the data fields in the data file and the name of the data file e the linear mixed model and the variance model s if required e output options including directives for tabulation and prediction Below is the ASReml command file for an RCB analysis of the NIN field trial data highlighting the main sections Note the order of the main sections title line gt NIN Alliance trial 1989 data field definition gt variety A id pid raw repl 4 nloc yield lat long row 22 data field definition gt column 11 data file nam
28. Model_Term Sigma Sigma Sigma SE C Residual ANTE UDU 1 0 268657E 01 0 268657E 01 2 44 OU Residual ANTE UDU 1 0 628413 0 628413 oi OU Residual ANTE UDU 2 372801E 01 0 372801E 01 2 41 oU Residual ANTE UDU 2 1 49108 1 49108 2 54 OU Residual ANTE UDU 3 0 599632E 02 0 599632E 02 2 43 o U Residual ANTE UDU 3 1 28041 1 28041 6 19 OU Residual ANTE UDU 4 0 789713E 02 0 789713E 02 2 44 OU Residual ANTE UDU 4 0 967815 0 967815 15 40 OU Residual ANTE UDU 5 0 390635E 01 0 390635E 01 2 45 OU Covariance Variance Correlation Matrix ANTE UDU 37 20 0 5946 0 3549 0 3114 0 3040 23 38 41 55 0 5968 0 5237 0 5112 34 83 61 89 258 9 0 8775 0 8565 44 58 79 22 331 4 550 8 0 9761 43 14 76 67 320 1 533 0 541 4 Wald F statistics Source of Variation DF Fine 8 Trait 5 188 84 1 tmt 1 4 14 9 TE tmt 4 Sok The iterative sequence converged and the antedependence parameter estimates are printed columnwise by time the column of U and the element of D L e 0 0269 1 0 6284 0 0 0 0 0373 0 1 1 4911 0 0 D diag 0 0060 U 0 0 1 1 2804 0 0 0079 0 0 0 1 0 9678 0 0391 0 0 0 0 1 Finally the input and output files for the unstructured model are presented below The REML estimate of X from the ANTE model is used to provide starting values 287 16 5 Balanced repeated measures Height yl y3 yo y7 y10 Trait tmt Tr tmt 120 14 1S2 Tr Y US 37 20 23 009 41 55 34 83 61 89 258 9 44 58 79 22 331 4 550 8 43 14 Y6 67 320 7 529 0 54
29. Much of the difficulty in conducting such analyses in ASReml centres on obtaining good starting values Derivative based algorithms such as the Al algorithm can be unreliable when fitting complex variance structures unless good starting values are available Poor starting values may result in divergence of the algorithm or slow convergence A particular problem with fitting unstructured variance models is keeping the estimated variance matrix positive definite These are not simple issues and in the following we present a pragmatic approach to them The data are taken from a large genetic study on Coopworth lambs A total of 5 traits namely weaning weight wwt yearling weight ywt greasy fleece weight gfw fibre di ameter fdm and ultrasound fat depth at the C site fat were measured on 7043 lambs The lambs were the progeny of 92 sires and 3561 dams produced from 4871 litters over 49 flock year combinations Not all traits were measured on each group No pedigree data was 327 16 11 Multivariate animal genetics data Sheep available for either sires or dams The aim of the analysis is to estimate heritability h of each trait and to estimate the genetic correlations between the five traits We will present two approaches a half sib analysis and an analysis based on the use of an animal model which directly defines the genetic covariance between the progeny and sires and dams The data fields included factors defining sire d
30. P 9 6 5 2 0000 17 units us Trait us Trait 13 G P 26 10 1 0000 18 units us Trait us Trait _14 G P 35 18 1 0000 19 units us Trait us Trait _15 G P 70 19 1 0000 Sometimes users wish to rerun a job making changes to the final values parametric con straints and relationships equality and scale between parameters A file msv is produced similar to tsv but containing final values that can be edited and used with MSV If TSV or MSV is specified ASReml will read the current created with the same PART number tsv or msv file If there is no current tsv or msv file a non current produced from a different PART of the same job tsv or msv file will be read Alternative ways of specifying TSV and MSV are CONTINUE 2 and CONTINUE 3 and these qualifiers can be used as options on the command line as C2 and C3 Note that the constraints in the tsv msv files take precedence over those in the as file 7 10 2 Using estimates from simpler models Sometimes we have estimates from simpler models and we wish to reduce the need for the user to type in updated starting values The CONTINUE command line qualifier instructs ASReml to update initial parameter values from a rsv file When it is specified ASRem1 first looks for a current rsv file and if found will read it and report the constructed initial values in the tsv file If there is no current rsv file it looks for the most recent noncurrent
31. SECTION site ROWFACTOR row COLUMNFACTOR col yield site r variety site variety f mv site 2 0 variance header line ASReml inserts the 10 lines required to define the R structure lines for the five sites here defines a spline model term with an explicit set of knot points The basic form of the spline model term sp1 v is defined in Table 6 1 where v is the underlying variate The basic form uses the unique data values as the knot points The extended form is spl v n which uses n knot points Use this SPLINE qualifier to supply an explicit set of n knot points p for the model term Using the extended form without using this qualifier results in n equally spaced knot points being used The SPLINE qualifier may only be used on a line by itself after the datafile line and before the model line When knot points are explicitly supplied they should be in increasing order and adequately cover the range of the data or ASReml will modify them before they are applied If you choose to spread them over several lines use a comma at the end of incomplete lines so that ASReml will to continue reading values from the next line of input If the explicit points do not adequately cover the range a message is printed and the values are rescaled unless NOCHECK is also specified Inadequate coverage is when the explicit range does not cover the midpoint of the actual range See KNOTS PVAL and SCALE 73 5 8 Job control qualifiers
32. Tabulation predicted values and functions of the variance components Data file preparation 4 1 4 2 MO ee a oe BA we Ph eee ee a Pee Bae A The dala ile o a eR EME eR EHS HESS SEEDER EES 4 2 1 Free format data files ee 0000004 42 2 Fixed format data files INE 4 2 3 Preparing data Tiles in Excel lt o oo lt s oe ee Gee eee eee eee es 4 2 4 Binary format data files o Command file Reading the data 51 5 2 5 3 5 4 5 5 5 6 5 7 5 8 IO o cas da ro e ESE a a SED O Important muis e iera be ee he e A A hee eee BS Te WHS oe ew a a a he wee ee ea eee ee ee eee ag Se IR Specifying and reading the data 2 0 00 00 00 2 ea 5 4 1 Data field definition syntax 2 24562 ee 400d as 5 4 2 Storage of alphabetic factor labels o oo aa aa 5 4 5 Ordering factor levels sic s a 6 ba Ge eriei eR eee eG 544 Skipping input fields lt 4 o eor aoe ig eo a eG ew eG ew ee ew Se Transforming the data lt lt cocos coges rodrs ee ee eee e 55 1 Transformation Synta o cc sec corner ra a G 5 5 2 QTL marker transformations 64 666 css ee ee 5 5 3 Remarks concerning transformations oaoa oaa a 5 5 4 Special note on covariates v v v v a a a 2 OPE te srren ee ey eo Be ed a ee GOR ar pA 8 561 Dota lesbi a ha ee EE AE GB EC ERE EERE EEE ES Data file qualifiers lt lt ee car a ee ee 5 7 1 Combining rows from separate files Job contro
33. and t r 88 95 at 95 at f n 88 95 cos v r 89 95 fac v y 88 95 fac v 88 95 g f n 96 giv f n 89 96 grm f n 89 h 96 i f 96 ide f 89 96 inv v r 89 96 1 f 96 leg v n 89 96 lin f 88 96 log v r 89 96 mal f 89 96 mai 89 96 mbf v 7 89 mu 88 97 mv 88 97 out 97 p v n 97 355 INDEX pol v n 89 97 pow z p 0 97 gt1O 98 s vL k 98 sin v r 89 98 spl v k 88 98 sqrt v r 89 98 uni f k 98 uni f n 90 uni f 89 units 88 98 vect v 90 xfa f k 90 99 reserved words AEXP 125 AGAU 125 AINV 127 ANTE 1 126 AR2 123 AR3 123 ARMA 124 AR 1 123 CHOL 1 126 CIR 125 CORB 124 CORGB 124 CORGH 124 CORU 124 DIAG 126 EXP 124 FACV 1 126 FA 1 126 GAU 125 GIV 127 GRM 127 IDH 126 ID 123 IEUC 125 IEXP 125 IGAU 125 LVR 125 MA2 124 MAT 126 MA 1 124 NRM 127 OWN 126 SAR2 124 SAR 123 SPH 125 US 126 XFA 1 127 residual error 5 likelihood 13 response 85 running the job 33 score 14 Score test 68 Segmentation fault 231 separable 114 Singularities 106 slow processes 209 sparse 106 sparse fixed 86 spatial analysis 289 data 1 model 113 specifying the data 46 split plot design 272 submodels 92 ISM 92 tabulation 31 qualifiers 177 syntax 177 tests of hypotheses 19 Timing processes 210 title line 30 46 TPREDICT 194 trait 41 152 transfor
34. are 1 and the variances are built into Rj e For multiple section univariate analyses g is 1 and 2 r can be used to initialize o commonly R is a correlation model e For univariate single section analyses including ASUV the default action is to estimate o possibly initialized using S2 r with o 1 and R being a correlation matrix Alternatively using S2 r fixes c 1 and o r a variance parameter may then be incorporated in Ri 137 7 7 Rules for combining variance models Table 7 4 List of R and G variance structure definition line qualifiers qualifier action SUBSECTION f allows many independent blocks of correlated observations to be modelled with common variance and correlation parameters when the data has one section and one component variance model The observations need to be sorted on a variable which defines the blocks The blocks can be of different sizes Any homogeneous variance correlation model defined in Table 7 3 may be used for the variance structure In this case R 6 3j so that R has a direct sum structure with common parameters So for generic times 1 1 O data sorted bids within auctions 0 O AR1 0 5 SUBSECTION auction and for explicit times 1 1 0 data sorted date within plot O date EXP 0 2 SUBSECTION plot IUSE f requests ASReml use the variance structure previously declared and named f see page 143 7 7 Rules for combining variance models As noted in Secti
35. female_parent are merged into a single list and the inverse relationship is formed before the data file is read when the data file is read data fields with the P qualifier are recoded according to the combined identity list the inverse relationship matrix is automatically associated with factors coded from the pedigree file unless some other covariance structure is specified The inverse relationship matrix is specified with the variance model name AINV the inverse relationship matrix is written to ainverse bin if ainverse bin already exists ASReml assumes it was formed in a previous run and has the correct inverse ainverse binisread rather than the inverse being reformed unless MAKE is specified this saves time when performing repeated analyses based on a particular pedigree delete ainverse bin or specify MAKE if the pedigree is changed between runs identities are printed in the sl1n file identities should be whole numbers less than 200 000 000 unless ALPHA is specified pedigree lines for parents must precede their progeny unknown parents should be given the identity number 0 if an individual appearing as a parent does not appear in the first column it is assumed to have unknown parents that is parents with unknown parentage do not need their own line in the file identities may appear as both male and female parents for example in forestry We refer the reader to the sheep genetics exampl
36. in a multivariate analysis provided it correctly identifies the number of levels of Trait either by including the last trait number or appending sufficient zeros Thus if the analysis involves 5 traits ISUBSET Trewe Trait 13400 sets hardcopy graphics file type to wmf Table 5 5 List of rarely used job control qualifiers qualifier action ATLOADINGS 2 controls modification to AI updates of loadings in extended Factor Ana lytic models After ASReml calculates updates for variance parameters it checks whether the updates are reasonable and sometimes reduces them over and above any STEPSIZE shrinkage The extra shrinkage has two levels Loadings that change sign are restricted to doubling in magni tude and if the average change in magnitude of loadings is greater than 10 fold they are all shrunk back Unless the user gives constraints ASReml sets them and rotates the load ings each iteration When AILOADINGS is specified it also prevents AI updates of some loadings during the first iterations For f gt 1 factors only the last factor is estimated conditional on the earlier ones in the first f 1 iterations Then pairs including the last are estimated until iteration t If AILOADINGS is not specified and CONTINUE is used and initializes the XFA model from a lower order the 7 parameter is set internally 74 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers
37. lt subname gt is a command line argument value If OUTFOLDER is specified without path the output filename pattern becomes lt basename gt lt subname gt lt basename gt lt ertension gt If path is specified the output filename pattern becomes lt path gt lt basename gt lt subname gt lt ertension gt There are a few files written by ASReml that do not follow this naming pattern for example ainverse bin and asrdata bin These remain unchanged that is they are not written to the output folder XML requests that the primary tables reported in the asr file and key output from pvs and sln files are written to a xml file in xml format The output is presented in the order of computation The first block written is a asr block and includes start and finish times the data summary the iteration sequence summary and information criteria then from the pvs file the tables and associated information then the summary of estimated variance structure parameters from the asr file then information from the sln file and then finally the Wald F statistics and completion information from the asr file The process is repeated for each cycle of analysis The intended use of this file is by programs written to parse ASReml output For further details including the status of intended future developments please contact support vsni co uk 199 11 3 Command line options 11 3 3 Debug command line options D E D and E DEBUG
38. mu 1 1 331 8483 331 8483 1 0000 25 0082 variety 56 55 2 2259 2 2259 0 9995 110 8419 A more useful example is obtained by adding split plot analysis oat a linear nitrogen contrast to the oats example blocks Section 16 2 nitrogen A subplots variety A The basic design is six replicates of three vetoes whole plots to which variety was randomised yield and four subplots which received 4 rates of oats asd skip 2 nitrogen A CONTRAST qualifier defines the CONTRAST linNitr nitrogen 6 model term linNitr as the linear covariate 0 4 0 2 0 0 representing ntrogen applied Fitting this be Binn e 3 yield mu variety linNitr fore the model term nitrogen means that this pa elas BHUN latter term represents lack of fit from a linear y ariety nitrogen response lr blocks blocks wplots The FCON qualifier requests conditional Wald F statistics As this is a small example denominator degrees of freedom are reported by default An extract from the asr file is followed by the contents of the aov file Results from analysis of yield Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients blocks 5 00 3175 06 12 0 4 0 1 0 blocks wplots 10 00 601 331 0 0 4 0 1 0 Residual Variance 45 00 177 083 0 0 0 0 1 0 Model_Term Gamma Sigma Sigma SE C blocks 6 6 1520116 214 477 1 27 OP blocks wplots 18 18 0 598937 106 062 1 56 0P Variance 72 60 1 00000 177 083 4
39. ne where ne is the number of columns on which the data is to be sorted See SECTION for more detail 69 5 8 Job control qualifiers Table 5 4 List of occasionally used job control qualifiers qualifier action DESIGN causes ASReml to write the design matrix not including the response variable to a des file It allows ASReml to create the design matrix required by the VCM process see Section 7 9 4 DISPLAY n is used to select particular graphic displays In spatial analysis of field trials four graphic displays are possible see Section 14 4 Coding these 1 variogram 2 histogram 4 row and column trends 8 perspective plot of residuals set n to the sum of the codes for the desired graphics The default is 9 1 8 These graphics are only displayed in versions of ASReml linked with Winteracter that is LINUX MAC and PC versions Line printer ver sions of these graphics are written to the res file See the G command line option Section 11 3 on graphics for how to save the graphs in a file for printing Use NODISPLAY to suppress graphic displays EPS sets hardcopy graphics file type to eps IG v is used to set a grouping variable for plotting see X GKRIGE p controls the expansion of PVAL lists for fac X Y model terms For IGROUPFACTOR tvp kriging prediction in 2 dimensions X Y the user will typically want to predict at a grid of values not necessarily just at data combinations The values at which
40. nin alliance trial lines but ASReml does not realise this be variety A cause the first line does not end with a comma The missing comma causes the 2 4 fault Error in variance header line R Repl nin89 asd skip 1 P yield mu variety as ASReml tries to interpret the second line of lr Repl the model see Last line read as the vari ance header line The asr file is displayed below Note that the data has now been successfully read as indicated by the data sum mary You should always check the data summary to ensure that the correct number of records have been detected and the data values match the names appropriately Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 1 is active Reading nin asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of 224 records retained of 242 read Model term Size miss zero MinNon0 Mean MaxNonO StndDevn 1 variety 56 0 0 t 28 5000 56 2 ag 0 0 1 000 28 50 56 00 16 20 3 pid 0 O 1101 2628 4156 1121 4 raw 0 o 21 00 510 5 840 0 149 0 5 repl 4 0 0 t 2 5000 4 6 nloc 0 O 4 000 4 000 4 000 0 000 7 yield Variate 0 O 1 050 25 53 42 00 7 450 8 lat 0 O 4 300 27 22 47 30 12 90 9 long 0 o 1 200 14 08 26 40 7 698 10 row 22 0 0 1 11 7321 22 11 column i 0 0 z 6 3304 11 12 mu 1 QUALIFIERS IR Repl Fault Error in variance header line IR Repl Last line read was IR Repl 0 0 0 0 ninerr4 variety id pid raw rep nloc yield lat
41. or a variance Strategies include letting ASReml supply an inital value and fitting a simpler model to gain an idea of the scale required It may be that the model is too sophisticated to be estimated from the data Satisfactory convergence is unlikely if the fitted model is not appropriate One user could not get an AR1 model to converge It turned out the data was simulated under an equal correlation model not an AR model and sometimes the correlation was greatest between the two most distant points when the AR model expected it to be smallest Another user had problems getting a model to converge when using a GIV variance structure The GIV matrix had 3 large negative eigen values and 5 negative diagonal elements which for certain parameter values resulted in negative roots to the mixed model equations In animal models the residual variance can be negative if appropriate fixed effects are not fitted and end up appearing as inflated genetic variance Alternatively the variance model may contain highly related terms which the data cannot effectively separate into two components In models with many variance parameters there may not be enough information to effec 150 7 11 Convergence issues tively estimate all the parameters or the natural estimates of the parameters may fall outside the conceptual parameter space If there are no actual block effects a block variance com ponent is just an independent estimate of the residual varian
42. re number the data units in order to achieve this structure In ASReml it is now straightforward to apply possibly different variance structures to each component of R In many cases the residual errors e can be expected to share a common variance structure In this case there is only one section s 1 Typically a variance structure is specified for each random model term and often more complex models than the simple IID model are specified ASReml offers a wide range of variance models to choose from A full listing is in Table 7 3 and details are provided in Chapter 7 2 1 6 Gamma parameterization for the linear mixed model The sigma parameterization of model 2 3 is one possible parameterization of var y In this parameterization both G o and R 0 are variance matrices and the variance structure parameters in cr and a are referred to as sigmas see above Other parameterizations 7 2 1 The general linear mixed model are possible and are sometimes useful For example in some of the early development of REML for the traditional mixed model of 2 5 the variance matrix was parameterized as the equivalent model b var y 0 Sazz 2 6 2 for yy being the ratio of the variance component for the random term u relative to error variance that is yy 0 0 In this case ASReml calculated a simple estimate of o2 and initial values for the iterative process were specified in terms of the ratios yy rather tha
43. requested by function lines beginning with an F phenvar 1 2 Sire Residual H The specific form of the directive is F genvar 1 4 Sire 4 H herit 4 3 genvar phenvar H label n d This calculates 02 0 and se o o7 where n and d are the names of the components or inte gers pointing to components v and vg that are to be used as the numerator and denominator respectively in the heritability calculation Note that covariances between ratios and other components are not generated so the ra tios are not numbered and cannot be used to derive other functions To avoid numbering confusion it is better to include H functions at the end of the VPREDICT block In the example H herit 4 3 or H herit genvar phenvar calculates the heritability by calculating component 4 from second line component 3 from first line that is genetic variance phenotypic variance S label i j when 1 j are assumed positive variance parameters inserts components which are the SQRT of components 7 7 X label i k inserts a component being the product of components i and k X label i j k inserts j i 1 components being the products of components 7 j and k 216 13 2 Syntax X label i 7 k l inserts a set of 1 1 components being the pairwise products of components i jgandk l The S and X functions are new in ASReml Release 4 The multiply option X allows a correlation in a CORUV structure to be converted to a covariance Th
44. rsv file and uses that to construct initial values As discussed below current means having the same basename and run number A non current file will have the same basename but a different run number When reading the rsv file if the variance structure for a term has changed ASReml will take results from some structures as supplying starting values for other structures The transitions recognised are CORUH to FA1 and XFA1 CORGH to US DIAG to CORUH DIAG to FA1 DIAG to XFA1 FAs to CORGH FAs to FA13 1 FAz to US XFA2 to XFAt 1 XFAz to US US to XFA1 XFA2 XFAS Users may wish to keep output from a series of runs This can be done by using RENAME 1 ARG runnumber on the first line of the command file or alternatively R1 basename runnum ber on the command line This ensures that the output from the various parts has runnumber appended to the base filename If an rsv file does not exist for the particular runnumber 149 7 11 Convergence issues you are running ASRem1 will retrieve starting values from the most recent rsv file formed by that job You can of course copy an rsv file building the new runnumber into its name so that ASReml uses that particular set of values The asr file keeps track of which rsv files have been formed If the user wishes to use different models with different runs then using DOPART 1 and specifying the different models in different parts will achieve this aim 7 1
45. tation on going testing of the software and numerous helpful discussions and insight Dave Butler has developed the ASReml R package Alison contributed to the development of many of the approaches for the analysis of multi section trials We also thank Ian White for his contribution to the spline methodology and Simon Harding for the licensing and installa tion software and for his development of the user interface program ASReml W The Mat rn function material was developed with Kathy Haskard and Brian Cullis and the denomina tor degrees of freedom material was developed with Sharon Nielsen a Masters student with Brian Cullis Damian Collins contributed the PREDICT PLOT material Greg Dutkowski has contributed to the extended pedigree options The asremload d11 functionality is provided under license to VSN Alison Kelly has helped with the review of the XFA models Finally we especially thank our close associates who continually test the enhancements Arthur Gilmour acknowledges the grace of God through Jesus Christ our Saviour In Him are hidden all the treasures of wisdom and knowledge Colossians 2 3 111 Contents Preface i List of Tables xii List of Figures xiv 1 Introduction 1 1 1 What ASReml can do siria id a CRS ee CES ER ESS 1 1 2 INMI casio sis pa dr rd a be ee 2 1 3 User Interlace oc ag bh ee we a age Ie d GES EE Ew i d Cho Rw ai Ce Ae oir OS 2 lad ASREMIAN cia ie og os sh he wi a EN 2 Lil ASGTEST caras obo e
46. the BLUP 1 qualifier might help A program limit has been breached Try simplifying the model use WORKSPACE qualifier to increase the workspace allocation It may be possible to revise the models to increase sparsity factors are probably not declared properly Check the number of levels Possibly use the WORKSPACE qualifier occurs when space allocated for the structure table is exceeded There is room for three structures for each model term for which G structures are explicitly declared The error might occur when ASReml needs to construct rows of the table for structured terms when the user has not formally declared the structures Increasing g on the variance header line for the number of G structures see page 119 will increase the space allocated for the table You will need to add extra explicit declarations also check the pedigree file and see any messages in the output Check that identifiers and pedigrees are in chronological order the A inverse factors are not the same size as the A inverse Delete the ainverse bin file and rerun the job Typically this arises when there is a problem processing the pedigree file Check the details for the distance based variance structure Check the distances specified for the distance based variance structure Try increasing workspace Otherwise send problem to VSN indicates ASReml has failed deep in its core It is likely to be an interaction between the data and the va
47. 0 o2I E p The variance header Pid line tells ASReml that there is one R struc 2 fea e repl 4 ture 1 which is a direct product of two vari ance models 2 there are no G structures 0 The next two lines define the components of he R structure A structure definition line Lun t the Sirue al nin89aug asd skip 1 must be specified for each component For yield mu variety mv V 0o71 p the first matrix is an iden 1 2 0 tity matrix of order 11 for columns ID the 11 column ID second matrix is a first order autoregressive 22 row AR1 0 3 correlation matrix of order 22 for rows AR1 and the variance scale parameter g is implicit Note the following row 22 e placing column and row in the second position on lines 1 and 2 respectively tells ASReml to internally sort the data rows within columns before processing the job This is to ensure that the data matches the direct product structure specified If column and row were replaced with 0 in these two lines ASReml would assume that the data were already sorted in this order which is not true in this case the 0 3 on line 2 is a starting value for the autoregressive row correlation Note that for spatial analysis in two dimensions using a separable model a complete matrix or array of plots must be present To achieve this we augmented the data with the 18 records for the missing yields as shown on page 29 In the augmented data file
48. 0 1 specified IDV in the ASReml command file see below and one parameter The initial values for the variance parameters are listed after the initial values for the correlation parameters For example in ARIV 0 3 0 5 0 3 is the initial spatial correlation parameter and 0 5 is the initial variance parameter value 128 7 5 Variance model description Similarly if Y i is the heterogeneous variance matrix corresponding to C then 5 DCD where D diag 0 In this case there are an additional w parameters For exam ple the heterogeneous variance model corresponding to ID is specified IDH in the ASReml command file see below involves the w parameters 07 02 and is the variance matrix o 0 0 0 g 0 X 0 0 g 7 5 2 Notes on the variance models These notes provide additional information on the variance models defined in Table 7 3 e the IDH and DIAG models fit the same diagonal variance structure the CORGH and US models fit the same completely general variance structure parameterized differently in CHOLk models LDL where L is lower triangular with ones on the diagonal D is diagonal and k is the number of non zero off diagonals in L in CHOLKC models 5 LDL where L is lower triangular with ones on the diagonal D is diagonal and kis the number of non zero sub diagonal columns in L This is somewhat similar to the factor analytic model in ANTEk models U DU where U is upp
49. 0 1 1 0 0 0 0 0 0 0 0 0 0 O 13 3 0 9579D 01 452 0 2494 0 07830 0 07218 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 14 3 0 9540D 01 452 0 2495 0 07797 0 07189 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 15 3 0 1089D 02 452 0 2465 0 08907 0 083022 1 0 0 1 0 41 0 0 0 0 0 0 0 0 0 0 0 16 3 0 2917D 01 452 0 2642 0 02384 0 01736 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 O 17 3 0 2248D 01 452 0 2657 0 01838 0 01187 001 10100000000000 18 3 0 1111D 02 452 0 2460 0 09088 0 08484 1 0 1 0 0 41 0 0 0 0 0 0 0 0 0 0 0 19 3 0 1746D 01 452 0 2668 0 01427 0 00773 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 20 3 0 1030D 02 452 0 2478 0 08423 0 07815 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 21 3 0 1279D 02 452 0 2423 0 10454 0 09990 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 22 3 0 8086D 01 452 0 2527 0 06609 0 05989 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 23 3 0 7437D 01 452 0 2542 0 06079 0 05456 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 24 3 0 1071D 02 452 0 2469 0 08755 0 08149 0 0 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 25 3 0 1370D 02 452 0 2403 0 11200 0 10611 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 ARK 2K 26 3 0 1511D 02 452 0 2372 0 12351 0 11777 1000 10 10000000000 ARK 2K 27 3 0 1353D 02 452 0 2407 0 11064 0 10473 0100 1010000000000 680 3 0 1057D 02 452 0 2472 0 08641 0 08035 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 The primary tables reported in the asr file are now also written in XML format to a xml file The intended use of this file is by programs written to parse Asreml output The information contained in the xml file includes start and finish
50. 00 NE87522 25 00 NE87612 21 80 NE87613 29 40 NE87615 25 69 NE87619 31 26 NE87627 23 23 The predict variety statement after the model statement in nin89 as results in the nin89 pvs file displayed below some output omitted containing the 56 predicted variety means also in the order in which they first appear in the data file column 2 together with standard errors column 3 An average standard error of difference among the predicted variety means is displayed immediately after the list of predicted values As in the asr file date time and trial information are given the title line The Ecode for each prediction column 4 is usually E indicating the prediction is of an estimable function Predictions of non estimable functions are usually not printed see Chapter 10 NIN alliance trial 1989 04 Apr 2008 17 00 47 nin89 Ecode is E for Estimable for Not Estimable Predicted values of yield The predictions are obtained by averaging across the hypertable 38 3 7 Tabulation predicted values and functions of the variance components calculated from model terms constructed solely from factors in the averaging and classify sets The ignored set repl Use AVERAGE to move table factors into the averaging set variety Predicted_Value Standard_Error Ecode LANCER 28 5625 3 8557 E predicted variety BRULE 26 0750 3 8557 E effects REDLAND 30 5000 3 8557 E CODY 21 2125 3 8557 E ARAPAHOE 29 4375 3 8557 E NE83404 27 3875 3 855
51. 0000 And the eigen analysis in the res file is Eigen Analysis of XFA matrix for xfa TrDam123 1 dam Eigen values 4 704 0 246 0 006 Percentage 94 919 4 957 0 124 1 0 6431 0 7647 0 0009 2 0 7637 0 6404 0 0743 3 0 0563 0 0484 0 9972 showing that the smallest eigenvalue is 0 006 On the basis of this ASReml with ARG 3 fits unstructured matrices for sire and litter and xfa1 for dam using initial values derived from the previous analysis in coopmf2 rsv Portions of the asr file from the Path 3 run are Notice ReStartValues taken from coopms2 rsv Notice LogL values are reported relative to a base of 20000 000 Notice US matrix updates modified 1 time s to keep them positive definite Notice 1084 singularities detected in design matrix 1 LogL 1488 11 52 1 00000 18085 df 11 components restrained 2 LogL 1486 27 52 1 00000 18085 df 2 components restrained 3 LogL 1483 34 S2 1 00000 18085 df 1 components restrained 4 LogL 1481 89 S2 1 00000 18085 df 5 LogL 1481 10 S2 1 00000 18085 df 6 LogL 1480 91 S2 1 00000 18085 df 7 LogL 1480 89 S2 1 00000 18085 df 8 LogL 1480 89 S2 1 00000 18085 df 9 LogL 1480 89 S2 1 00000 18085 df 333 16 11 Multivariate animal genetics data Sheep Results from analysis of wwt ywt gfw fdm fat US structures were modified 1 times to make them positive definite If ASReml has fixed the structure flagged by B it may not have converged to a maximum likelihood solut
52. 146 12 SEX GRP E NA 0 36 NA The effects in this analysis are on a logistic scale with a variance of 3 28987 77 3 and 321 16 10 Generalized Linear Mixed Models so the heritability on the underlying logistic scale is 0 296 root This can be calculated in ASReml with the pin file commands F GenVar 1 4 F TotVar 1 4 3 28987 H heritability 3 4 Repeating the analysis on the Probit scale by inserting PROBIT after BIN in the model line produces a Sire component of 0 0514 on the Probit scale which has an underlying variance of 1 0 The heritabily estimate is then 0 196 Given the incidence 0 034 the heritability on the probit scale is expected to be around 0 215 0 0364 z pq where z 0 0758 is the ordinate of a Normal 0 1 corresponding to p 1 q 0 034 The preceding Wald F Statistics pertain to the working variable created as part of the PQL analysis The SEX GRP interaction is clearly not significant even though ASReml was not able to calculate a plausible value for the Denominator DF for this summarized data The predicted means shown below are not that different from those obtained from analysis on the 0 1 scale but the standard errors are very different These predicted means have been backtransformed by ASReml from the underlying logistic scale to the probablity scale The initial analysis on the 0 1 probability scale ignores the variance differences associated with binomial data Sex PxP 1980 BRxP 1980 BxR 1
53. 163 IGP 137 IGRAPHICS 198 IGROUPFACTOR 70 IGROUPSDF 168 IGROUPS 163 IGU 137 IGZ 137 IG 49 68 70 IHARDCOPY 198 HOLD 80 IHPGL 79 IDENTITY link 101 IDLIMIT 71 INBRED 163 IINCLUDE 65 I INTERACTIVE 198 II 48 JOIN 68 71 lJddm 56 lJmmd 56 lJyyd 56 IKEEP 212 IKEY 71 212 IKNOTS 83 ILAST 80 163 ILOGARITHM 101 ILOGFILE 198 ILOGIT 101 ILOGIT link 101 ILOG link 101 ILONGINTEGER 164 IL 47 INDEX IMAKE 164 IMATCH 64 IMAXIT 68 IMAX 56 IMBF 71 IMERGE 64 IMEUWISSEN 164 IMGS 164 IMIN 56 IMM transformation 56 58 IMOD 56 IMVREMOVE 72 IM 56 INAME 137 143 144 INA 56 INEGBIN GLM 102 INOCHECK 83 INODUP 212 INOGRAPHS 198 INOKEY 71 INOREORDER 83 INORMAL 56 INORMAL GLM 101 INOSCRATCH 83 OFFSET variable 102 ONERUN 198 QUTFOLDER 198 QUTLIER 18 IOWN 80 IPEARSON residuals 102 IPLOT 185 IPNG 80 IPOISSON GLM 101 IPOLPOINTS 83 IPPOINTS 83 IPRINTALL 185 IPRINT 80 IPROBIT 101 IPROBIT 101 IPS 80 IPVAL 72 IPVR GLM fitted values 102 IPVSFORM 80 IPVW GLM fitted values 102 IP 48 IQUASS 164 QUIET 198 354 IREAD 64 IRECODE 64 IRENAME 71 198 IREPEAT 164 IREPLACE 56 IREPORT 84 IRESCALE 56 IRESIDUALS 81 IRESPONSE residuals 102 IRFIELD 71 IROWFAC 69 72 IRREC 64 IRSKIP 65 1S2 1 137 1 2 r 137 ISAMEDATA 205 206 ISARGOLZAET 164 ISAVEGIV 167 ISAVE 81 ISCALE 84 ISCOR
54. 2 NE83498 12 1112 492 1 4 24 6 8 6 6 5 2 NE84557 13 1113 509 1 4 25 45 8 6 7 2 6 2 NE83432 14 1114 268 1 4 13 4 8 6 8 4 7 2 NE85556 15 1115 633 1 4 31 65 8 6 9 6 8 2 NE85623 16 1116 513 1 4 25 65 8 6 10 8 9 2 CENTURAK78 17 1117 632 1 4 31 6 8 6 12 10 2 NORKAN 18 1118 446 1 4 22 3 8 6 13 2 11 2 KS831374 19 1119 684 1 4 34 2 8 6 14 4 12 2 28 3 3 The ASReml data file These data are analysed again in Chapter 7 using spatial methods of analysis see model 3a in Section 7 3 For spatial analysis using a separable error structure see Chapter 2 the data file must first be augmented to specify the complete 22 row x 11 column array of plots These are the first 20 lines of the augmented data file nin89aug asd with 242 data rows Note that Release 4 can automatically augment spatial data see ROWFACTOR COLUMNFACTOR variety id pid raw repl nloc yield lat long row column optional field labels LANCER 1 NA NA 1 4 NA 4 3 1 2 1 1 file augmented by missing LANCER 1 NA NA 1 4 NA 4 3 2 4 2 1 values for first 15 plots and 3 LANCER 1 NA NA 1 4 NA 4 3 3 6 3 1 buffer plots and variety coded LANCER 1 NA NA 1 4 NA 4 3 4 8 4 1 LANCER to complete 22x11 LANCER 1 NA NA 1 4 NA 4 365 1 array LANCER 1 NA NA 1 4 NA 4 3 7 2 6 1 LANCER 1 NA NA 1 4 NA 4 3 8 4 7 1 LANCER 1 NA NA 1 4 NA 4 3 9 6 8 1 LANCER 1 NA NA 1 4 NA 4 3 10 8 9 1 LANCER 1 NA NA 1 4 NA 4 3 12 10 1 LANCER 1 NA NA 1 4 NA 4 3 13 2 11 1 LANCER 1 NA NA 1 4 NA 4 3 14 4 12 1
55. 2 Qualifiers relating to data input and output qualifier action RSKIP mie allows ASReml to skip lines at the heading of a file down to and includ ing the nth instance of string s For example to read back the third set predicted values in a pvs file you would specify IRREC RSKIP 4 Ecode since the line containing the 4th instance of Ecode immediately pre cedes the predicted values The RREC qualifier means that ASReml will read until the end of the predict table The keyword Ecode which occurs once at the beginning and then immediately before each block of data in the pvs file is used to count the sections 5 7 1 Combining rows from separate files ASReml can read data from multiple files provided the files have the same layout The file specified as the primary data file in the command file can contain lines of the form INCLUDE lt filename gt SKIP n where lt filename gt is the path name of the data subfile and SKIP n is an optional qualifier indicating that the first n lines of the subfile are to be skipped After reading each subfile input reverts to the primary data file Typically the primary data file will just contain INCLUDE statements identifying the subfiles to include For example you may have data from a series of related experiments in separate data files for individual analysis The primary data file for the subsequent combined analysis would then just contain a set of INC
56. 22 468 0 50789 0 40378 0 28124E 01 0 88137 0 35903E 01 0 17958 0 41634E 02 0 89091 0 28008 1 2037 0 34725 0 24528 0 32 75E 91 4 5409 0 21411 0 85028 0 10023 2 4831 0 12849 0 78609E 01 0 11170E 01 0 11589 0 99338E 01 1 6318 0 49595E 01 2 75 phenWYG 60 2 77 phenWYG 62 2 80 phenWYG 65 3 84 phenD 10 69 3 89 phenF 15 74 24 SQR Trait 23 Trait 25 26 SQR Trait 23x Trait 28 27 SQR Trait 25 Trait 28 29 SQR Trait 23 Trait 32 30 SQR Trait 25 Trait 32 31 SQR Trait 28 Trait 32 33 SQR Trait 23 Trait 37 34 SQR Trait 25 Trait 37 35 SQR Trait 28 Trait 37 36 SQR Trait 32 Trait 37 91 SQR Mater 90 Mater 92 93 SQR Mater 90 Mater 95 94 SQR Mater 92 Mater 95 their approximate standard errors 16 11 2 Animal model In this section we will illustrate the use of a pedigree file to define the genetic relationships be tween animals This is an alternate method of estimating additive genetic variance for these data The data file has been modified by adding 10000 to the dam ID now 10001 13561 so that the lamb sire and dam ID s are distinct They appear as the first 3 fields of the data file pcoop fmt and no historical genetic relationships are available for this data so the data files doubles as the pedigree file The multi trait additive genetic variance matrix 24 of the animals sires dams and lambs 338 SOO SO So OSOS l 1507 2591 3087 1344 0785 7045 2970 0188 1947
57. 3 Trials classified by region and location location Region L1 L2 L3 L4 L5 L6 L7 L8 R1 T1 T2 T3 T4 T5 T6 R2 T7 T8 T9 T10 T11 T12 T13 T14 T15 Table 10 4 Trial means Tl T2 T3 T4 T5 T6 Tr Ts T9 T10 T11 T12 T13 T14 T15 10 12 11 12 13 13 11 13 11 12 13 10 12 10 10 Assuming a simplified linear model yield mu region location trial the predict statement predict trial ASSOCIATE region location trial will reconstruct the 15 trial means from the fitted mu region location and trial effects Given these trial means it is fairly natural to form location means by averaging the trials in each location to get the location means in Table 10 5 Table 10 5 Location means Li L2 L3 L4 Ld L6 L7 L8 11 12 13 12 12 11 10 10 These are given by predict location ASSOCIATE region location trial ASAVERAGE trial or equivalently predict location ASSOCIATE region location trial since the default is to average the base associate factor trial within the associated classify factor location 189 10 3 Prediction By contrast by specifying predict location or equivalently predict location AVERAGE region AVERAGE trial ASReml would add the average of all the trial effects and the average of the region effects into all of the location means which is not appropriate With ASSOCIATE it knows which trials to average and which region effects include to form each location mean That is ASReml knows ho
58. 3 4 5 6 tree y y y y y y age tree y y y y y y covariance n n n n n y spl age 7 y y y y n y tree spl age 7 y y y n y y fac age n y y n n n season n n y y y y REML log likelihood 97 78 94 07 87 95 91 22 90 18 87 43 An extract of the ASReml input file is circ mu age r Tree 4 6 Tree age 000094 spl age 7 1 spl age 7 Tree 2 3 fac age 13 9 001 Tree 2 20 US 4 6 00001 000094 500 predict age Tree IGNORE fac age We stress the importance of model building in these settings where we generally commence with relatively simple variance models and update to more complex variance models if ap propriate Table 16 12 presents the sequence of fitted models we have used Note that the REML log likelihoods for models 1 and 2 are comparable and likewise for models 3 to 6 The REML log likelihoods are not comparable between these groups due to the inclusion of the fixed season term in the second set of models We begin by modelling the variance matrix for the intercept and slope for each tree X as a diagonal matrix as there is no point including a covariance component between the intercept and slope if the variance component s for one or both is zero Model 1 also does not include a non smooth component at the overall level that is fac age Abbreviated output is shown below 12 Lopl 97 7788 S2 6 3550 33 df Model_Term Gamma Sigma Sigma SE C Tree 5 5 4 79025 30 4420 1 24 0 P Tree age 5 5 0 939436E 04 0 5970
59. 4 row 22 column 11 nin89 asd skip 1 yield mu variety repl need to be formally declared when it has the default IID structure 2a Random effects RCB analysis The random effects RCB model has 2 random terms to indicate that the total variation in the data is comprised of 2 components a ran dom replicate effect u N 0 y 0 T where yr 07 07 and error as in 1 This model in volves both the original implicit IID R struc ture and an implicit IID G structure for the random replicates In ASReml e IID variance structure is the default for ran dom terms in the model For this reason the only change to the former command file is the insertion of r before rep1 Important All random terms other than error which is implicit must be written after r in the model specification line s 111 NIN Alliance Trial 1989 variety A id pid raw repl 4 row 22 column 11 nin89 asd skip 1 yield mu variety r repl 7 3 A sequence of structures for the NIN data 2b Random effects RCB analysis with a G structure specified This model is equivalent to 2a but we explic itly specify the G structure for rep1 that is u N 0 y 0 I to introduce the syntax The 0 0 1 line is called the variance header line In general the first two elements of this line refer to the R structures and the third el ement is the number of G structures In this case O O tells ASReml that there are no ex plicit
60. 5 1484 27 lt 001 4 tmt 1 60 4 469 36 lt 001 The estimated variance components from this analysis are given in column a of table 16 8 The variance component for the variety main effects is large There is evidence of tmt variety interactions so we may expect some discrimination between varieties in terms of tolerance to bloodworms Given the large difference p lt 0 001 between tmt means we may wish to allow for hetero geneity of variance associated with tmt Thus we fit a separate variety variance for each level of tmt so that instead of assuming var uz g3 188 we assume 2 0 var u2 Te 2 SL as 0 ox where o3 and 03 are the tmt variety interaction variances for control and treated respec tively This model can be achieved using a diagonal variance structure for the treatment part of the interaction We also fit a separate run variance for each level of tmt and heterogeneity at the residual level by including the uni tmt 2 term We have chosen level 2 of tmt as 303 16 8 Paired Case Control study Rice Table 16 8 Estimated variance components from univariate analyses of bloodworm data a Model with homogeneous variance for all terms and b Model with heterogeneous variance for interactions involving tmt a b source control treated variety 2 318 2 334 tmt variety 0 492 1 505 0 372 run 0 321 0 319 tmt run 1 748 1 388 2 223 variety run pair 0 976 0 987 tmt pair 1 315 1 156 1 359 REML log li
61. 9 Notice The parameter estimates are followed by their approximate standard errors The first 8 lines are based on the asr file 23 2055 2 50402 1 66292 1 45821 0 130280 or H heritA 10 7 or H heritB 12 9 or R phencorr 7 8 9 or R gencorr 4 6 0 344376E 01 0 2365 0 0812 0 4071 0 5814 13 3 VPREDICT PIN file processing There are four forms of the VPREDICT directive 0 0612 0 0394 0 0183 0 2039 OS E Go 522176 134915 506679E 01 398418 678542E 01 169643E 01 e Ifthe pin file exists and has the same name as the jobname including any suffix appended by using RENAME just specify the VPREDICT directive e If the pin file exists but has a different name to the jobname specify the VPREDICT directive with the pin file name as its argument e If the pin file does not exist or must be reformed a name argument for the file is optional 219 13 3 VPREDICT PIN file processing but the DEFINE qualifier should be set Then the lines of the pin file should follow on the next lines terminated by a blank line An alternative to using VPREDICT is to process the contents of the pin file by running ASReml with the P command line option specifying the pin file as the input file Note that in this case the code must be self contained and any substitution variable used needs defining in the pin file For example if we wish to use sub to indicate fullname then the assignment of fullname to
62. A format statement is enclosed in parentheses and may include 1 level of nested parentheses for example e g FORMAT 4x 3 14 f8 2 Field descriptors are e rX to skip r character positions e rAw to define r consecutive fields of w characters width e rIw to define r consecutive fields of w characters width and e rFw d to define r consecutive fields of w characters width d indicates where to insert the decimal point if it is not explicitly present in the field where r is an optional repeat count In ASReml the A and I field descriptors are treated identically and simply set the field width Whether the field is interpreted alphabetically or as a number is controlled by the A qualifier Other legal components of a format statement are e the character required to separate fields blanks are not permitted in the format e the character indicates the next field is to be read from the next line However a on the end of a format to skip a line is not honoured e BZ the default action is to read blank fields as missing values and NA are also honoured as missing values If you wish to read blank fields as zeros include the string BZ e the string BM switches back to blank missing mode e the string Tc moves the last character read pointer to line position c so that the next field starts at position c 1 For example TO goes back to the beginning of the line e the string D invokes debug mode A forma
63. A C mu ABC FOWN A B C mu ABC A B B C A C would request the Wald F statistics based on see page 20 A mu B C sparse B mu A C sparse C mu A B sparse A B mu ABC B C A C sparse mu A BC A B A C sparse mu A B C A B B C sparse and C mu ABC A B A C B C sparse EE B C A C A B Warnings e For computational convenience ASReml calculates FOWN tests using a full rank parameterization of the fitted model with rank numerator de grees of freedom NumDF of terms generated by the incremental Wald F tests e Unfortunately if some terms in the implicit model defined by the re quested FOWN test would have more or less NumDF than are present in the full rank parameterization because aliased effects are reordered it can not be calculated correctly from the full rank parameterization In this case ASReml reverts to the conditional test but identifies the terms that need to be reordered in the fitted model to obtain the FOWN test s specified It is necessary to rerun ASReml after reordering these terms to obtain the FOWN test s specified Several reruns may be needed to perform all FOWN tests specified e Any model terms in the FOWN lists which do not appear in the actual model are ignored without flagging an error e Any model terms which are omitted from FOWN statements are tested with the usual conditional test e If any model terms are listed twice only the first test is performed F con tests
64. B C or implicitly e g term REGION cannot be adjusted for LOCATION when locations are actually nested in regions al though they are coded independently FOWN on page 78 provides a way of replacing the conditional Wald F statistic by specifying what terms are to be adjusted for provided its degrees of freedom are unchanged from the incremental test 67 5 8 Job control qualifiers Table 5 3 List of commonly used job control qualifiers qualifier action IMAXIT n SUM IX v IY v IG v JOIN sets the maximum number of iterations the default is 10 ASReml iter ates for n iterations unless convergence is achieved first Convergence is presumed when the REML log likelihood changes less than 0 002 cur rent iteration number and the individual variance parameter estimates change less than 1 If the job has not converged in n iterations use the CONTINUE qualifier to resume iterating from the current point To abort the job at the end of the current iteration create a file named ABORTASR NOW in the directory in which the job is running At the end of each iteration ASReml checks for this file and if present stops the job producing the usual output but not producing predicted values since these are calculated in the last iteration Creating FINALASR NOW will stop ASReml after one more iteration during which predictions will be formed On case sensitive operating systems eg Unix the filename ABOR
65. DEBUG 2 invoke debug mode and increase the information written to the screen or asl file This information is not useful to most users On Unix systems if ASReml is crashing use the system script command to capture the screen output rather than using the L option as the as1 file is not properly closed after a crash 11 3 4 Graphics command line options G H I N Q Graphics are produced in the PC Linux and SUN 32bit versions of ASReml using the Win teracter graphics library The I INTERACTIVE option permits the variogram and residual graphics to be displayed This is the default unless the L option is specified The N NOGRAPHICS option prevents any graphics from being displayed This is the default when the L option is specified The Gg GRAPHICS g option sets the file type for hard copy versions of the graphics Hard copy is formed for all the graphics that are displayed H g HARDCOPY g replaces the G option when graphics are to be written to file but not displayed on the screen The H may be followed by a format code e g H22 for eps Q QUIET is used when running under the control of ASReml W to suppress any POP UPs PAUSES from ASReml ASReml writes the graphics to files whose names are built up as lt basename gt lt args gt lt type gt lt pass gt lt section gt lt ezt gt where square parenthe ses indicate elements that might be omitted lt basename gt is the name portion of the as file
66. Hat 1 0 10000E 36 0 1000E 36 0 1000E 36 2 0 10000E 36 0 1000E 36 0 1000E 36 14 0 10000E 36 0 1000E 36 0 1000E 36 22 14 4 Other ASReml output files NIN alliance trial 1989 Residuals vs Fitted values Residuals Y 24 87 15 91 Fitted values X 16 77 35 94 o o o o o 9 o o o vo o o 8 gt o 8 o o o 7 o o aie o o o o 56 o 00 Oo 6 g e 8 o D po Y o o vo Bb o o 99 O eo a 8 o Dl o Oo po o o o gt o o e go 8 og 2 Ni a a o a Bo p 8 a s R o 9 o 89 9 A o o o 9 Ro Oy 9 o o 8 28 o o gt 8 o o o o 0 o o o o o r o oo o o o o o o o o o o o o o Figure 14 1 Residual versus Fitted values 15 0 10000E 36 0 1000E 36 0 1000E 36 16 24 088 5 162 6 074 17 27 074 4 476 6 222 18 28 195 6 255 6 282 19 23 775 6 325 6 235 20 27 042 6 008 5 862 240 24 695 1 855 6 114 241 25 452 0 1475 6 158 242 22 465 4 435 6 604 14 4 Other ASReml output files 14 4 1 The aov file This file reports details of the calculation of Wald F statistics particularly as relating to the conditional Wald F statistics not computed in this demonstration In the following table relating to the incremental Wald F statistic the columns are e model term e columns in design matrix 228 14 4 Other ASReml output files e numerator degrees of freedom e simple Wald F statistic e Wald F statistic scaled by A e A as defined in Kenward amp Roger e denominater degrees of freedom
67. Hg HARDCOPY 200 INTERACT 200 NoGraphs 200 ONERUN 201 QUIET 200 RENAME 201 WorkSpace 202 WorkSpace 202 XML 198 command line options 197 commonly used functions 88 conditional distribution 13 Conditional F Statistics 20 conditional factors 93 constraining variance parameters 141 constraints on variance parameters 118 contrasts 67 Convergence criterion 68 Convergence issues 150 correlated effects 16 correlation 217 between traits 152 KI IN 9 6 0 4 FH 349 INDEX model il covariance model ii covariates 40 61 105 cubic splines 98 data field syntax 47 data file 28 40 binary format 43 fixed format 42 free format 41 using Excel 42 data file line 31 datafile line 61 qualifiers 62 syntax 61 datasets barley asd 290 coop fmt 328 grass asd 283 harvey dat 159 nin89 asd 28 oats asd 272 orange asd 311 rat dat 152 rats asd 276 ricem asd 306 voltage asd 280 wether dat 156 wheat asd 296 debug options 200 Denominator Degrees of Freedom 20 dense 106 design factors 105 Deviance 322 diagnostics 17 diallal analysis 95 direct product 9 109 discussion list 3 Dispersion parameter 102 distribution conditional 13 marginal 13 Ecode 38 Eigen analysis 243 EM update 137 environment variable job control 65 equations mixed model 15 errors 247 Excel 42 execution time 243 F statistics 20 Factor qualifier DATE 49 DMY 49 LL Label Le
68. Models Model_Term Sigma Sigma Sigma SE C 326 16 11 Multivariate animal genetics data Sheep SIRE 34 34 0 174697 0 174697 2 00 0 P Wald F statistics Source of Variation NumDF DenDF Fine Prob 11 Trait 2 tiles 405 40 lt 001 3 SEX 1 129 0 5 61 0 020 2 GRP 4 30 0 8 03 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using numerical derivatives Warning These Wald F statistics are based on the working variable and are not equivalent to an Analysis of Deviance Standard errors are scaled by the variance of the working variable not the residual deviance Solution Standard Error T value T prev 2 GRP 2 D T21195 0 273336 2 00 3 1 76491 0 356573 4 95 2483 4 1 19399 0 273168 4 37 1 61 5 0 915605 0 242677 ma 1 16 3 SEX 1 0 197719 0 856093E 01 2 31 11 Trait 1 1 54993 0 200125 7 74 3 82051 0 216314 17 66 od gle 4 SIRE 34 effects fitted Finished 18 Jun 2008 12 35 09 062 LogL Converged 16 11 Multivariate animal genetics data Sheep The analysis of incomplete or unbalanced multivariate data often presents computational difficulties These difficulties are exacerbated by either the number of random effects in the linear mixed model the number of traits the complexity of the variance models being fitted to the random effects or the size of the problem In this section we illustrate two approaches to the analysis of a complex set of incomplete multivariate data
69. NOID CSKIP co Regressors m NONAMES SKIP s where M grr is the name of the file to be read ICSKIP c indicates c fields are to be skipped before the factor identifiers are read Factor is the name of the variable in the data that is associated with the regressors f sets the maximum number of levels default 1000 of Factor with regressor data ASReml will count the actual number NOID indicates that the factor identifiers are not present in the grr file CSKIP c indicates cz fields are to be skipped before the regressor variables are read Regressors is the name for the set of regressor variables m sets the number of regressor variables default is the number of names found must be set if there are extraneous fields to be ignored ISKIP s specifies how many lines are to be skipped before reading the regressor data NONAMES indicates there is no line containing the individual names of the regressor variables otherwise names are taken from the first non skipped line in the file If the factor identifiers are not present NOID ASReml assumes that the order of the factor classes in the data file matches the order in the grr file If the factor identifiers are present ASReml uses the identifiers obtained from the grr file to define the order of the factor classes when the data is read any extra identifiers in the data not in the grr file are appended at the end of the factor level name list If NOID is set identifier
70. P setstat regulatr 80 64 0 601817 0 307771E 01 3 64 OP teststat 4 4 0 642752E 01 0 328706E 02 0 98 0 P setstat teststat 40 40 0 100000E 08 0 511404E 10 0 00 OB Variance 256 255 1 00000 0 511404E 01 9 72 0 P Warning Code B fixed at a boundary GP F fixed by user liable to change from P to B P positive definite C Constrained by user VCC U unbounded S Singular Information matrix The convergence criteria has been satisfied after six iterations A warning message in printed below the summary of the variance components because the variance component for the setstat teststat term has been fixed near the boundary The default constraint for vari ance components GP is to ensure that the REML estimate remains positive Under this constraint if an update for any variance component results in a negative value then ASReml sets that variance component to a small positive value If this occurs in subsequent iterations the parameter is fixed to a small positive value and the code B replaces P in the C column of the summary table The default constraint can be overridden using the GU qualifier but it is not generally recommended for standard analyses Figure 16 2 presents the residual plot which indicates two unusual data values These values are successive observations namely observation 210 and 211 being testing stations 2 and 3 for setting station 9 J regulator 2 These observations will not be dropped from the following analyse
71. R functions at the end of the VPREDICT block In the example R phencorr 7 8 9 or R phencorr phenvar calculates the phenotypic covariance by calculating component 8 ycomponent 7 x component 9 where components 7 8 and 9 are created with the first line of the pin file and R gencorr 4 6 or R gencorr Sire Trait us Trait calculates the genotypic covariance by calculating component 5 ycomponent 4 x component 6 where components 4 5 and 6 are variance 217 13 2 Syntax components from the analysis 13 2 4 A more detailed example The following example for a bivariate sire model is a little more complicated The job file bsiremod as contains coop fmt ywt fat Trait Trait age c brr sex sex age r Trait sire f Tr grp dd 0 0 ID Trait 0 US GP Trait sire 2 Trait 0 US GP sire 0 ID VPREDICT DEFINE F phenvar Residual Sire Trait 1 3 4 6 F addvar sire 4 4 6 4 H heritA addvar 1 phenvar 1 10 7 H heritB addvar 3 phenvar 3 129 R phencorr phenvar 789 R gencorr addvar 4 6 The relevant lines of the asr file are Model_Term Sigma Sigma Sigma SE C Residual 8140 effects Residual vsv i 1 23 2055 23 2055 44 44 OP Residual VSC 2 1 2 50402 2 50402 18 56 OP Residual VvV 2 2 1 66292 1 66292 32 82 OP Trait sire VSV 1 1 1 45821 1 45821 3 66 OP Trait sire US_C 2 1 0 130280 0 130280 1 92 0 P Trait sire US V 2 2 0 344376E 01 0 344376E 01 2 03 0 P Numbering the parameters reported in bsir
72. Table 5 4 List of occasionally used job control qualifiers qualifier action ISTEP r SUBGROUP t v p SUBSET t v p WMF reduces the update step sizes of the variance parameters The default value is the reciprocal of the square root of MAXIT It may be set between 0 01 and 1 0 The step size is increased towards 1 each iteration Starting at 0 1 the sequence would be 0 1 0 32 0 56 1 This option is useful when you do not have good starting values especially in multivariate analyses forms a new group factor t derived from an existing group factor v by selecting a subset p of its variables A subgroup factor may not be used in a PREDICT or TABULATE directive forms a new factor t derived from an existing factor v by selecting a subset p of its levels Missing values are transmitted as missing and records whose level is zero are transmitted as zero The qualifier occupies its own line after the datafile line but before the linear model e g ISUBSET EnvC Env 3 5 8 9 15 21 33 defines a reduced form of the factor Env just selecting the environments listed It might then be used in the model in an interaction A subset factor can be used in a TABULATE directive but not in a PREDICT directive The intention is to simplify the model specification in MET Multi En vironment Trials analyses where say Column effects are to be fitted to a subset of environments It may also be used on the intrinsic factor Trait
73. The PLOT qualifier has the following options Table 10 2 List of predict plot options option action Lines and data addData superimposes the raw data 186 chooses an arrangement for plotting the predictions by However the user is able to 10 3 Prediction Table 10 2 List of predict plot options option action addlabels factors addlines factors noSEs semult r joinmeans superimposes the raw data with the data points labelled using the given factors which must not be prediction factors This option may be useful to identify individual data points on the graph for instance potential outliers or alternatively to identify groups of data points e g all data points in the same stratum superimposes the raw data with the data points joined using the given factors which must not be prediction factors This option may be useful for repeated measures data specifies that no error bars should be plotted by default they are plotted specifies the multiplier of the SE used for creating error bars default 1 0 specifies that the predicted values should be joined by lines by default they are only joined if the x axis variable is numeric Predictions involving two or more factors xaxis factor superimpose factors condition factors Layout goto n saveplot filename layout rows cols pycols plankpanels n extrablanks n and
74. The VCM statement must be placed after any residual definition line s 7 9 5 Writing out a design matrix The new qualifier DESIGN on the datafile line causes ASReml to write the design matrix not including the response variable to a des file It allows ASReml to create the design matrix required by the VCM process see Section 7 9 4 For example using a control file vcmdes as containing Create VCM Design for H F model Row Col Off Y vo vemdes asd DESIGN Y Row and Row 0 5 and Col 0 5 Off and a data file vemdes asd containing L Y a ead 22 0 a 1 i 3 2 lt 1 33 0 4 1 1 e ab ill 4 3 1 44 0 SL i 32 1 So 1 5 4 1 55 0 then the file vcmdes des will be generated which contains the values used in fitting the variance model for the HuynhFeldt model given in Section 7 9 4 146 7 10 Ways to present initial values to ASReml 7 10 Ways to present initial values to ASReml In complex models the Average Information algorithm can have difficulty maximising the REML log likelihood when starting values are not reasonably close to the REML solution ASReml has several internal strategies to cope with this problem When the user needs to provide better starting values than those generated by ASReml three of the methods are inserting explicit initial values in the as file doing a preliminary run to obtain tsv or msv files and then modifying the parametric information in one of those files Secti
75. The ignored set blocks wplots nitrogen Predicted_Value Standard_Error Ecode 0 6_cwt 123 3889 7 1747 E 0 4_cwt 114 2222 7 1747 E 0 2_cwt 98 8889 7 1747 E O_cwt 79 3889 7 1747 E SED Overall Standard Error of Difference 4 436 te i ee 5 Sica ee pa ee a a GS Predicted values of yield The averaging set nitrogen The ignored set blocks wplots variety Predicted_Value Standard_Error Ecode Marvellous 109 7917 TOTO E Victory 97 6250 F POTO E Golden_rain 104 5000 T7 7975 E SED Overall Standard Error of Difference 7 079 n es us 3 eee muaa es as ee A Predicted values of yield The ignored set blocks wplots nitrogen variety Predicted_Value Standard_Error Ecode 0 6_cwt Marvellous 126 8333 9 1070 E 0 6_cwt Victory 118 5000 9 1070 E 0 6_cwt Golden_rain 124 8333 9 1070 E 0 4_cwt Marvellous 117 1667 9 1070 E 0 4_cwt Victory 110 8333 9 1070 E 0 4_cwt Golden_rain 114 6667 9 1070 E 0 2_cwt Marvellous 108 5000 9 1070 E 0 2 cwt Victory 89 6667 9 1070 E 0 2_cwt Golden_rain 98 5000 9 1070 E 0_cwt Marvellous 86 6667 9 1070 E 0_cwt Victory 71 5000 9 1070 E 0_cwt Golden_rain 80 0000 9 1070 E Predicted values with SED PV 126 833 118 500 9 71503 124 833 9 71503 9 71503 275 16 3 Unbalanced nested design Rats 117 167 7 68295 9 71503 9 71503 110 833 9 71503 7 68295 9 71503 9 71503 114 667 9 71503 9 71503 7 68295 9 71503 9 71503 108 500 7 6829
76. These lines also mark progress through the iteration 14 4 3 The dpr file The dpr file contains the data and residuals from the analysis in double precision binary form The file is produced when the RES qualifier Table 4 3 is invoked The file could be renamed with filename extension dbl and used for input to another run of ASReml Alternatively it could be used by another Fortran program or package Factors will have level codes if they were coded using A or I All the data from the run plus an extra column of residuals is in the file Records omitted from the analysis are omitted from the file 231 14 4 Other ASReml output files 14 4 4 The pvc file The pvc file contains functions of the variance components produced by running a pin file on the results of an ASReml run as described in Chapter 13 The pin and pvc files for a half sib analysis of the Coopworth data are presented in Section 16 11 232 14 4 Other ASReml output files 14 4 5 The pvs file The pvs file contains the predicted values formed when a predict statement is included in the job Below is an edited version of nin89a pvs See Section 3 6 for the pvs file for the simple RCB analysis of the NIN data considered in that chapter nin alliance trial 14 Jul 2005 12 41 18 title line nin89a Ecode is E for Estimable for Not Estimable Warning mv_estimates is ignored for prediction Predicted values of yield variety Predicted_Value Standar
77. Trait grp 128 1 R STRUCTURE WITH 2 COMPONENTS AND 5 G STRUCTURES 0 0 O INDEPENDENT ACROSS ANIMALS Trait 0 US IGP TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp 0 ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp O ID xfa Trait 1 sire 2 xfa Trait 1 XFA1 IGP sire O ID xfa TrDam123 1 dam 2 xfa TrDam123 1 O XFA1 IGP dam O ID xfa TrLit1234 1 1it 2 xfa TrLit1234 1 O XFA1 GP lit 0 ID IPART 3 CHANGE XFA1 TO UNSTRUCTURED FOR SIRE AND LITTER wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS Trait sire xfa TrDam123 1 dam TrLit1234 1it If Trait grp 126 1 R STRUCTURE WITH 2 COMPONENTS AND 5 G STRUCTURES O O O INDEPENDENT ACROSS ANIMALS Trait 0 US IGP TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp 0 ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID Tralt sire 2 Trait 0 US IGP sire 0 ID xfa TrDam123 1 dam 2 331 16 11 Multivariate animal genetics data Sheep xfa TrDam123 1 O XFA1 GP dam O ID TrLit1234 1it 2 TrLiti234 0 US GP lit Y ID IPART 3 WORK OUT FUNCTIONS OF PARAMETERS VPREDICT DEFINE X Damv xfa TrDami23 1 defines 54 59 F phenWYG Residual 1 6 sire 1 6 TrLit1234 1it 1 6 Damv defines 60 65 126 23 28 44 49 54 59 F phenD Residual 7 10 Trait sire 7 10 TrLit1234 1it 7 10 defines 66 69 7 10 29 32 50 53 F phenF Residual
78. YLD FDIAM wether dat skip 1 GFW FDIAM Trait Trait YEAR lr Trait TEAM Trait SheepID predict YEAR Trait 122 1 R and 2 G structures 1485 0 ID units Trait 0 US traits HASReml generates initial values Trait TEAM 2 1st G structure Trait 0 US GP 3 0 TEAM O ID Trait SheepID 2 2nd G struct Trait 0 US GP 3 0 SheepID O ID the exact number of units in the data is not known to the user the error variance matrix is specified by the model Trait 0 US the initial values are for the lower triangle of the symmetric matrix specified row wise finding reasonable initial values can be a problem If initial values are written on the next line in the form new in Release 4 or q x O where q is t t 1 2 and t is the number of traits ASReml will take half of the phenotypic variance matrix of the data as an initial value see as file in code box for example the variance component matrices for the TEAM and SheepID strata are specified as Trait o US GP with starting values 3x0 on the next line The size of the US structure is taken from the number of traits 2 here Since the initial values are given as 3 0 ASReml will 155 8 4 The output for a multivariate analysis plug in values derived from the observed phenotypic variance matrix GP requests that the resulting estimated matrix be kept within the parameter space i e it is to be positive definite e the special qualifiers relating to mul
79. basic aspects of the ASReml command file to running an ASReml job and interpreting the output files You are encouraged to read this chapter before moving to the later chapters e a real data example is used in this chapter for demonstration see below e the same data are also used in later chapters e links to the formal discussion of topics are clearly signposted by margin notes This example is of a randomised block analysis of a field trial and is only one of many forms of analysis that ASReml can perform It is chosen because it allows an introduction to the main ideas involved in running ASReml However some aspects of ASReml in particular pedigree files see Chapter 9 and multivariate analysis see Chapter 8 are only covered in later chapters ASReml is essentially a batch program with some optional interactive features The typical sequence of operations when using ASReml is e Prepare the data typically using a spreadsheet or data base program e Export that data as an ASCII file for example export it as a csv comma separated values file from Excel e Prepare a job file with filename extension as e Run the job file with ASReml e Review the various output files e revise the job and re run it or 25 3 2 Nebraska Intrastate Nursery NIN field experiment e extract pertinent results for your report You will need a file editor to create the command file and to view the various output files On unix syst
80. commonly used job control qualifiers oao a aa a 66 List of occasionally used job control qualifiers 69 List of rarely used job control qualifiers 74 List of very rarely used job control qualifiers 83 Summary of reserved words operators and functions 88 Alphabetic list of model functions and descriptions 95 Link dual era and functions gt lt s io hE ek bee RR Eee ee eS 100 GLM distribution qualifiers The default link is listed first followed by per mitted alternatiyes o s oro AG Ew ARSED RHA ER EH ER RE 101 Examples of aliassing in ASReml 0 i644 ee ee ewe cad 107 Sequence of variance structures for the NIN field trial data 116 Schematic outline of variance model specification in ASReml 118 Details of the variance models available in ASReml 123 List of R and G structure qualifiers o 137 Examples of constraining variance parameters in ASReml 140 List of pedigree file qualifiers ee o 163 List of prediction qualifiers 6 lt 4 8s 465 48 he aart Eee 184 List Of predict plot HPS e ss aca osk biona a ee Ee RS 186 Trials classified by region and location 2 0000 189 ar o cda a ea e EP SE ees SB ee 189 Location means cos seo ee EE dia Kora ea Oe ko do eoa 189 Command In Options 00 do REE ERE pre Se SE IR pee a E Se TB 198 The use
81. default method for forming A is based on the algorithm of Meuwissen and Luo 1992 indicates that the third identity is the sire of the dam rather than the dam The original routine for calculating A in ASReml was based on Quaas 1976 tells ASReml to ignore repeat occurrences of lines in the pedigree file Warning Use of this option will avoid the check that animals occur in chronological order but chronological order is still required an alternative procedure for computing A was developed by Sargolzaei et al 2005 allows partial selfing when third field is unknown It indicates that progeny from a cross where the second parent male_parent is unknown is assumed to be from selfing with probability s and from outcrossing with probability 1 s This is appropriate in some forestry tree breeding studies where seed collected from a tree may have been pollinated by the mother tree or pollinated by some other tree Dutkowski and Gilmour 2001 Do not use the SELF qualifier with the INBRED or MGS qualifiers allows you to skip n header lines at the top of the file causes ASReml to sort the pedigree into an acceptable order that is parents before offspring before forming the A Inverse The sorted pedigree is written to a file whose name has srt appended to its name requests the formation of the inverse relationship matrix for the X chromosome as described by Fernando and Grossman 1990 for species where the male is X
82. environment variety trials PhD thesis De partment of Statistics University of Adelaide Goldstein H and Rasbash J 1996 Improved approximations for multilevel models with binary response Journal of the Royal Statistical Society A General 159 505 513 Goldstein H Rasbash J Plewis I Draper D Browne W Yang M Woodhouse G and Healy M 1998 A user s guide to MLwiN Institute of Education London URL http multilevel ioe ac uk Green P J and Silverman B W 1994 Nonparametric regression and generalized linear models Chapman and Hall Harvey W R 1977 Users guide to LSML76 The Ohio State University Columbus Harville D A 1997 Matrix Algebra from a statisticians perspective Springer Verlaag Harville D and Mee R 1984 A mixed model procedure for analysing ordered categorical data Biometrics 40 393 408 Haskard K A 2006 Anisotropic Mat rn correlation and other issues in model based geostatistics PhD thesis BiometricsSA University of Adelaide Kammann E E and Wand M P 2003 Geoadditive models Applied Statistics 52 1 1 18 Keen A 1994 Procedure IRREML GLW DLO Procedure Library Manual Agricultural Mathematics Group Wageningen The Netherlands pp Report LWA 94 16 Kenward M G and Roger J H 1997 The precision of fixed effects estimates from restricted maximum likelihood Biometrics 53 983 997 Lane P W and Nelder J A 1982
83. fields PRIMARY DAT skip 1 IMERGE 6 SECOND DAT SKIP 1 MATCH 1 6 would obtain the first five fields from PRIMARY DAT and the next five from SECOND DAT checking that the first field in each file has the same value Thus each input record is obtained by combining information from each file before any transformations are performed formally instructs ASReml to read n data fields from the data file It is needed when there are extra columns in the data file that must be read but are only required for combination into earlier fields in transfor mations or when ASReml attempts to read more fields than it needs to is required when reading a binary data file with pedigree identifiers that have not been recoded according to the pedigree file It is not needed when the file was formed using the SAVE option but will be needed if formed in some other way see Section 4 2 causes ASReml to read n records or to read up to a data reading error if n is omitted and then process the records it has This allows data to be extracted from a file which contains trailing non data records for example extracting the predicted values from a pvs file The argument n specifies the number of data records to be read Tf not supplied ASReml reads until a data reading error occurs and then processes the data it has Without this qualifier ASReml aborts the job when it encounters a data error See RSKIP 64 5 8 Job control qualifiers Table 5
84. file 160 Performance issues 209 power 132 Predict TP 98 ITP 185 ITURNINGPOINTS 185 PLOT suboptions 186 PRWTS 191 predicted values 37 prediction 32 177 qualifiers 184 predictions estimable 38 prior mean 16 qualifier 85 UpArrow 54 le 54 lt 54 lt gt 54 I 54 I gt 54 gt 54 lx 54 I 54 I 54 54 las 137 l 54 lA L 48 ABS 54 ADJUST 77 IAIF 163 ATLOADINGS 74 IAISINGULARITIES 75 IALPHA 163 AOD Analysis of Deviance 102 IARCSIN 54 ARGS 198 ASK 198 ASMV 69 ASSIGN 205 ASSOCIATE in PREDICT 189 ASSOCIATE 184 352 INDEX ASUV 69 IAS 48 IA 47 IBINOMIAL GLM 101 IBLOCKSIZE 142 IBLUP 76 IBMP 75 IBRIEF 75 198 ICHECK 212 ICINV 83 ICOLFACTOR 69 ICOLFAC 69 ICOMPLOGLOG 101 ICOMPLOGLOG 101 ICONTINUE 66 198 ICONTRAST 67 ICOS 55 ICSV 62 ICYCLE 205 IDATAFILE 62 IDDF 67 IDEBUG 198 IDEC 185 IDEFINE 220 IDENSEGIV 166 IDENSE 76 IDESIGN 70 IDEVIANCE residuals 102 IDF 77 319 IDIAG 163 IDISPLAY 70 IDISP dispersion 102 IDOM dominance 59 IDOPART 206 IDOPATH 206 IDO 55 IDV 55 ID 55 IEMFLAG 77 ENDDO 55 IEPS 70 EXCLUDE 62 EXP 55 EXTRA 78 IFACPOINTS 83 IFACTOR 71 IFCON 23 67 353 IFGEN 163 IFIELD 71 FILTER 62 IFINAL 198 FOLDER 62 IFORMAT 63 IFOR 207 IFOWN 23 78 IGAMMA GLM 101 IGDENSE 79 IGF 137 IGIV 163 IGKRIGE 70 IGLMM 79 IGOFFSET
85. first to speed up calculations However the order must be preserved if the user defines a structure for a term which also covers the following term s a way of defining a covariance structure across model terms Grouping is specifically required if the model terms are of differing sizes number of effects For example for traits weaning weight and yearling weight an animal model with maternal weaning weight should specify model terms Trait animal at Trait 1 dam when fitting a genetic covariance between the direct and maternal effects The model can be split into submodels with SM qualifiers 92 6 5 Interactions and conditional factors 6 5 Interactions and conditional factors 6 5 1 Interactions e interactions are formed by joining two or more terms with a or a for example a b is the interaction of factors a and b interaction levels are arranged with the levels of the second factor nested within the levels of the first labels of factors including interactions are restricted to 31 characters of which only the first 20 are ever displayed Thus for interaction terms it is often necessary to shorten the names of the component factors in a systematic way for example if Time and Treatment are defined in this order the interaction between Time and Treatment could be specified in the model as Time Treat remember that the first match is taken so that if the label of each field begins with a different let
86. for a variance component being zero is a monotone function of the F statistic for the associated term To compare two or more non nested models we can evaluate the Akaike Information Cri teria AIC or the Bayesian Information Criteria BIC for each model These are given by AIC 2 ni 2t BIC 2 p t logy 2 22 where f is the number of variance parameters in model and y n p is the residual degrees of freedom AIC and BIC are calculated for each model and the model with the smallest value is chosen as the preferred model 2 4 2 Diagnostics In this section we will briefly review some of the diagnostics that have been implemented in ASReml for examining the adequacy of the assumed variance matrix for either R or G structures or for examining the distributional assumptions regarding e or u Firstly we note that the BLUP of the residual vector is given by y WB 17 2 4 Inference Random effects R Py 2 23 It follows that E 0 var R WC w The matrix WC W under the sigma parameterization is the so called extended hat matrix ASReml includes the o in the hat matrix under the gamma parameterization It is the linear mixed effects model analogue of 0 X X X X for ordinary linear models The diagonal elements are returned in the fourth field of the yht file The OUTLIER qualifier invokes a partial implementation of research by Alison Smith Ari Verbyla and Brian Cullis
87. for all x R If Ax is nonnegative definite and in addition the null vector O is the only value of for which x Aa 0 then the quadratic form is said to be positive definite Hence the matrix A is said to be positive definite if a Aa is positive definite see Harville 1997 pp 211 7 2 Variance model specification in ASReml The variance models are specified in the AS qin Alliance Trial 1989 Reml command file after the model line as variety A shown in the code box In this case just one variance model is specified for replicates see column 11 model 2b below for details predict and nin89 asd skip 1 tabulate lines may appear after the model yield mu variety r repl line and before the first variance structure 1 line These are described in Chapter 10 ere gt repl 0 IDV 0 1 Table 7 3 presents the full range of variance models available in ASReml The identifiers for specifying the individual variance models in the command file are described in Section 7 5 under Specifying the variance models in ASReml Many of the models are correlation models However these are generalized to homogeneous variance models by appending V to the base identifier They are generalized to heterogeneous variance models by appending H to the base identifier 71 3 A sequence of structures for the NIN data Eight variance structures of increasing complexity are now considered for the NIN field trial data see C
88. from flanking marker information at position r of the linkage group f see MM to define marker locations r may be specified as TPn where TPn has been previously internally defined with a predict statement see page 185 r should be given in Morgans forms sine from v with period r Omit r if v is radians If v is degrees r is 360 In order to fit spline models associated with a variate v and k knot points in ASReml vis included as a covariate in the model and spl v k as a random term The knot points can be explicitly specified using the SPLINE qualifier Table 5 4 If k is specified but SPLINE is not specified equally spaced points are used If k is not specified and there are less than 50 unique data values they are used as knot points If there are more than 50 unique points then 50 equally spaced points will be used The spline design matrix formed is written to the res file An example of the use of spl0 is price mu week r spl week forms the square root of v r This may also be used to transform the response variable is used with multivariate data to fit the individual trait means It is formally equivalent to mu but Trait is a more natural label for use with multivariate data It is interacted with other factors to estimate their effects for all traits creates a factor with a level for every record in the data file This is used to fit the nugget variance when a correlation structure is applied to the residual
89. from the as1 file on the line 4 45751 SSPD before inserting the YSS qualifier The transformations in the code which follows convert Scald and Rot to missing for group 4 Lamb data from ARG thesis page 177 8 Year GRP 5 IV99 V2 4 M1 SEX SIRE I Total Fol FSZ Scald V 99 Rot 1 V199 pRot Rot Total 1 1 1 101 3933 6 6 1 LAMB DAT skip 1 IDF 1904 YSS 62 54249 pRot TOTAL Total mu SEX GRP r SIRE predict SEX 0 1 GRP 1235 The pertinant results are 319 16 10 Generalized Linear Mixed Models Univariate analysis of pRot Summary of 56 records retained of 68 read Model term Size miss zero MinNonO Mean MaxNonO StndDevn 1 Year 0 O 1 000 1 536 2 000 0 5032 2 GRP 5 0 0 1 3 1429 5 3 SEX 0 28 1 000 0 5000 1 000 0 5045 4 SIRE 34 0 0 1 17 0714 34 5 Total Weight 0 o 16 00 35 00 64 00 12 89 6 FS1 0 6 6 000 23 46 50 00 10 76 Y FS2 0 O 3 000 10 14 30 00 5 661 8 Scald 0 i3 1 000 2 071 16 00 3 458 9 Rot 0 19 1 000 1 196 4 000 1 151 10 pRot Variate 0 19 0 1754E 01 0 3606E 01 0 1818 0 3833E 01L 11 mu il 12 SEX GRP 5 3 SEX 1 2 GRP 5 Forming 46 equations 12 dense Initial updates will be shrunk by factor 0 224 Notice Algebraic Denominator DF calculation is not available Numerical derivatives will be used Notice 4 singularities detected in design matrix 1 LogL 2423 41 S2 0 32397E 01 1952 df i 1 components restrained 2 LogL 2431 71 S2 0 32792E 01 1952 df 0 6325E 02 1 000 3 LogL 2431 80 S2 0 32737E 01 1952 df
90. generation variety trial Wheat 295 16 8 Paired Case Control study Rice 0 e 300 16 8 1 Standard analysis eS A is 301 16 8 2 A multivariate approach o ce ca sco ocer tuc RR RR RR ie 305 16 8 3 Interpretation of results 2 2 6 aaa eee ee 308 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines IN e kee E NN 309 16 10 Generalized Linear Mixed Models 319 16 10 1 Binomial analysis of Footrot score o o ee ee 319 16 10 2 Bivariate analysis of Foot score 0 323 16 10 3 Multinomial Ordinal GLM analysis of Cheese taste 325 16 10 4 Multinomial Ordinal GLMM analysis of Footrot score 326 16 11 Multivariate animal genetics data Sheep 0 ee ee ea 327 16 11 1 Half sib analysis os ec o ersa is rd ee E ee u 328 16 11 2Animal mod l ecs s wees aba a Gr Re REE EES eS 338 Bibliography 345 Index 349 xi List of Tables 21 3 1 5 1 5 2 5 3 5 4 5 9 5 6 6 1 6 2 6 3 6 4 6 5 i 12 7 3 7 4 7 5 10 1 10 2 10 3 10 4 10 5 11 1 11 2 11 3 12 1 Combination of models for G and R structures 13 Trial layout and allocation of varieties to plots in the NIN field trial 27 List of transformation qualifiers and their actions with examples 54 Qualifiers relating to data input and output 62 List of
91. genetically linked via a pedigree The genetic effects are therefore correlated and assuming normal modes of inheritance the correlation expected from additive genetic effects can be derived from the pedigree provided all the genetic links are in the pedigree The additive genetic relationship matrix sometimes called the numerator relationship matrix can be calculated from the pedigree It is actually the inverse relationship matrix that is formed by ASReml for analysis Users new to this subject might find notes by Julius van der Werf helpful http http www vsni co uk products asreml user geneticanalysis pdf titled Mixed Models for Genetic analysis pdf For the more general situation where the pedigree based inverse relationship matrix is not the appropriate required matrix the user can provide a particular general inverse variance GIV matrix explicitly in a giv file In this chapter we consider data presented in Harvey 1977 using the command file harvey as 9 2 The command file In ASReml the P data field qualifier indicates Pedigree file example that the corresponding data field has an asso animal P ciated pedigree The file containing the pedi sire A gree harvey ped in the example for animal dem is specified after all field definitions and before as the datafile definition See below for the first R il aile 20 lines of harvey ped together with the cor harvey ped ALPHA responding lines of the data file ha
92. in Table 6 5 are presented to facilitate an understanding of over parameterised models It is assumed that var is a factor with 4 levels trt with 3 levels and rep with 3 levels and that all var trt combinations are present in the data Table 6 5 Examples of aliassing in ASReml model number of order of fitting singularities yield var r rep 0 rep var yield mu var r rep 1 rep mu var first level of var is aliassed and set to Zero yield var trt r rep 1 rep var trt var fully fitted first level of trt is aliassed and set to zero yield mu var trt var trt r rep 8 rep mu var trt var trt first levels of both var and trt are aliassed and set to zero together with subsequent interactions yield mu var trt r 8 var trt rep mu var trt rep var trt fitted before mu var and trt Lf yar trt var trt fully fitted mu var and trt are completely singular and set to zero The order within var trt rep is de termined internally 6 11 Wald F Statistics The so called ANOVA table of Wald F statistics has 4 forms Source NumDF F inc Source NumDF F inc F con M Source NumDF DDF_inc F inc P inc Source NumDF DDF_con F inc F con M P con depending on whether conditional Wald F statistics are reported requested by the FCON qualifier and whether the denominator degrees of freedom are reported ASReml always 107 6 11 Wald F Statistics reports incremental Wald F statistics F inc for the fixed model terms in t
93. in the variance model so that the model can be fitted For instance if ASUV is specified you may also need S2 1 Only rarely will it be reasonable to specify the ATSINGULARITIES qualifier sets hardcopy graphics file type to bmp suppresses some of the information written to the asr file The data summary and regression coefficient estimates are suppressed This quali fier should not be used for initial runs of a job until the user has confirmed from the data summary that the data is correctly interpreted by ASReml Use BRIEF 2 to cause the predicted values to be written to the asr file instead of the pvs file Use BRIEF 1 to get BLUE fixed effect estimates reported in asr file The BRIEF qualifier may be set with the B command line option 15 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action BLUP n IDENSE n is used to calculate the effects reported in the sln file without calcu lating any derived quantities such as predicted values or updated vari ance parameters For argument values 1 3 ASReml solves for the effects directly while for values 4 19 it solves the mixed model equations by it eration allowing larger models to be fitted With direct solution the estimation REML iteration routine is aborted after n 1 forming the estimates of the vector of fixed and random effects by matrix inversion n 2 forming the estimates of the vector o
94. individual variance parameters associated with the linear model term can be specified by number or sequence of numbers n m by appending these in square braces after the linear model term for example C Trait 3 or Residual 4 6 Users may contract names if they do not cause ambiguity for example Sire Trait might be contracted to Sire if there are no other random terms including Sire If the user is in doubt of the name or number of a parameter then running the program with VPREDICT DEFINE and a blank line will construct a pvc file with the names and numbers of parameters identified The original implementation was based entirely on the numbers but it will generally be better to use the names since the order model terms are reported cannot always be predicted Critical change For generalised linear models in ASReml Release 4 the pvc file reports and numbers for completeness a residual or dispersion parameter both when the parameter is estimated or when it is fixed By contrast ASReml 3 does not report nor number if the parameter is fixed by default at 1 Hence the parameters might be numbered differently in ASReml 4 and ASReml 3 13 2 1 Functions of components First ASReml extracts the variance compo VPREDICT DEFOE nents from the asr file and their variance F phenvar 1 2 Sire Residual matrix from the vvp file The F S V and F genvar 1 4 Sire 4 X functions create new components which are H herit 4 3 genvar
95. is often given as 1 indicating that the actual path to use is specified as the first argument on the command line see Section 11 4 See Sections 16 7 and 16 11 for examples The default value of n is 1 DOPATH n can be located anywhere in the job but if placed on the top job control line it cannot have the form DOPATH 1 unless the arguments are on the command line as the DOPATH qualifier will be parsed before any job arguments on the same line are parsed 206 11 4 Advanced processing arguments High level qualifiers qualifier action FOR forlist DO command IFOR Markern DO MBF IFOR Markers DO MBF IIF stringi string2 text The FOR DO command is intended to simplify coding when a series of similar lines are required in the command file which differ in a single argument The list of arguments is placed after FOR and the command is written after DO with S indicating where the argument is to be inserted forlist may be an assign string since they are processed before the FOR command is expanded Furthermore if forlist is entirely integer numbers 7 7 notation can be used For example ASSIGN Markern 35 75 125 ASSIGN Markers M35 M75 M125 mbf Geno 1 markers csv key 1 RFIELD S RENAME M S pas lr Markers is expanded to IMBF mbf Geno 1 markers csv key 1 RFIELD 35 RENAME M35 IMBF mbf Geno 1 markers csv key 1 RFIELD 75 RENAME M75 IMBF mbf Geno 1 markers csv key 1 RFIEL
96. lines define the R structures variance models for error as specified in the variance header line G structure header and definition lines define the G structures variance models for the additional random terms in the model as specified in the variance header line these lines are always placed after any R structure definition lines e variance parameter constraints are included if parameter constraints are to be imposed see the VCC c qualifier in Table 5 5 and Section 7 9 4 on constraints between and within variance structures A schematic outline of the variance model specification lines variance header line and R and G structure definition lines is presented in Table 7 2 using the variance model of 4 for demonstration Table 7 2 Schematic outline of variance model specification in ASReml general syntax model 4 variance header line s c g 121 R structure definition lines S1 C1 11 column AR1 0 3 C_2 22 row AR1 0 3 C_c S_2 C_1 Cc S_s C1 C_c G structure definition lines G_1 repl 1 4 0 IDV 0 1 G_2 s Gg 7 118 7 4 Variance structures Table 7 2 Schematic outline of variance model specification in ASReml eneral syntax model 4 g y 7 4 2 Variance header line The variance header line is of the form s c al NIN Alliance Trial 1989 variety A e sand c relate to the R structures g is the id number of G structures row 22 column 11 nin89aug asd skip 1 yield mu varie
97. lt 001 291 16 6 Spatial analysis of a field experiment Barley Slat Varlogram o Hall exam dal Outer displacement Inner displacement Ple 26 aud 2002 17 08 51 Figure 16 5 Sample variogram of the residuals from the AR1xXAR1 model 6 variety 24 80 0 13 04 AR1 x AR1 units 1 LogL 740 735 Ss2 33225 125 dE 2 LogL 723 595 s2 11661 125 df 3 LogL 698 498 S2 46239 125 di 4 LogL 696 847 S2 44725 125 df 5 LogL 696 823 S2 45563 125 df 6 LogL 696 823 S2 45753 125 df 7 LogL 696 823 S2 45796 125 df Model Term Gamma Sigma units 150 150 0 106154 4861 48 Variance 150 125 1 00000 45796 3 Residual AR AutoR 15 0 843795 0 843795 Residual AR AutoR 10 0 682686 0 682686 Wald F statistics Source of Variation NumDF DenDF F_inc 8 mu il 345 259 81 6 variety 24 tout 10 21 Sigma SE 2 72 2 74 12 33 6 68 lt 001 2 components constrained 1 components constrained 000503 qaqw va Prob lt 001 lt 001 The lattice analysis with recovery of between block information is presented below This variance model is not competitive with the preceding spatial models The models can be formally compared using the BIC values for example 292 16 6 Spatial analysis of a field experiment Barley IB analysis 1 LogL 734 184 S2 26778 125 df 2 LogL 720 060 s2 16591 125 df 3 LogL 711 119 s2 11173 125 df 4 LogL 707 937 S2 8562 4 125 df 5 LogL 707 786 s2 8091 2 12
98. model extends 3a by specifying a first qin Alliance Trial 1989 order autoregressive correlation model of or variety A der 11 for columns AR1 The R structure id in this case is therefore the direct product of two autoregressive correlation matrices that row 22 is V o2D p O Er pr giving a two column di eae dimensional first order separable autoregres eee ee i y yield mu variety f mv sive spatial structure for error The starting 4 5 o column correlation in this case is also 0 3 11 column AR1 0 3 Again note that o is implicit 22 row AR1 0 3 114 7 3 A sequence of structures for the NIN data 3c Two dimensional separable autoregressive spatial model with mea surement error This model extends 3b by adding a random units term Thus V 02 Las Ecl pe 6 Er pr The re served word units tells ASReml to construct an additional random term with one level for each experimental unit so that a second in dependent error term can be fitted A units term is fitted in the model in cases like this where a variance structure is applied to the errors Because a G structure is not explic itly specified here for units the default IDV structure is assumed The units term is often NIN Alliance Trial 1989 variety A id row 22 column 11 nin89aug asd skip 1 yield mu variety r units If mv 124 11 column AR1 0 3 22 row AR1 0 3 fitted in spatial models for field trial da
99. numbers so that the following lines are honoured if any one of the listed path numbers is active The PATH qualifier must appear at the beginning of its own line after the DOPATH qualifier A sequence of path numbers can be written using a b notation For example mydata asd DOPATH 4 PATH 2 4 6 10 One situation where this might be useful is where it is necessary to run simpler models to get reasonable starting values for more complex variance models The more complex models are specified in later parts and the CONTINUE command is used to pick up the previous estimates Example The following code will run through 1000 models fitting 1000 different marker variables to some data For processing efficiently the 1000 marker variables are held in 1000 separate files in subfolder MLIB and indexed by Genotype Marker screen Genotype yield PhenData txt ICYCLE 1 1000 IMBF mbf Genotype MLIB Marker I csv rename Marker I yld mu r Marker I Having completed the run the Unix command sequence grep LogL screen asr sort gt screen srt sorts a summary of the results to identify the best fit The best fit can then be added to the model and the process repeated Assuming Marker35 was best the revised job could be Marker screen Genotype yield PhenData txt ICYCLE 1 1000 IMBF mbf Genotype MLIB Marker I csv rename Marker l IMBF mbf Genotype MLIB Marker35 csv rename MKRO35 yld mu r MKRO35 Marker I 208 11 5 Per
100. of the residuals from the AR1xAR1 model for the Tulli DIEM Aati o s ee oe eee ee hee AR 298 Sample variogram of the residuals from the AR1xAR1 pol column 1 model for the Tullibigeal data o 299 Rice bloodworm data Plot of square root of root weight for treated versus 2 AAA IE AI 301 BLUPs for treated for each variety plotted against BLUPs for control 308 Estimated deviations from regression of treated on control for each variety plotted against estimate for control o ee ee ee ee 309 Estimated difference between control and treated for each variety plotted against estimate for control ee ee ee o 310 Trellis plot of trunk circumference for each tree 311 Fitted cubic smoothing spline for tree l 313 Plot of fitted cubic smoothing spline for model 1 316 Trellis plot of trunk circumference for each tree at sample dates adjusted for season effects with fitted profiles across time and confidence intervals 317 Plot of the residuals from the nonlinear model of Pinheiro and Bates 318 XIV 1 Introduction 1 1 What ASReml can do ASReml pronounced A S Rem el is used to fit linear mixed models to quite large data sets with complex variance models It extends the range of variance models available for the analysis of experimental data ASReml has application in the analysis of e un balanced longitudinal data
101. offset is reported in the asr file Twice the difference in the likelihoods for two models is commonly used as the basis for a likelihood ratio test see 223 14 3 Key output files page 16 This is not valid for generalised linear mixed models as the reported LogL does not include components relating to the reweighting Furthermore it is not appropriate if the fixed effects in the model have changed In particular if fixed effects are fitted in the sparse equations the order of fitting may change with a change in the fitted variance structure resulting in non comparable likelihoods even though the fixed terms in the model have not changed The iteration sequence terminates when the maximum iterations see MAXIT on page 68 has been reached or successive LogL values are less than 0 002 apart The following is a copy of nin89a asr ASReml 3 01d 01 Apr 2008 NIN alliance trial 1989 version amp title Build e 01 Apr 2008 32 bit 10 Apr 2008 16 47 40 140 32 Mbyte Windows nin89a date amp workspace Licensed to NSW Primary Industries permanent FA AO CCC ACA I IK a A I IK CA A I I CA A I A A kkk kkk kkk kkk kkk kkk kk Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au BECO ORK ARG Folder C data asr3 ug3 manex variety A QUALIFIERS SKIP 1 IDISPLAY 15 QUALIFIER DOPART 1 is active Reading nin89aug asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of 242
102. path name in quotes if it contains embedded blanks e the qualifiers tell ASReml to modify either the reading of the data and or the output produced see Table 5 2 below for a list of data file related qualifiers the operation of ASReml see Tables 5 3 to 5 6 for a list of job control qualifiers e the data file related qualifiers must appear on the data file line e the job control qualifiers may appear on the data file line or on following lines e the arguments to qualifiers are represented by the following symbols f a filename n an integer number typically a count 61 5 7 Data file qualifiers p a vector of real numbers typically in increasing order r a real number s a Character string t a model term label v the number or label of a data variable vlist a list of variable labels 5 7 Data file qualifiers Table 5 2 lists the qualifiers relating to data input Use the Index to check for examples or further discussion of these qualifiers Table 5 2 Qualifiers relating to data input and output qualifier action Frequently used data file qualifier ISKIP n causes the first n records of the non binary data file to be ignored Typically these lines contain column headings for the data fields Other data file qualifiers ICSV used to make consecutive commas imply a missing value this is auto matically set if the file name ends with csv or CSV see Section 4 2 Wa
103. pid raw rep nloc yield lat long row column Finished 27 Jul 2005 15 41 40 068 Missing faulty SKIP or A needed for variety Fixing the error by changing slip to skip however still produces the fault message Missing faulty SKIP or A needed for variety The portion of output given below shows that ASReml has baulked at the name LANCER in the first field on the first data line This alphabetic data field is not declared as alphabetic The correct data field definition for variety is variety A to indicate that variety is a character field Folder C asr ex manex QUALIFIERS SKIP 1 Reading nin89 asd FREE FORMAT skipping 1 lines Univariate analysis of yield Field 1 LANCER of record 1 line 1 is not valid Since this is the first data record you may need to skip some header lines hint see SKIP or append the A qualifier to the definition of factor variety Fault Missing faulty SKIP or A needed for variety Last line read was LANCER 1 NA NA 1 4 NA 4 3 1 2 1 1 ninerr3 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS mu 0 0 000 variety 0 0 000 12 factors defined max 500 O variance parameters max 900 2 special structures Last line read was LANCER 1 NA NA 1 4 NA 4 3 1 2 1 1 Finished 28 Jul 2005 09 51 12 817 Missing faulty SKIP or A needed for variety 254 15 4 An example 4 A missing comma and 5 A misspelt factor name in linear model The model has been written over two
104. prediction model is equivalent to predicting at a zero covariate value which is often not appropriate unless the covariate is centred Before considering the syntax it is useful to consider the conceptual steps involved in the prediction process Given the explanatory variables fixed factors random factors and co variates used to define the linear mixed model the four main steps are a Choose the explanatory variable s and their respective level s value s for which pre dictions are required the variables involved will be referred to as the classify set and together define the multiway table to be predicted Include only one from any set of associated factors in the classify set b Note which of the remaining variables will be averaged over the averaging set and which will be ignored the ignored set The averaging set will include all remaining variables involved in the fixed model but not in the classify set Ignored variables may be explicitly added to the averaging set The combination of the classify set with these averaging variables defines a multiway hyper table Only the base factor in a set of associated factors formally appears in this hyper table regardless of whether it is fitted as fixed or random Note that variables evaluated at only one value for example a covariate at its mean value can be formally introduced as part of the classify or averaging set 179 10 3 Prediction c Determine which terms fro
105. probably a problem with the output from MY OWNGDG Check the files including the time stamps to check the gdg file is being formed properly if you read less data than you expect there are two likely expla nations First the data file has less fields than implied by the data structure definitions you will probably read half the ex pected number Second there is an alphanumeric field where a numeric field is expected check the STEP qualifier argument either all data is deleted or the model fully fits the data error with the variance header line Often some other error has meant that the wrong line is being interpreted as the variance header line Commonly the model is written over several lines but the incomplete lines do not all end with a comma an error reading the error model Maybe you need to include mv in the model to stop ASReml discarding records with missing values in the response variable Without the ASUV qualifier the multivariate error variance MUST be specified as US Apparently ASReml could not open a scratch file to hold the transformed data On unix check the temp directory tmp for old large scratch files this is a Unix memory error It typically occurs when a mem ory address is outside the job memory The first thing to try is to increase the memory workspace using the WORKSPACE see Section 11 3 on memory command line option Otherwise you may need to send your data and the as files to Cust
106. requests ASReml use Expectation Maximization EM rather than Av erage Information AI updates when the AI updates would make a US structure non positive definite This only applies to US structures and is still under development When GP is associated with a US structure ASReml checks whether the updated matrix is positive definite PD If not it replaces the AI update with an EM update If the non PD char acteristic is transitory then the EM update is only used as necessary If the converged solution would be non PD there will be a EM update each iteration even though EM is omitted EM is notoriously slow at finding the solution and ASReml includes several modified schemes discussed by Cullis et al 2004 particularly relevant when the AI update is consistently outside the parameter space These include optionally performing extra local EM or PXEM Parame ter Expanded EM iterates These can dramatically reduce the number of iterates required to find a solution near the boundary of the parameter space but do not always work well when there are several matrices on the boundary The options are EMFLAG 1 Standard EM plus 10 local EM steps EMFLAG 2 Standard EM plus 10 local PXEM steps PXEM 2 Standard EM plus 10 local PXEM steps EMFLAG 3 Standard EM plus 10 local EM steps EMFLAG 4 Standard EM plus 10 local EM steps EMFLAG 5 Standard EM only EMFLAG 6 Single local PXEM EMFLAG 7 Standard EM plus 1 local EM step EMFLAG 8 Sta
107. set to be used together The variables will be treated as factor variables if the second argument 1 setting the number of levels is present it may be For example is eguivalent to X1 X2 X3 X4 X5 y X G5y data dat data dat y mu X1 X2 X3 X4 X5 y mu X DATE specifies the field has one of the date formats dd mm yy dd mm ccyy dd Mon yy dd Mon ccyy and is to be converted into a Julian day where dd is a 1 or 2 digit day of the month mm is a 1 or 2 digit month of the year Mon is a three letter month name Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec yy is the year within the century 00 to 99 cc is the century 19 or 20 The separators and must be present as indicated The dates are converted to days starting 1 Jan 1900 When the century is not specified yy of 0 32 is taken as 2000 2032 33 99 taken as 1933 1999 DMY specifies the field has one of the date formats dd mm yy or dd mm ccyy and is to be converted into a Julian day MDY specifies the field has one of the date formats mm dd yy or mm dd ccyy and is to be converted into a Julian day TIME specifies the field has the time format hh mm ss and is to be converted to seconds past midnight where hh is hours 0 to 23 mm is minutes 0 59 and ss is seconds 0 to et 59 The separator must be present e transformations are described below 5 4 2 Storage of alphabetic factor labels Space is allocated dynamically for the stora
108. size is 1 For example HOLD 1 20 30 40 ILAST lt factor gt lt lev gt lt faca gt lt leva gt lt facz gt lt lev3 gt OUTLIER IOWN f IPRINT n PNG IPS PVSFORM n limits the order in which equations are solved in ASReml by forcing equations in the sparse partition involving the first lt lev gt equations of lt factor gt to be solved after all other equations in the sparse partition It is intended for use when there are multiple fixed terms in the sparse equations so that ASReml will be consistent in which effects are identified as singular The test example had Ir Anim Litter f HYS where genetic groups were included in the definition of Anim Consequently there were 5 singularities in Anim The default reordering allows those singularities to appear anywhere in the Anim and HYS terms Since 29 genetic groups were defined in Anim LAST Anim 29 forces the genetic group equations to be absorbed last and therefore incorporate any singularities In the more general model fitting lr Tr Anim Tr Lit f Tr HYS without LAST the location of singularities will almost surely change if the G structures for Tr Anim or Tr Lit are changed invalidating Like lihood Ratio tests between the models performs the outlier check described on page 18 This can have a large time penalty in large models supplies the name of a program supplied by the user in association with the OWN variance model page 134 c
109. smoothness parameter T is the gamma function K is the modified Bessel function of the third kind of order v Abramowitz and Stegun 1965 section 9 6 and d is the distance defined in terms of X and Y axes hy x 2 hy Yi Yj Se cos a hy sin a hy sy sin a h cos a hy d 9 82 s 6 For a given v the range parameter affects the rate of decay of p with increasing d The parameter y gt 0 controls the analytic smoothness of the underlying process u the process being v 1 times mean square differentiable where v is the smallest integer greater than or equal to y Stein 1999 page 31 Larger y correspond to smoother processes ASReml uses numerical derivatives for v when its current value is outside the interval 0 2 5 When y m 4 with m a non negative integer pu is the product of exp d and a polynomial of degree m in d Thus v 3 yields the exponential correlation func tion pu d 3 exp d 6 and y 1 yields Whittle s elementary correlation function pM d 1 d K d p Webster and Oliver 2001 When y 1 5 then pu d 1 5 exp d 1 d which is the correlation function of a random field which is continuous and once differentiable This has been used recently by Kammann and Wand 2003 As y gt oo then py tends to the gaussian correlation function The metric parameter A is not estimated by ASReml it is usually set to 2 for
110. specified in FOWN statements are given model codes 0 P The FOWN statements are parsed by the routine that parses the model line and so accepts the same model syntax options Care should be taken to ensure term names are spelt exactly as they appear in the model is used to have the first random term included in the dense equations if it is a GRM GIV variance structure This will result in faster processing when the GRM inverse matrix is not sparse sets the number of inner iterations performed when a iteratively weighted least squares analysis is performed Inner iterations are iterations to es timate the effects in the linear model for the current set of variance parameters Outer iterations are the AI updates to the variance param eters The default is to perform 4 inner iterations in the first round and 2 in subsequent rounds of the outer iteration Set n to 2 or more to increase the number of inner iterations sets hardcopy graphics file type to HP GL An argument of 2 sets the hardcopy graphics file type to HP GL 2 79 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action HOLD list allows the user to temporarily fix the parameters listed Parameter num bers have been added to the reporting of input values to facilitate use of this and other parameter number dependent qualifiers The list should be in increasing order using colon to indicate a sequence step
111. sub using ASSIGN sub fullname needs to be in the pin file 220 14 Description of output files 14 1 Introduction With each ASReml run a number of output files are produced ASReml generates the out put files by appending various filename extensions to basename A brief description of the filename extensions is presented in Table 14 1 Table 14 1 Summary of ASReml output files file description Key output files asr contains a summary of the data and analysis results Msv contains final variance parameter values in a form that is easy to edit for reset ting the initial values if MSV or CONTINUE 3 is used see Table 5 4 pvc contains the report produced with the P option pvs contains predictions formed by the predict directive res contains information from using the polO sp1 and fac functions the iteration sequence for the variance components and some statistics derived from the residuals ISV contains the final parameter values for reading back if the CONTINUE qualifier is invoked see Table 5 4 sln contains the estimates of the fixed and random effects and their corresponding standard errors tab contains tables formed by the tabulate directive yht contains the predicted values residuals and diagonal elements of the hat matrix for each data point Other output files asl contains a progress log and error messages if the L command line option is specified aov contains details of
112. the asr pvs and sln files be also written in the xml file 198 11 3 Command line options 11 3 1 Prompt for arguments A A ASK makes it easier to specify command line options in Windows Explorer One of the options available when right clicking a as file invokes ASReml with this option ASReml then prompts for the options and arguments allowing these to be set interactively at run time With ASK on the top job control line it is assumed that no other qualifiers are set on the line For example a response of Hor 123 would be equivalent to ASReml h22r basename 1 2 3 11 3 2 Output control B OUTFOLDER XML B b BRIEF b suppresses some of the information written to the asr file The data summary and regression coefficient estimates are suppressed by the options B B1 or B2 This option should not be used for initial runs of a job before you have confirmed by checking the data summary that ASReml has read the data as you intended Use B2 to also have the predicted values written to the asr file instead of the pvs file Use B 1 to get BLUE estimates reported in asr file QUTFOLDER path allows most of the output files to be written to a folder other than the working folder This qualifier must be placed on the top command line as it needs to be processed before any output files are opened Most files produced by ASReml have a filename structure lt basename gt lt subname gt lt exrtension gt where
113. the ANOVA calculations apj is an ASReml project file created by ASReml W 221 14 2 An example Table 14 1 Summary of ASReml output files file description ask holds the RENAME ARG argument from the most recent run so that ASReml can retrieve restart values from the most recent run when CONTINUE is specified but there is no particular rsv file for the current ARG argument asp contains transformed data see PRINT in Table 5 2 ass contains the data summary created by the SUM qualifier see page 68 dbr dpr spr contains the data and residuals in a binary form for further analysis see IRESIDUALS Table 5 5 veo holds the equation order to speed up re running big jobs when the model is unchanged This binary file is of no use to the user vll holds factor level names when data residuals are saved in binary form See ISAVE on page 81 vrb contains the estimates of the fixed effects and their variance VVp contains the approximate variances of the variance parameters It is designed to be read back with the P option for calculating functions of the variance parameters was basename was is open while ASReml is running and deleted when it finishes It will normally be invisible to the user unless the job crashes It is used by ASReml W to tell when the job finishes xml xml contains key information from the asr pvs and res files in a form easier for computers to read An ASReml run generates ma
114. the analysis of balanced longitudinal data The implementation of cubic smoothing splines in ASReml was originally based on the mixed model formulation presented by Verbyla et al 1999 More recently the technology has been enhanced so that the user can specify knot points in 309 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges control BLUP exposed BLUP ang onuos Figure 16 11 Estimated difference between control and treated for each variety plotted against estimate for control the original approach the knot points were taken to be the ordered set of unique values of the explanatory variable The specification of knot points is particularly useful if the number of unique values in the explanatory variable is large or if units are measured at different times The data we use was originally reported by Draper and Smith 1998 ex24N p559 and has recently been reanalysed by Pinheiro and Bates 2000 p338 The data are displayed in Figure 16 12 and are the trunk circumferences in millimetres of each of 5 trees taken at 7 times All trees were measured at the same time so that the data are balanced The aim of the study is unclear though both previous analyses involved modelling the overall growth curve accounting for the obvious variation in both level and shape between trees Pinheiro and Bates 2000 used a nonlinear mixed effects modelling approach in which they mode
115. the anisotropy parameters of this metric d since inverting and adding 5 to a gives the same distance This non uniqueness can be removed by considering 0 lt a lt 5 and gt 0 or by considering 0 lt a lt m and either 0 lt 6 lt 1 or 2 1 With A 2 isotropy occurs when 1 and then the rotation angle a is irrelevant correlation contours are circles compared with ellipses in general With A 1 correlation contours are diamonds 131 7 5 Variance model description 7 5 4 Notes on power models Power models rely on the definition of distance for the associated term for example the distance between time points in a one dimensional longitudinal analysis the spatial distance between plot coordinates in a two dimensional field trial analysis Information for determining distances is supplied by the key argument on the structure line For one dimensional cases key may be the name of a data field containing the coordinate values when it relates to an R structure 0 in which case a vector of coordinates of length order must be supplied after all R and G structure lines fac x when it relates to model term fac x In two directions IEXP IGAU IEUC AEXP AGAU MATn the key argument also depends on whether it relates to an R or G structure For an R structure use the form rrcc where rr is the number of a data field containing the coordinates for the first dimension and cc is the number of a d
116. the covariance parameter between the intercept and slope for each tree in model 6 This ensures that the covariance model will be translation invariant A portion of the output file for model 6 is 8 LogL 87 4291 S2 5 6303 32 at Model_Term Gamma Sigma Sigma SE C spl age 7 5 5 2 1 7239 ee ole 1 09 0 P spl age 7 Tree 25 25 1 38565 7 80160 1 47 OP 316 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges Variance 35 32 1 00000 5 63028 1 72 g P Tree UnStru 1 1 5 62219 31 6545 1 26 OU Tree UnStru 2 1 0 124202E 01 0 699290E 01 0 85 9 y Tree UnStru 2 2 0 1083 7E 03 0 610192E 03 1 40 OU Covariance Variance Correlation Matrix UnStructured 21 05 0 5032 0 6993E 01 0 6102E 03 Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 4 0 169 87 lt 001 3 age 1 4 0 92 78 lt 001 5 Season 1 8 9 108 60 lt 001 Trunk circumference mm gt a S o o o N S I o 3 3 oe a o o o 5 0 8 o amp E i 8 WN H Y A 8 a s 8 5 E fa NE o E 8 Figure 16 15 Trellis plot of trunk circumference for each tree at sample dates adjusted for season effects with fitted profiles across time and confidence intervals 317 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges Figure 16 15 presents the predicted growth over time for individual trees and a marginal prediction for trees with approximate
117. the job with TSV You may only change values in the last 4 fields Fields are GN Term Type PSpace Initial value RP_GN RP scale 147 7 10 Ways to present initial values to ASReml 5 units ue Trait us Trait 1 G P 4 7911110 5 1 6 units us Trait us Trait 2 6 P 5 0231481 6 1 7 units us Trait us Trait _3 G P 15 298889 7 1 8 6 1 9 9 1 m its us Trait ua Trait 4 G P 48438271 units ns Trait zus Trait 5 G P 11 264815 10 units us Trait us Trait _6 G P 26 095692 10 1 11 wmits us Trait sus Trait 7 G P 4 6882715 11 1 12 units us Trait us Trait _8 G P 10 824074 12 1 13 wnits us Trait us Trait _9 G P 27 332887 13 1 14 units us Trait us Trait _10 G P 71 875403 14 1 15 wits us Trait sus Trait 11 6 P 3 9083333 15 1 16 units us Trait us Trait _12 G P 10 292592 16 1 17 units us Trait us Trait _13 G P 34 137962 17 1 18 units us Trait us Trait _14 G P 69 287036 18 1 19 units us Trait us Trait _15 G P 141 97296 19 1 Parameter constraints and initial values can be changed by editing the values in the PSpace and Initial_value columns Scale relationships can be introduced by noting that the full set of parameters can be related to a subset of parameters and scale factors such as parameter subset parameter scale or GN column parameter RP_GN column parameter RP_scale value
118. the number target or field of a data field the data field is used or modified depending on the context e Vfield may be replaced by the label of the field if it already has a label e in the first three forms the operation is performed on the current field this will be the field associated with the label unless the focus has been reset by specifying a new target in a preceding transformation 53 5 5 Transforming the data e the last four forms change the focus of subsequent transformations to target e in the last two forms a value is assigned to the target field For example V22 V1i1 copies existing field 11 into field 22 Such a statement would typically be followed by more transformations If there are fewer than 22 variables labelled then V22 is used in the transformation stage but not kept for analysis e only the DOM and RESCALE transformations automatically process a set of variables defined with the G field definition All other transformations always operate on only a single field Use the DO ENDDO transformations to perform them on a set of variables Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples I v used to overwrite create a variable half 0 5 with v It usually implies the vari zero 0 able is not read see examples on page 52 I l bx v usual arithmetic meaning note yield 10 17 that 0 0 gives 0 but v 0 gives a missi
119. the residual term The fixed effects include the main effects of both variety and nitrogen and their interaction The tables of predicted means and associated stan dard errors of differences SEDs have been requested These are reported in the pvs file Abbreviated output is shown below Results from analysis of yield Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients blocks 5 00 3175 06 12 0 4 0 1 9 blocks wplots 10 00 601 331 0 0 4 0 1 0 Residual Variance 45 00 177 083 0 0 0 0 1 0 Model_Term Gamma Sigma Sigma SE C blocks 6 1 21416 214 477 1 27 UP blocks wplots 18 18 0 598937 106 062 1 56 OP Variance 72 60 1 00000 177 083 4 74 OP Wald F statistics Source of Variation NumDF DenDF F_inc Prob 273 16 2 Split plot design Oats 7 mu 1 5 0 245 14 lt 001 4 variety 2 10 0 1 49 0 272 2 nitrogen 3 45 0 37 69 lt 001 8 variety nitrogen 6 45 0 0 30 0 932 For simple variance component models such as the above the default parameterisation for the variance component parameters is as the ratio to the residual variance Thus ASReml prints the variance component ratio and variance component for each term in the random model in the columns labelled Gamma and Component respectively A table of Wald F statistics is printed below this summary The usual decomposition has three strata with treatment effects separating into different strata as a consequence of the balanced desi
120. the variance structure Vel where gt is the variance matrix for sites This would imply that the varieties are independent random effects within each site have different variances at each site and are correlated across sites Important Whenever a random term is formed as the interaction of two factors you should consider whether the IID assumption is sufficient or if a direct product structure might be more appropriate See Chapter 7 for details on specifying separable G structures in ASReml 2 1 13 Range of variance models for R and G structures A range of models are available for the components of both R and G structures They include correlation C models that is where the diagonals are 1 or covariance V models and are discussed in detail in Chapter 7 Among the range of correlation models are e identity that is independent and identically distributed with variance 1 e autoregressive order 1 or 2 e moving average order 1 or 2 e ARMA 1 1 e uniform e banded e general correlation Among the range of covariance models are e scaled identity that is independent and identically distributed with homogenous vari ances e diagonal that is independent with heterogeneous variances e antedependence e unstructured e factor analytic 1 2 2 Estimation There is also the facility to define models based on relationship matrices including additive relationship matrices generated by pedigrees and usin
121. there are missing values in the response variable and the user has not specified that they be estimated The last applies here so we must change the model line to read yield mu variety mv Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 2 is active Reading nin asd FREE FORMAT skipping 1 lines Univariate analysis of yield Using 224 records of 242 read Model term Size miss zero MinNon0 Mean MaxNon0 1 variety 56 0 0 1 28 5000 56 11 column 11 0 0 1 6 3304 11 12 mu 11 AR AutoReg 0 1000 22 AR AutoReg 0 1000 Maybe you need to include mv in the model Fault R structures imply 0 242 records only 224 e Last line read was 22 column AR1 0 100000 ninerr9 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 SECTIONS 242 3 1 STRUCT 11 1 1 4 1 1 10 22 1 1 5 1 1 11 12 factors defined max 500 5 variance parameters max1500 2 special structures Final parameter values 0 0000 10000E 360 10000 0 10000 Last line read was 22 column AR1 0 100000 Finished 11 Apr 2008 20 07 11 046 R structures imply 0 242 records only 224 exist 10 Field layout error in a spatial analysis The final common error we highlight is the misspecification of the field layout In this case we have accidently switched the levels in rows and columns However ASReml can detect 259 15 4 An example this error because we have also asked it to sort the data into field o
122. times the data summary the iteration sequence summary the summary of estimated variance structure parameters and the Wald F statistics Developers are advised to parse the xm1 file in redeveloping code to handle the changes with the new release 14 3 2 The sln file The sln file contains estimates of the fixed and random effects with their standard errors in an array with four columns labelled as Model_Term Level Effect seEffect Note that the error presented for the estimate of a random effect is the square root of the prediction error variance In a genetic context for example where a relationship matrix A is involved the accuracy is 1 Ti where s is the standard error reported with the BLUP u for the ith individual f is the inbreeding coefficient reported when DIAG qualifier is given on a pedigree file line 1 f is the diagonal element of A and g is the genetic variance The sl1n file can easily be read into a GENSTAT spreadsheet or an S PLUS data frame Below is a truncated copy of nin89a sln Note that e the order of some terms may differ from the order in which those terms were specified in the model statement e the missing value estimates appear at the end of the file in this example 226 14 3 Key output files e the format of the file can be changed by specifying the SLNFORM qualifier In particular more significant digits will be reported e use of the OUTLIER qualifier will generate extra co
123. to a residual variance or a non parent record of c a c If there is no direct information on parents the parent term is replaced by zero where zero is a variable with zero elements If dad is unknown the and dad term is dropped The BLUPs of a non parent will need to be calculated outside ASReml by adding y 7 times its residual to the average of the parental BLUPs Prediction of parental values with assumed heritability was the main motivation for the development of the reduced animal model Estimation of genetic variance parameters is a little more complicated and the computational gains of removing non parent genetic values from the estimation procedure only apply if it is reasonable to form a small number of groups with roughly similar Aldiag values If AIG is this group factor then one can estimate residual variances in each group using SECTION ROWFAC COLFAC and use the variance parameter linear model facilities to constrain the residual variances and the parent variance to be a function of the genetic and residual variances 9 8 Factor effects with large Random Regression models One use of the GRM matrix is to allow more computationally efficient fitting of random regression models associating u a vector of f factor effects with v a vector of m regression effects through the model u Mv where the matrix M contains m regressor variables for each of the f levels of the factor Direct fitting of the regression effect
124. to read something when it does not need to or there is an error in the way something is specified 265 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy Error reading the data Error reading the DATA FILENAME line Error reading the model factor list Error setting constraints VCC on variance components Error setting dependent variable Error setting MBF design matrix MBF mbf x k filename Error structures are wrong size Error when reading knot point values Failed forming R G scores Failed ordering Level labels Failed to parse R G structure line Failed to read R G structure line Failed to process MYOWNGDG files Failed when sorting pedigree Failed when processing pedigree file Failed while ordering equations FORMAT error reading factor Definitions the data file could not be interpreted alphanumeric fields need the A qualifier data file name may be wrong the model specification line is in error a variable is probably misnamed The VCC constraints are specified last of all and require know ing the position of each parameter in the parameter vector the specified dependent variable name is not recognised It is likely that the covariate values do not match the values supplied in the file The values in the file should be in sorted order th
125. u and the residual errors e are assumed pairwise uncorrelated and to each be normally distributed with mean zero and variance given by var ui o Iy and var e o7I 2 1 The general linear mixed model where I and I are identity matrices of dimension q and n respectively In this case b var y Y o ZiZ 02In 2 5 i 1 2 1 4 Partitioning the residual error term As for the fixed and random model terms it is often useful or appropriate to consider a partitioning of the vector of residual errors e according to some conditioning factor We use the term section to describe this partitioning and the most common example of the use of sections in e is when we wish to allow sections in the data to have different variance structures For example in the analysis of multi environment trials METs it is natural to expect that each trial will require a separate possibly spatial error structure In this case for s sections we have e e e e assuming that the data vector is ordered by section and where e represents the vector of errors for the j section 2 1 5 R structure for the residual error term T For e partitioned as e el el e we allow the matrix R to have a similar direct P 1 gt 2 gt a sum structure with R 0 0 0 0 Rao 0 0 R ja Rys 3 boi cu 0 oO Rn 0 0 oO 0 R for s gt 1 sections and the data ordered by section Note that it may be necessary to re order
126. variable Y to specify the y variable and G to specify a grouping variable JOIN joins the points when the z value increases between consecutive records The grouping variable may be omitted for a simple scatter plot Omit Y y produce a histogram of the z variable For example X age Y height G sex Note that the graphs are only produced in the graphics versions of AS Reml Section 11 3 68 5 8 Job control qualifiers Table 5 3 List of commonly used job control qualifiers qualifier action For multivariate repeated measures data ASReml can plot the response profiles if the first response is nominated with the Y qualifier and the fol lowing analysis is of the multivariate data ASReml assumes the response variables are in contiguous fields and are equally spaced For example Response profiles Treatment A Yi Y2 Y3 Y4 Y5 rat asd Y Y1 G Treatment JOIN Yi Y2 Y3 Y4 Y5 Trait Treatment Trait Treatment Table 5 4 List of occasionally used job control qualifiers qualifier action ASMV n ASUV COLUMNFACTOR v ICOLFAC v indicates a multivariate analysis is required although the data is pre sented in a univariate form Multivariate Analysis is used in the narrow sense where an unstructured error variance matrix is fitted across traits records are independent and observations may be missing for particular traits see Chapter 8 for a complete discussion The data is presumed a
127. variety 001 predict factors qualifiers epl i repl 0 IDV 0 1 e predict must be the first element of the predict statement commencing in column 1 in upper or lower case e factors is a list of the variables defining a multiway table to be predicted each variable may be followed by a list of specific levels values to be predicted or the name of the file that contains those values e the qualifiers listed in Table 10 1 modify the predictions in some way e a predict statement may be continued on subsequent lines by terminating the current line with a comma e several predict statements may be specified ASReml parses each predict statement before fitting the model If any syntax problems are encountered these are reported in the pvs file after which the statement is ignored the job is completed as if the erroneous prediction statement did not exist The predictions are formed as an extra process in the final iteration and are reported to the pvs file Consequently aborting a run by creating the ABORTASR NOW file see page 68 will cause any 180 10 3 Prediction predict statements to be ignored Create FINALASR NOW instead of ABORTASR NOW to make the next iteration the final iteration in which prediction is performed By default factors are predicted at each level simple covariates are predicted at their overall mean and covariates used as a basis for splines or orthogonal polynomials are predicted at their d
128. was conducted at Slate Hall Farm UK in 1976 and was designed as a balanced lattice square with replicates laid out as shown in Table 16 6 The data fields were Rep RowB1k ColBlk row column and yield Lattice row and column numbering is typically within replicates and so the terms specified in the linear model to account for the lattice row and lattice column effects would be Rep latticerow Rep latticecolumn However in this example lattice rows and columns are both numbered from 1 to 30 across replicates see Table 16 6 The terms in the linear model are therefore simply RowB1k ColBlk Additional fields row and column indicate the spatial layout of the plots The ASReml input file is presented below Three models have been fitted to these data The lattice analysis is included for comparison in PATH 3 In PATH 1 we use the separable first order autoregressive model to model the variance structure of the plot errors Gilmour et al 1997 suggest this is often a useful model to commence the spatial modelling process The form of the variance matrix for the plot errors R structure is given by E N 8 5 16 5 where X and X are 15 x 15 and 10 x 10 matrix functions of the column and row autoregressive parameters respectively 289 16 6 Spatial analysis of a field experiment Barley Gilmour et al 1997 recommend revision of the current spatial model based on the use of diagnostics such as the sample variogram of th
129. where GN RP_GN and RP_scale are columns in the tsv file The relationships generated by VCC 2 56811 157 29 212 2 16 2 parameters 6 8 11 15 are equal to 5 7 9 12 16 are twice 5 10 13 17 parameters 13 and 17 are equal to 10 the full set of parameters 5 19 can therefore be expressed in terms of the subset parameters 5 10 14 18 and 19 can be introduced by editing the RN_GN and RP_scale columns Some users would prefer to insert initial values into this tsv file under the Initial value column As an example the file below contains values based on using 4 8 26 70 35 and 70 for parameters 5 10 14 18 and 19 The data values in the tsv file become GN Term Type PSpace Initial value RP_GN RP scale 5 units us Trait us Trait _1 G P 4 8 5 1 0000 6 units us Trait us Trait _2 G P 4 8 5 1 0000 7 units us Trait us Trait _3 G P 9 6 5 2 0000 8 units us Trait us Trait _4 G P 4 8 5 1 0000 9 units us Trait us Trait _5 G P 9 6 5 2 0000 10 units us Trait us Trait 6 G P 26 10 1 0000 11 units us Trait us Trait _7 G P 4 8 5 1 0000 12 units us Trait us Trait _8 P 9 6 5 2 0000 13 mits us Trait us Trait 9 G P 26 10 1 0000 gt 148 7 10 Ways to present initial values to ASReml 14 unite ws Trait suetirait 10 6 F 70 14 1 0000 15 uwnits us Trait us Trait 11 G P 4 8 5 1 0000 16 units us Trait sus Trait 12 G
130. which instruct ASReml to set up R structures for analysing a multi environment trial with a separable first order autoregressive model for each site environment When the number of rows columns is less than or equal to v the structure is set to ID instead of AR1 v has a default value of 5 and cannot be reset to less than 3 is used to join lines in plots see X specified on a separate line after the datafile line predefines the model term mbf v n as a set of n covariates indexed by the data values in vari able v MBF stands for My Basis Function and uses the same mechanism as the leg pol and sp1 model functions but with covariates sup plied by the user It is used for reading in specialized design matrices indexed by a factor in the data including genetic marker covariables By default the file f should contain 1 n fields where the first field the key field contains the values which are in the data variable or at which pre diction is required and the remaining n fields define the corresponding covariate values If n is omitted all fields after the key field are taken unless FACTOR is specified for which n is 1 and the covariate values are treated as coding for a multilevel factor RENAME t changes the name of the the term from mbf to the new name t This is necessary when several mbf terms are being defined which would otherwise have the same name label For example IMBF mbf entry mlib m35 csv rename Marker35
131. would give region predictions of 11 67 and 10 84 respectively derived from the location predictions in Table 10 5 Note that because location is nested in region the location weights should sum to 1 0 within levels of region when forming region means The AVERAGE ASAVERAGE qualifier allows the weights to be read from a file which the user can create elsewhere Thus the code ASAVERAGE trial Tweight csv 2 will read the weights from the second field of file Tweight csv The user must ensure the weights are in the coding order ASReml uses trial order in this instance given in the sln file or by using the TABULATE command It was noted that it is the base ASSOCIATE factor that is formally included in the hyper table If the lowest stratum is random it may be appropriate to ignore it Omitting it from 190 10 3 Prediction the ASSOCIATE list will allow it to reenter the Ignore set Specifying it with the IGNORE qualifier will exclude its effects from the prediction but not ignore the structural information implied by the association Normally it is not necessary for any model term to involve more than 1 of the associated factors One exception is if an interaction is required so that the variance can differ between sections For example fitting the terms at region trial as random effects would allow the trials in region 1 to have a different variance component to those in region 2 Prediction in these cases is more complicated
132. 0 IDV lt gt v the logical operator o which have v yield DV lt 1 IDV lt v in the field but keeps records with DV gt 100 IDV lt missing value in the field if DV DV gt is used after A or I v should re IDV gt fer to the encoded factor level rather than the value in the data file see also Section 4 2 Use DV to dis InitialWt DV card just those records with a miss ing value in the field ID v is equivalent to DV DV v DO Info i causes ASReml to perform the fol See below lowing transformations n times de fault is variables in current term incrementing the target by i de fault 1 and the argument if present by i default 0 Loops may not be nested A loop is ter minated by ENDDO another DO or a new field definition DOM f copies and converts additive marker ChrAadd G 10 IMM covariables 1 0 1 to dominance ChrAdom DOM ChrAadd marker covariables see below ENDDO terminates a DO transformation See below block EXP takes antilog base e no argument Rate EXP required 55 5 5 Transforming the data Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples Jddm Jmmd Jyyd IM M lt gt IM lt M lt IM IM gt IMAX IMIN MOD IMM INA INORMAL IREPLACE IRESCALE SEED Jddm converts a number represent ing a date in the form ddmmccyy ddmmyy or dd
133. 0 4351 UMN 1397 01 416 1 34916 0 00000 176 10 Tabulation of the data and prediction from the model 10 1 Introduction This chapter describes the tabulate directive and the predict directive introduced in Sec tion 3 4 under Prediction Tabulation is the process of forming simple tables of averages and counts from the data Such tables are useful for looking at the structure of the data and numbers of observations associated with factor combinations Multiple tabulate directives may be specified in a job Prediction is the process of forming a linear function of the vector of fixed and random effects in the linear model to obtain an estimated or predicted value for a quantity of interest It is primarily used for predicting tables of adjusted means If a table is based on a subset of the explanatory variables then the other variables need to be accounted for It is usual to form a predicted value either at specified values of the remaining variables or averaging over them in some way 10 2 Tabulation A tabulate directive is provided to enable simple summaries of the data to be formed for the purpose of checking the structure of the data The summaries are based on the same records as are used in the analysis of the model fitted in the same run In particular it will ignore records that exist in the data file but were dropped as the data was read into ASReml either explicitly using DV or implicitly because the dependent variable had mi
134. 0 0 0000 0 0922 0 2857 91 1 2 0 1422 100 0 0 0000 0 2819 0 2506 Q eo poo tono oops tooo tooontioot fvyerage 0 2343 89 1 0 0372 0 3651 0 0763 In the figure 1 indicates the proportion of TotalVar explained by the first loading 2 indicates the proportion explained by first and second provided it plots right of 1 Consequently the distance from 2 to the right margin represents PsiVar expl reports the percentage of TotalVar explained by all loadings The last row contains column averages 14 4 7 The rsv file The rsv file contains the variance parameters from the most recent iteration of a model The primary use of the rsv file is to supply the values for the CONTINUE qualifier see Table 238 14 4 Other ASReml output files Residuals V Hoy aad 00h B s ibin a 14 gut 2005 12 41 18 Figure 14 4 Plot of the marginal means of the residuals Hist Pier dey RSS dag d RA 2005 41 18 Peak Count 17 Range 24 87 15 91 MT m ul L i M Figure 14 5 Histogram of residuals 239 14 4 Other ASReml output files 5 4 and the C command line option see Table 11 1 It contains sufficient information to match terms so that it can be used when the variance model has been changed This is nin89a rsv 46 6 1711 121 This rsv file holds parameter values between runs of ASReml and is not normally modified by the User The current values of the the variance parameters are listed as a bloc
135. 0 242 05 lt 001 testing fixed 1 variety 55 165 0 0 88 0 708 effects Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives 5 repl 4 effects fitted Finished 04 Apr 2008 17 00 50 296 LogL Converged 3 6 2 The sln file The following is an extract from nin89 sln containing the estimated variety effects intercept and random replicate effects in this order column 3 with standard errors column 4 Note that the variety effects are returned in the order of their first appearance in the data file see replicate 1 in Table 3 1 Model_Term Level Effect seEffect variety LANCER 0 000 0 000 variety BRULE 2 487 4 979 variety REDLAND 1 938 4 979 variety CODY aoi 4 979 variety ARAPAHOE 0 8750 4 979 variety NE83404 1 15 4 979 variety NE83406 4 287 4 979 variety NE83407 5 875 4 979 variety CENTURA 6 912 4 979 variety SCOUT66 1 037 4 979 variety COLT 1 562 4 979 variety NE83498 1 563 4 979 36 3 7 Tabulation predicted values and functions of the variance components variety NE84557 8 037 4 979 variety NE83432 8 837 4 979 variety NE87615 2 975 4 979 variety NE87619 2 700 4 979 variety NE87627 6 33 4 979 mu 1 28 56 3 856 repl 1 1 880 1 755 repl 2 2 843 1 155 repl 3 0 8713 1 755 repl 4 3 852 1 755 3 6 3 The yht file The following is an extract from nin89 yht containing the predicted values of the observa tions column 2 the residuals column 3 a
136. 0 9265E 02 1 000 4 LogL 2431 80 S2 0 32738E 01 1952 df 0 9200E 02 1 000 Final parameter values 0 92543E 02 1 0000 Results from analysis of pRot Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients SIRE 25 70 0 506971E 01 59 7 1 0 Residual Variance 15 83 0 327367E 01 0 0 1 0 Model_Term Gamma Sigma Sigma SE C SIRE 34 34 0 918415E 02 0 300659E 03 0 98 22 P Variance 56 1952 1 00000 0 327367E 01 2 81 OP Wald F statistics Source of Variation NumDF DenDF F_inc Prob 11 mu 1 19 9 42 79 lt 001 3 SEX 1 16 2 0 02 0 882 2 GRP 3 21 9 2 04 0 139 12 SEX GRP 2 16 1 0 39 0 763 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using numerical derivatives 4 SIRE 34 effects fitted 6 are zero Two things stand out in this analysis From a genetic perspective the heritability estimate is 0 0364 a This can be calculated in ASReml with the pin file commands F GenVar 1x4 F TotVar 1 2 320 16 10 Generalized Linear Mixed Models H heritability 3 4 Secondly there is little evidence of significant difference between classes The predicted values are Sex PxP 1980 BRxP 1980 BxR 1980 BRxP 1981 0 0 0183 0 0130 0 0432 0 0126 0 0758 0 0268 0 0305 0 0111 1 0 0152 0 0132 0 0375 0 0124 0 0603 0 0244 0 0425 0 0108 An analysis of footrot as a binomial variable using the logistic link is performed by the model line a
137. 000 4 000 0 000 7 yield Variate 18 0 1 050 25 53 42 00 7 450 8 lat 0 O 4 300 25 80 47 30 13 63 9 long 0 o 1 200 13 80 26 40 7 629 10 row 22 0 0 1 11 5000 22 11 column 11 0 0 1 6 0000 11 12 mu a 13 mv_estimates 18 11 AR AutoReg 5 5 0 5000 22 AR AutoReg 6 6 0 5000 Forming 75 equations 57 dense Initial updates will be shrunk by factor 0 316 Notice 1 singularities detected in design matrix 1 LogL 401 827 S2 42 467 168 df 1 000 0 5000 0 5000 convergence 2 LogL 400 780 S2 43 301 168 df 1 000 0 4876 0 5388 3 LogL 399 807 S2 45 066 168 df 1 000 0 4698 0 5895 4 LogL 399 353 S2 47 745 168 df 1 000 0 4489 0 6395 5 LogL 399 326 S2 48 466 168 df 1 000 0 4409 0 6514 6 LogL 399 324 S2 48 649 168 df 1 000 0 4384 0 6544 7 LogL 399 324 S2 48 696 168 df 1 000 0 4377 0 6552 8 LogL 399 324 S2 48 708 168 df 1 000 0 4375 0 6554 Final parameter values 1 0000 0 43748 0 65550 Results from analysis of yield 250 15 3 Things to check in the asr file Model_Term Sigma Sigma Variance 242 168 1 00000 48 7085 Residual AR AutoR 11 0 437483 0 437483 Residual AR AutoR 22 0 655505 0 655505 Wald F statistics Source of Variation NumDF DenDF F 186 12 mu 1 25 0 331 85 1 variety 55 110 8 2 22 Sigma SE 6 81 5 43 11 63 C 0 P O U 0 U Prob lt 001 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives 13 mv_estimates 18 effects fit
138. 020 0 00026 age grp 0 ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID xfa Trait 2 tag 2 xfa Trait 2 O XFA2 GP tag O AINV xfa TrDam12 1 dam 2 xfa TrDam12 1 O XFA1 GP dam O ID TrLiti234 1it 2 TrLit1234 0 US GP lit 0 ID PATH 5 wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS xfa Trait 3 tag xfa TrDam12 1 dam TrLit1234 1it If Trait grp 128 000 Trait 0 US IGP TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp O ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID 341 16 11 Multivariate animal genetics data Sheep xfa Trait 3 tag 2 xfa Trait 3 O XFA3 GP tag O AINV xfa TrDam12 1 dam 2 xfa TrDam12 1 O XFA1 GP dam O ID TrLi61234 11 2 TrLit1234 0 US GP lit 0 ID The term Tr tag now replaces the Tr sire and picks up part of Tr dam variation present in the half sib analysis This analysis uses information from both sires and dams to estimate additive genetic variance The dam variance component is this analysis estimates the ma ternal variance component It is only significant for the weaning and yearling weights The litter variation remains unchanged Notice again how the maternal effect is only fitted for the first 2 traits and the litter effect for the first 4 traits The critical detail is that SUBSET is used to setup TrDam12 a variable using the first two traits ASReml uses the rela
139. 026E 01 0 721026E 01 0 22 o P TrLiti2Z34 1it US_C 4 2 0 794020 0 794020 1 55 O P TrLit1234 1it US_C 4 3 0 417001E 01 0 417001E 01 0 76 OP TrLiti234 1it US V 4 4 0 897161 0 897161 2 29 OP Covariance Variance Correlation Matrix US Residual 9 461 0 5689 0 2355 0 1640 0 2164 7 342 17 60 0 4231 0 2494 0 4633 0 2720 0 6680 0 1416 0 3995 0 1635 0 9630 1 998 0 2870 3 644 0 4753E 01 0 8503 2 483 0 7861E 01 0 1159 1 632 Covariance Variance Correlation Matrix US Trait sire 0 5939 0 7045 0 2970 0 1947 0 2924 0 6773 1 556 0 1883E 01 0 1326 0 5913 0 2805E 01 0 2879E 02 0 1502E 01 0 9808E 01 0 3960E 01 0 5962E 01 0 6570E 01 0 4776E 02 0 1579 0 6577 0 4073E 01 0 1333 0 8771E 03 0 4723E 01 0 3267E 01 Covariance Variance Correlation Matrix XFA xfa TrDam123 1 dam 2 158 0 9961 0 8035 0 9961 2 225 eala 0 8066 1 0000 0 1623 0 1687 0 1891E 01 0 8066 1 463 1 521 0 1109 1 0000 Covariance Variance Correlation Matrix US TrLit1234 1it 3 553 0 5111 0 1190 0 4039E 01 1 540 2 565 0 2041 0 5244 0 3101E 01 0 4509E 01 0 1910E 01 0 3185 0 7210E 01 0 7940 0 4170E 01 0 8972 Wald F statistics Source of Variation NumDF Fine 19 Trait age 5 100 11 20 Trait brr 15 116 72 21 Trait sex 5 TEOT 23 Trait age sex 4 4 17 27 TrSG123 sex grp 147 effects fitted 37 are zero 25 TrAG1245 age grp 196 effects fitted 69 are zero 32 Trait grp 180 effects fitted 65 singular 28 Trait sire 460 effects fitted 20 are zero 30 xfa TrDam123 1 dam 10683 effects fitted
140. 1 tabulate yield variety yield mu variety r repl predict variety 001 repl i repl 0 IDV 0 1 NIN Alliance trial 1989 variety A column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 001 repl i repl 0 IDV 0 1 in Table 7 3 Since IDV is the default variance structure for random effects the same anal ysis would be performed if these lines were omitted New R4 If the initial value 0 1 for the variance parameter is replaced by ASReml will calculate an initial value for the variance parameter 32 3 5 Running the job 3 5 Running the job Assuming you have located the nin89 asd file under Windows it will typically be located in ASRemlPath Examples we suggest copying the data file to the users workspace as the Examples folder is sometimes write protected and created the ASCII command file nin89 as as described in the previous section and in the same folder you can run the job ASRemlPath is typically C Program Files ASRem14 under Windows Installation details vary with the implementation and are distributed with the program You could use ASReml W or ConText to create nin89 as These programs can then run ASReml directly after they have been configured for ASReml An ASReml job is also run from a command line or by clicking the as file in Windows Explorer The basic command to run an ASReml job is ASRemlPath bin ASRem1 basename l as where base
141. 1 21 y Pp 0 00000 0 00 OB 0 108621E 02 0 00 OF 0 180299 2 46 OP 0 219418 2 890 OP 0 221424E 01 0 06 OP 0 177555 0 94 0 P 1 17362 0 00 OF 0 531936E 01 0 00 OF 0 8017 905 01 1 24 OP 0 285498 0 95 OP 16 11 Multivariate animal genetics data Sheep xfa Trait 3 yfa Trait 3 xfa Trait 3 xtallrait 3 xfa Trait 3 tag xfa Trait 3 tag xfa TrDam12 1 dam xfa TrDam12 1 dam xfa TrDam12 1 dam xfa TrDam12 1 dam TrLit1234 lit TrLit1234 1it IrLiti234 115 Trlit 234 115 TrLit1234 11t TrLit1234 1it TrLat1234 115 TrLit1234 1it TrLit1234 1it TrLit1234 1it Warning Code tag tag tag tag Gs g S S means there is no information in the data for this parameter XFA L 2 5 0 XFAL 3 1 0 AFAL 3 2 0 XFAL 3 3 0 XFAL 3 4 0 XFA L 3 5 0 XFAV O 1 XFAV O 2 XFA_L 1 1 FAL 1 2 US_V 1 1 US_C 2 1 USV 2 2 Ua C 3 1 0 1 6 3 2 Q USV 3 3 0 US_C 4 1 0 US_C 4 2 0 US_C 4 3 0 USV 4 4 0 fixed at a boundary E liable to change from P to B P Constrained by user VCC U 5BDNORROO 456561E 01 0 456561E 01 120878 0 120878 937495E 01 0 937495E 01 115709 0 115709 440376 0 440376 288994 0 288994 00000 0 00000 00000 0 00000 27024 1 27024 15348 1 15348 84733 3 84733 52267 2 52267 07859 4 07859 767746E 01 0 767746E 01 206274 0 206274 250360E 01 0 250360E 01 118279 0 118279 824055 0 824055 491371E 01 0 491371E 01 704917 0 704917 GP Singular Information matrix
142. 1 4 1 LogL 160 368 s2 1 0000 60 df 2 LogL 159 027 s2 1 0000 60 df 3 LogL 158 247 s2 1 0000 60 df 4 LogL 158 040 s2 1 0000 60 df 5 LogL 158 036 s2 1 0000 60 df Model_Term Sigma Sigma Sigma SE C Residual US UnStr 1 37 2262 Of 2262 2 45 a Y Residual US UnStr 1 20 3935 23 3935 1 77 OU Residual US UnStr 2 41 5195 41 5195 2 45 o Y Residual US UnStr 1 51 6524 51 6524 1 61 OU Residual US UnStr 2 61 9169 61 9169 1 78 0 U Residual US UnStr 3 209 121 259 121 2 45 OU Residual US UnStr 1 70 8113 70 8113 1 54 oU Residual US UnStr 2 57 6146 57 6146 1 23 o U Residual US UnStr 3 331 307 331 807 2 29 o U Residual US UnStr 4 551 507 551 507 2 45 0 y Residual US UnStr 1 Tos TOB 13 7857 1 60 OU Residual US UnStr 2 62 5691 62 5691 1 09 o U Residual US UnStr 3 330 651 320 851 2 29 0 y Residual US UnStr 4 539 90 533 190 2 42 0 y Residual US UnStr 5 542 175 542 175 2 45 Q y Covariance Variance Correlation Matrix US UnStructu RIPPE 0 5950 0 5259 0 4942 0 5194 23 39 41 52 0 5969 0 3807 0 4170 51 65 61 92 259 1 O 877T 0 8827 70 81 57 61 201 8 551 5 0 9761 tore 62 57 330 9 533 8 542 2 The antedependence model of order 1 is clearly more parsimonious than the unstructured model Table 16 5 presents the incremental Wald F statistics for each of the variance models There is a surprising level of discrepancy between models for the Wald F statistics The main effect of treatment is significant for the uniform power and antedependence models 288 16 6 Spatial
143. 1 Convergence issues ASReml does not always converge to a satisfactory solution and this section raises some of the issues In terms of the iteration sequence the usual case is that the REML loglikelihood increases smoothly and quadratically with each iteration to an effective maximum Con vergence problems are indicated when the LogL oscillates between two values or decreases usually dramatically They are also indicated if the mixed model coefficient matrix ceases to be positive semidefinite that is has negative pivots discovers new singularities after the first iteration or generates a negative residual sum of squares Failure to converge can arise because e the variance model does not suit the data or e the initial variance parameters are too far from the REML solution and the Average Information updates overshoot When convergence failure occurs it is sometimes helpful to examine the sequence of pa rameter values which is reported in the res file This may indicate which parameters are the problem ASReml requires the user to supply initial values for the variance parameters except for simple variance component terms where ASReml inserts an initial value of 0 1 if the user supplies none In some common cases ASReml will provide plausible initial values if the supplied value is zero Initial values may be in the wrong order or on the wrong scale Is the parameter a correlation a variance ratio independent of the scale of the data
144. 10 0 1 ISEED 848586 5 5 Transforming the data Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples SET SETN SETU SUB SEQ TARGET IUNIFORM vlist vlist for vlist a list of n values the data values 1 n are replaced by the cor responding element from vlist data values that are lt 1 or gt n are re placed by zero vlist may run over several lines provided each incom plete line ends with a comma i e a comma is used as a continuation symbol see Other examples below ISETN v n replaces data values 1 n with normal random variables having variance v Data values out side the range 1 n are set to 0 replaces data values 1 n with uni form random variables having range 0 v Data values outside the range 1 n are set to 0 replaces data values v with their index i where vlist is a vector of n values Data values not found in vlist are set to 0 vlist may run over several lines if necessary pro vided each incomplete line ends with a comma ASReml allows for a small rounding error when matching It may not distinguish properly if val ues in vlist only differ in the sixth decimal place see Other examples below replaces the data values with a se quential number starting at 1 which increments whenever the data value changes between successive records the current field is presumed to de fin
145. 10 11 12 13 14 15 4 1 2 3 4 5 6 T 8 9 10 11 12 13 14 15 5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 6 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 7 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 8 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 9 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 10 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Slate Hall example Rep 6 Six replicates of 5x5 plots in 2x3 arrangement RowBlk 30 Rows within replicates numbered across replicates Co1B1k 30 Columns within replicates numbered across replicates row 10 Field row column 15 Field column variety 25 yield barley asd skip 1 DOPATH 1 PATH 1 AR1 x ARI y mu var LZ 15 column AR1 0 1 Second field is specified so ASReml can sort 10 row ARI 0 1 records properly into field order 290 16 6 Spatial analysis of a field experiment Barley IPATH 2 AR1 x AR1 units y mu var r units 1 2 15 column ARI 0 1 10 row ARi 0 1 PATH 3 incomplete blocks y mu var r Rep Rowb1k Colblk IPATH O predict variety TWOSTAGEWEIGHTS Abbreviated ASReml output file is presented below The iterative sequence has converged to column and row correlation parameters of 68377 45859 respectively The plot size and orientation is not known and so it is not possible to ascertain whether these values are spa tially sensible It is generally found that the closer the plot centroids the higher the spatial correlation This is not always the case and if t
146. 11E 03 1 41 y P spl age 7 5 5 100 513 638 759 1 55 OP spl age 7 Tree 25 25 1 1178 7 10033 1 44 0 P Variance 35 33 1 00000 6 35500 1 74 OP 315 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 4 0 47 04 0 002 3 age 1 4 0 95 00 lt 001 217 Predicted values of circ Figure 16 14 Plot of fitted cubic smoothing spline for model 1 A quick look suggests this is fine until we look at the predicted curves in Figure 16 14 The fit is unacceptable because the spline has picked up too much curvature and suggests that there may be systematic non smooth variation at the overall level This can be formally examined by including the fac age term as a random effect This increased the log likelihood 3 71 P lt 0 05 with the spl age 7 smoothing constants heading to the boundary There is a possible explanation in the season factor When this is added Model 3 it has an F ratio of 107 5 P lt 0 01 while the fac age term goes to the boundry Notice that the inclusion of the fixed term season in models 3 to 6 means that comparisons with models 1 and 2 on the basis of the log likelihood are not valid The spring measurements are lower than the autumn measurements so growth is slower in winter Models 4 and 5 successively examined each term indicating that both smoothing constants are significant P lt 0 05 Lastly we add
147. 1326 0981 2924 5913 0396 6577 4277 7267 0703 So g xx es fo 6 2 6 co 6 8 0 amp 0396 0626 0717 0713 0388 1024 1720 1808 3521 3249 3874 2747 2026 2687 3854 5305 4388 9688 16 11 Multivariate animal genetics data Sheep is given by var ua N 189 A where A is the inverse of the genetic relationship matrix and ua are the trait BLUPs ordered animals within traits There are a total of 10696 92 3561 7043 animals in the pedigree Multivariate analysis involving several strata here animal direct additive genetic dam maternal and litter typically involves several runs The ASReml input file presented below has five parts which show the use of FA and US variance structures to get initial values for estimation of unstructured matrices and their use when estimated unstructured matrices are not positive definite as is the case with the tag matrix in this case but omits earlier runs involved with linear model selection and obtaining initial values This model is not equivalent to the sire dam litter model with respect to the animal litter components for gfw fd and fat IRENAME 1 ARG 1 CHANGE 1 TO 2 3 4 OR 5 FOR OTHER PATHS Multivariate Animal model IDOPART 1 tag P Bire 92 lI dam P grp 49 sex brr 4 litter 4871 age wwt IMO IMO identifies missing values ywt IMO gfw IMO fdm IMO fat MO pcoop fmt read pedigree from first three fields IPART 1 pco
148. 14 df Dev DF 0 6178 5014 df Dev DF 0 6144 5014 df Dev DF 0 6109 5014 df Dev DF 0 6085 5014 df Dev DF 0 6077 5014 df Dev DF 0 6076 5014 df 1 components restrained 5014 df Dev DF 0 6076 5014 df Dev DF 0 6076 5014 3046 50 0 64 Variance heterogeneity factor Deviance DF Results from analysis of Scorel YVar Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed Models Model_Term Residual Residual Trait SIRE Trait SIRE Trait SIRE Covariance Variance Correlation Matrix UnStructured 1 Covariance Variance Correlation Matrix UnStructured UnStructured 2 UnStructured 2 UnStructured 1 1 UnStructured 2 1 Sigma 162615E 03 1 Q 2 0 255609 0 166092 UnStructured 2 2 0 303900 000 0 3216E 03 0 1626E 03 0 2556 0 1661 0 3303E 02 0 3039 44 12 0 1470E 01 Source of Variation Trait SEX Trait GRP variance parameters using numerical derivatives 0 330313E 02 Sigma 162615E 03 0 03 0 255609 0 166092 0 0 330313E 02 0 07 303900 Wald F statistics NumDF DenDF_con F_inc 2 10 NA 40 9 393 15 1993 52 Residual Sigma SE C OP 35 20 0 P ZlS 0U 0 y 3 TO oU Trait SIRE F_con M P_con 76 10 A NA 1993 52 A lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular The YVar data was artificially creat
149. 18 0 P Trait sire US_V 2 2 1 55632 1 55632 3 90 0 P Trait sire US C 3 1 0 280482E 01 0 280482E 01 1 53 o P Trait sire Ua 6 3 2 0 287 861E 02 0 287861E 02 0 10 0 P Trait sire US Y 3 3 0 150192E 01 0 150192E 01 4 01 GP Trait sire US C 4 1 0 596227E 01 0 596227E 01 0 54 0P Trait sire US_C 4 2 0 657014E 01 0 657014E 01 0 41 0 P Trait sire US_C 4 3 0 477561E 02 0 477561E 02 4 25 0P Trait sire US_V 4 4 0 157854 0 157854 1 84 YP Trait sire US_C 5 1 0 407282E 01 0 407282E 01 0 99 0 P Trait sire Vet amp 2 133336 0 133338 1 98 0 P Trait sire US C 5 3 0 871122E 03 0 877122E 03 0 15 0 P Trait sire US_C 5 4 0 472300E 01 0 472300E 01 1 53 OP Trait sire US_V 5 5 0 326718E 01 0 326718E 01 2 00 0 P xfa TrDam123 1 dam XFAV O 1 0 126746E 01 0 126746E 01 0 03 O P xfa TrDam123 1 dam XFAV O 2 0 00000 0 00000 0 00 0 F xfa TrDam123 1 dam XFAV 0 3 0 661114E 02 0 661114E 02 1 265 O P xfa TrDam123 1 dam XFA_L 1 1 1 46479 1 46479 8 06 GP xfa TrDam123 1 dam AFA L 1 2 1 51911 1 61911 1 30 0 P 334 16 11 Multivariate animal genetics data Sheep xfa TrDam123 1 dam XFA L 1 3 0 110770 0 110770 5 08 uP TrLit1234 Lit VE Y 1 1 3 50275 3 568275 8 54 OP TrLit1234 1lit Ve c 2 1 1 53980 1 53980 2 90 o P TrLat1234 115 US V 2 2 2 55497 2 55497 3 19 0 P TrLati2394 115 US_C 3 1 0 310141E 01 0 310141E 01 0 73 0 P TrLit1234 11 US_C 3 2 0 450851E 01 0 450851E 01 0 74 0 P TrLati2s4 146 US_V 3 3 0 191030E 01 0 191030E 01 2 43 0 P TrLiti234 lit US 4 1 0 721
150. 224 records retained of 224 read data summary Model term Size miss zero MinNon0 Mean MaxNonO StndDevn 1 variety 56 0 0 1 28 5000 56 2 id 0 O 1 000 28 50 56 00 16 20 3 pid 0 G T101 2628 4156 pe ae 4 raw 0 o 21 00 510 5 840 0 149 0 5 repl 4 0 0 1 2 5000 4 6 nloc 0 O 4 000 4 000 4 000 0 000 7 yield Variate 0 1 050 25 53 42 00 7 450 8 lat 0 O 4 300 21 22 47 30 12 90 9 long 0 o 1 200 14 08 26 40 7 698 10 row 22 0 0 1 11 7321 22 11 column 11 0 0 1 6 3304 11 12 mu 1 4 identity L 5 5 0 1000 Structure for repl has 4 levels defined Forming 61 equations 57 dense Initial updates will be shrunk by factor 0 316 Notice 1 singularities detected in design matrix 35 3 6 Description of output files 1 LogL 454 807 S2 50 329 168 df 1 000 0 1000 convergence 2 LogL 454 663 e2 60 120 168 df 1 000 0 1173 sequence 3 LogL 454 532 S2 49 868 168 df 1 000 0 1463 4 LogL 454 472 S2 49 637 168 df 1 000 0 1866 5 LogL 454 469 S2 49 585 168 df 1 000 0 1986 6 LogL 454 469 S2 49 582 168 df 1 000 0 1993 7 LogL 454 469 S2 49 582 168 df 1 000 0 1993 Final parameter values 1 0000 0 19932 Results from analysis of yield Akaike Information Criterion 912 94 assuming 2 parameters Bayesian Information Criterion 919 19 Model_Term Gamma Sigma Sigma SE C Residual SCA_V 224 1 000000 49 5824 9 08 0 P parameter repl ID_V 1 0 199323 9 36291 1 12 0 Uestimates Wald F statistics Source of Variation NumDF DenDF F_inc Prob 12 mu 1 3
151. 25 331 Schall R 1991 Estimation in generalized linear models with random effects Biometrika 78 4 719 27 Searle S R 1971 Linear Models New York John Wiley and Sons Inc Searle S R 1982 Matrix algebra useful for statistics New York John Wiley and Sons Inc Searle S R Casella G and McCulloch C E 1992 Variance Components New York John Wiley and Sons Inc Self S C and Y L K 1987 Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under non standard conditions Journal of the American Statistical Society 82 605 610 Smith A B Cullis B R Gilmour A and Thompson R 1998 Multiplicative models for interaction in spatial mixed model analyses of multi environment trial data Proceedings of the International Biometrics Conference Smith A Cullis B R and Thompson R 2001 Analysing variety by environment data using multiplicative mixed models and adjustments for spatial field trend Biometrics 57 1138 1147 347 BIBLIOGRAPHY Smith A Cullis B R and Thompson R 2005 The analysis of crop cultivar breeding and evaluation trials an overview of current mixed model approaches review Journal of Agricultural Science 143 449 462 Stein M L 1999 Interpolation of Spatial Data Some Theory for Kriging Springer Verlag New York Stevens M M Fox K M Warren G N Cullis B R Coombes N E and Lewin L G 1999
152. 3 165 SIRE_9 G3 It is usually appropriate to allocate a genetic group identifier where the parent is unknown 9 6 Reading a user defined inverse relationship matrix Sometimes an inverse relationship matrix is required other than the one ASReml can produce from the pedigree file We call this a GIV G inverse matrix The user can prepare a giv file containing this matrix and use it in the analysis Alternatively the user can prepare the relationship matrix in a grm file and ASReml will invert it to form the GIV matrix The syntax for specifying a G matrix file say name grm or the G inverse file say name giv is name s d grm SKIP n DENSEGRM o GROUPDF n ND PSD NSD PRECISION n or name s d giv SKIP n DENSEGIV o GROUPDF n SAVEGIV f e the named file must have a giv grm sgiv sgrm dgiv or dgrm extension e sgiv and sgrm files are binary format files and will be read lower triangle row wise assuming single precision e dgiv and dgrm files are binary format files and will be read lower triangle row wise assuming double precision e the G inverse files must be specified on the line s immediately prior to the data file line after any pedigree file 165 9 6 Reading a user defined inverse relationship matrix e up to 98 G inverse matrices may be defined e the file must be in SPARSE format unless the DENSE qualifier is specified e a dense format file has the
153. 3 The data file line The data file name is specified immediately after the last data field definition Data file qualifiers that relate to data input and out put are also placed on this line if they are required In this example skip 1 tells AS Reml to ignore skip the first line of the data file nin89 asd the line containing the field labels The data file line can also contain qualifiers that control other aspects of the analysis These qualifiers are presented in Section 5 8 3 4 4 Tabulation Optional tabulate statements provide a sim ple way of exploring the structure of a data They should appear immediately before the model line In this case the 56 simple vari ety means for yield are formed and written to a tab output file See Chapter 10 for a discussion of tabulation 31 NIN Alliance trial 1989 variety A id pid row 22 column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 00 1 repl i repl 0 IDV 0 1 column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 3 4 The ASReml command file 3 4 5 Specifying the terms in the mixed model The linear mixed model is specified as a list of model terms and qualifiers All elements must be space separated ASReml accommodates a wide range of analyses See Section 2 1 for a brief discussion and general algebraic formu lation of the linear mixed mod
154. 4 13 4 8 6 8 4 7 2 4 31 65 8 6 9 6 8 2 4 25 65 8 6 10 8 Y 2 14 8 6 28 3 8 6 18 15 2 738 61 19 1 4 20 1 N 4 3 26 4 22 1 8 6 1 2 1 2 38 6 3 6 32 4 8 4 2 an 1 6 8 6 12 10 2 8 6 13 2 11 2 2 8 6 14 4 12 2 2 5 15 6 13 2 16 8 14 2 9 2 16 2 4 2 The data file The standard format of an ASReml data file is to have the data arranged in columns fields with a single line for each sampling unit The columns contain variates and covariates 40 4 2 The data file numeric factors alphanumeric traits response variables and weight variables in any order that is convenient to the user The data file may be free format fixed format or a binary file 4 2 1 Free format data files The data are read free format SPACE COMMA or TAB separated unless the file name has extension bin for real binary or db1 for double precision binary see below Important points to note are as follows e files prepared in EXCEL must be saved to comma or tab delimited form e blank lines are ignored e column headings field labels or comments may be present at the top of the file See Generating a template on page 34 provided that the skip qualifier Table 5 2 is used to skip over them e NA and are treated as coding for missing values in free format data files if missing values are coded with a unique data value for example 0 or 9 use the transformation M value to flag them as missing or DV value to drop t
155. 5 Warning Fewer levels found in MatOrder than specified 5 MatOrder 914 0 0 1 432 5760 6 rep 8 0 0 1 4 4837 7 iblk 80 0 0 1 40 1164 8 tree 0 0 1 0000 7 473 9 row 0 0 1 0000 28 52 10 col 0 O 1 0000 10 50 MaxNon0 StndDevn 71 26 37 926 860 80 14 00 56 00 20 00 4 018 16 09 5 760 9 8 Factor effects with large Random Regression models Warning Fewer levels found in prop than specified 11 prop 2 0 0 1 1 0000 1 12 culture 2 0 0 1 1 4945 13 treat 2 0 0 1 1 4945 2 Warning Fewer levels found in measure than specified 14 measure 2 0 0 1 1 0000 1 15 SURV 0 6 1 0000 0 9991 1 0000 0 3061E 01 16 DBH6 4 0 0 3000E 01 11 29 18 80 2 400 17 HT6 Variate 0 0 76 20 838 6 1286 163 6 18 HT8 83 O 91 44 1148 1576 170 6 19 CWAC6 3167 O 97 54 301 3 542 5 52 26 20 mu 1 21 culture rep 16 12 culture 2 6 rep 8 Warning GRM matrix is too SMALL 22 grm1 Clone 923 23 rep iblk 640 6 rep 8 7 iblk 80 Forming 2508 equations 19 dense Initial updates will be shrunk by factor 0 316 Notice LogL values are reported relative to a base of 30000 000 Notice 11 singularities detected in design matrix 1 LogL 2845 97 S2 8956 5 6390 df 2 LogL 2799 30 S2 8568 1 6390 df 3 LogL 2759 03 S2 8131 3 6390 df 4 LogL 2741 99 S2 7766 2 6390 df 5 LogL 2741 40 S2 7702 9 6390 df 6 LogL 2741 40 s2 7700 1 6390 df Results from analysis of HT6 Akaike Information Criterion 65490 79 assuming 4 parameters Bayesian Informa
156. 5 436 380 436 380 2 52 OU Residual POW EXP 5 382 369 382 369 212 OY Covariance Variance Correlation Matrix POWER 61 11 O 8227 0 6769 0 5569 0 4156 54 88 72 80 0 8227 0 6769 0 5051 93 12 123 5 309 7 0 8227 0 6140 91 02 120 7 302 7 437 1 0 7462 63 57 84 34 211 4 305 3 382 9 Wald F statistics Source of Variation DF F_inc 8 Trait 5 127 95 1 tmt il 0 00 9 Tr tmt 4 4 75 The last two models we fit are the antedependence model of order 1 and the unstructured model These require as starting values the lower triangle of the full variance matrix We use the REML estimate of X from the heterogeneous power model shown in the previous output The antedependence model models 5 by the inverse cholesky decomposition UDU where D is a diagonal matrix and U is a unit upper triangular matrix For an antedepen dence model of order q then u 0 for j gt 1 q 1 The antedependence model of order 1 has 9 parameters for these data 5 in D and 4 in U The input is given by y1 y3 y5 y7 y10 Trait tmt Tr tmt 12 14 S2 Tr 0 ANTE 60 16 286 16 5 Balanced repeated measures Height 54 65 73 65 91 50 123 3 306 4 89 17 120 2 298 6 431 8 62 21 83 85 208 3 301 2 379 8 The abbreviated output file is 1 LogL 171 501 s2 1 0000 60 df 2 LogL 170 097 s2 1 0000 60 df 3 LogL 166 085 s2 1 0000 60 df 4 LogL 161 335 s2 1 0000 60 df 5 LogL 160 407 s2 1 0000 60 d 6 LogL 160 370 s2 1 0000 60 df Y LogL 160 369 s2 1 0000 60 df
157. 5 9 71503 9 71503 7 68295 9 71503 9 71503 89 6667 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 98 5000 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 86 6667 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 71 5000 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 80 0000 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 7 68295 9 71503 9 71503 SED Standard Error of Difference Min 7 6830 Mean 9 1608 Max 9 7150 16 3 Unbalanced nested design Rats The second example we consider is a data set which illustrates some further aspects of testing fixed effects in linear mixed models This example differs from the split plot example as it is unbalanced and so more care is required in assessing the significance of fixed effects The experiment was reported by Dempster et al 1984 and was designed to compare the effect of three doses of an experimental compound control low and high on the maternal performance of rats Thirty female rats dams were randomly split into three groups of 10 and each group randomly assigned to the three different doses All pups in each litter were weighed The litters differed in total size and in the numbers of males and females Thus the additional covariate littersize was included in the analysis The differential effect of the compound on male and female pups was also of interest Three litters had to be dropped
158. 5 df 6 LogL 707 786 S2 8061 8 125 df T LogL 707 786 S2 8061 8 125 df Results from analysis of yield Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients Rep 5 00 266657 25 0 5 0 5 0 1 0 RowBlk 24 00 74887 8 0 0 4 3 0 0 1 0 Co1B1k 23 66 71353 5 0 0 0 0 4 3 1 0 Residual Variance 72 34 8061 81 0 0 0 0 0 0 1 0 Model_Term Gamma Sigma Sigma SE C Rep 6 6 0 528714 4262 39 0 02 0 P RowBlk 30 30 1 93444 15595 1 3 06 OP Co1B1k 30 30 1 83725 14811 6 3 04 OP Variance 150 125 1 00000 8061 81 6 01 OP Wald F statistics Source of Variation NumDF DenDF F_inc Prob 8 mu 1 5 0 1216 29 lt 001 6 variety 24 79 3 8 84 lt 001 Finally we present portions of the pvs files to illustrate the prediction facility of ASReml The first five and last three variety means are presented for illustration The overall SED printed is the square root of the average variance of difference between the variety means The two spatial analyses have a range of SEDs which are available if the SED qualifier is used All variety comparisons have the same SED from the third analysis as the design is a balanced lattice square The Wald F statistic statistics for the spatial models are greater than for the lattice analysis We note the Wald F statistic for the AR1XAR1 units model is smaller than the Wald F statistic for the AR1XAR1 Predicted values of yield AR1 x AR1 variety Predicted_Value Standard_Error Eco
159. 6 10 Generalized Linear Mixed Models the weights in the analysis changing the reported variances and standard deviations If d is not supplied it is estimated from the residual as the model is fitted to the working variable ASReml solves for the linear effects twice see the GLMM qualifier each iteration of the vari ance components so that the variance component updates are based on solutions obtained using the same variance parameters I e We start with a set of solutions and some param eters We use these to update the solutions Then use the updated solutions to update the variance parameter 16 10 2 Bivariate analysis of Foot score The data file BINNOR txt contains the expanded version 2513 records of the lamb data from the previous example augmented with an extra simulated variable YVar It was created from the summarized data without knowing which actual individuals had which combinations of trait values The binary variable Score1 indicates whether all four feet are sound The following code produces a bivariate analysis of Score1 on the underlying logistic scale and YVar on the Normal scale Lamb data from ARG thesis page 177 8 Year GRP 5 IV99 V2 4 IM 1 SEX SIRE II Scorel Score2 Scald V99 Rot V99 YVar binnor txt skip 1 IASUV MAXIT 40 Scorel YVar bin Trait SEX Trait GRP Ir Trait SIRE 121 2513 2 0 US GFPP 1 01 0 25 Trait SIRE 2 Trait 0 US 0 015 0 01 1 05 SIRE There are several issues ad
160. 63 The example continued 0 000 eee ee 169 9 7 The reduced animal model RAM o o 169 9 8 Factor effects with large Random Regression models 171 10 Tabulation of the data and prediction from the model 177 TO TO Sse ee et ewe ee Oh ee A eee ee we 177 WS OPA y be eu ee eo Be Bo a he Oe Cea GOS wee Oe 177 103 MOU an Ee he ODE SS ORE a 178 10 3 1 Underlying principles 22k kb eee eee ee eee essa 178 103 2 Predict Smak ca oa ee he ee ha SRS SEY AO eee BS 180 10 2 5 Predict TANS ak ee wee ee ee ee eee eee ee RES A eG 183 10 3 4 Associated factors o lt sooo ra sacco eee ee ee ee we eo 189 10 3 5 Complicated weighting with IPRESENT 191 10 3 0 Examples lt s Re RARE eh ewe eS ee eR OAS 193 10 3 7 New R4 Prediction using two way interaction effects 193 11 Command file Running the job 195 TUL A eee de ee we ode Be oe ee Ce wie Bae ee eee TR 195 11 2 The command ine scce eee dG dee EERE RRR EE ERR REE eS 195 ML Nomalum coco eee ee ee Se eee ES we eS ES 195 11 22 Processing a BM coi iii e 196 11 2 3 Forming a job template from a data file 196 11 3 Command line options lt lt e ee sau ec rs ars G repra 197 11 3 1 Prompt for arguments A 2 a gar ee AE AR i ee tu 199 11 3 2 Output control B OUTFOLDER XML 199 11 3 3 Debug command line options D E 200 11 3 4 Graphics comma
161. 6527 5 NE83498 NE86607 NE87627 ROUGHRIDER NE83406 KS831374 NES3T12 CENTURA NE86507 NE87451 6 NE84557 ROUGHRIDER NE86527 COLT COLT NE86507 NE83432 ROUGHRIDER NE87409 7 NE8S3432 VONA CENTURA SCOUT66 NE87522 NE86527 TAM200 NE87512 VONA GAGE 8 NE85556 SIOUXLAND NE85623 NE86509 NORKAN VONA NE87613 ROUGHRIDER NE83404 NE83407 9 NE85623 GAGE CODY NE86606 NE87615 TAM107 ARAPAHOE NE83498 CODY NE87615 10 CENTURAK 78 NE88T12 NE86582 NE84557 NE85556 CENTURAK 78 SCOUT66 NE87463 ARAPAHOE 11 NORKAN NES86T666 NE87408 KS831374 TAM200 NE87627 NE87403 NE86T666 NE86582 CHEYENNE 12 KS831374 NE87408 NE87451 GAGE LANCOTA NE86T666 NE85623 NE87403 NE87499 REDLAND 13 TAM200 NE87408 NE83432 NE87619 NE86503 NE87615 NE86509 NE87512 NORKAN NE83432 14 a NES86482 NES87409 CENTURAK 78 NE87499 NE86482 NE86501 NE85556 NE87446 SCOUT66 NE87619 15 HOMESTEAD NE87446 NE83T12 CHEYENNE BRULE NE87522 HOMESTEAD CENTURA NE87513 NE83498 16 LANCER LANCOTA NE87451 NE87409 NE86607 NE87612 CHEYENNE NE83404 NE86503 NE83T12 NE87613 17 BRULE NE86501 NES87457 NE87513 NE83498 NE87613 SIOUXLAND NE86503 NE87408 CENTURAK 78 NE86501 18 REDLAND NE86503 NE87463 NE87627 NE83404 NE86T666 NES87451 NE86582 COLT NE87627 TAM200 19 CODY NE86507 NE87499 ARAPAHOE NE87446 GAGE NE87619 LANCER NE86606 NE87522 20 ARAPAHOE NE86509 NE87512 LANCER SIOUXLAND NE86607 LANCER NE87463 NE83406 NE87457 NE84557 21 NE8S3404 TAM107 NE87513 TAM107 HOMESTEAD LANCOTA NE8S7446 NE86606 NE86607 NE86509 TAM107 22 NE83406 CH
162. 7 E NE83406 24 2750 3 8557 E NE83407 22 6875 3 8557 E CENTURA 21 6500 3 8557 E SCOUT66 27 5250 3 8557 E COLT 27 0000 3 8557 E NE87613 29 4000 3 8557 E NE87615 25 6875 3 8557 E NE87619 31 2625 3 8557 E NE87627 23 2250 3 8557 E SED Overall Standard Error of Difference 4 979 39 4 Data file preparation 4 1 Introduction The first step in an ASReml analysis is to prepare the data file Data file preparation is discussed in this chapter using the NIN example of Chapter 3 for demonstration The first 25 lines of the data file are as follows CODY 4 NE83404 NE83406 NE83407 CENTURA SCOUT66 COLT 11 NE83498 NE84557 NE83432 NE85556 NE85623 NE86482 LANCOTA CENTURK78 17 1117 632 NORKAN 18 1118 446 1 4 22 Ks831374 19 1119 684 1 4 3 TAM200 20 1120 422 1 4 2 HOMESTEAD 22 1122 566 1 4 variety id pid raw repl nloc yield lat long row column BRULE 2 1102 631 1 4 31 55 4 3 20 4 17 1 REDLAND 3 1103 701 1 4 35 05 4 3 21 6 18 1 4 3 22 8 ARAPAHOE 5 1105 661 1 4 33 05 4 3 1104 602 1 4 30 1 6 1106 605 1 4 30 2 7 1107 704 1 4 35 2 8 1108 388 1 4 19 4 9 1109 487 1 4 24 3 10 1110 511 1 4 25 1111 502 1 4 25 1 3 12 1112 492 13 1113 509 14 1114 268 15 1115 633 16 1116 513 ererrer 3 ae 4 1 1 21 1121 560 1 4 28 23 1123 514 1 4 25 NE86501 24 1124 635 1 4 31 75 8 6 20 4 17 2 NE86503 25 1125 840 1 4 42 8 6 21 6 18 2 25 4 3 25 2 21 1 58 6 2 4 2 2 8 4 24 6 8 665 2 4 25 45 8 6 7 2 6 2
163. 74 2174 s2 0 19670 315 df 0 1000 1 000 2 LogL 79 1579 S2 0 18751 315 df 0 1488 1 000 3 LogL 83 9408 S2 0 17755 315 df 0 2446 1 000 4 LogL 86 8093 52 0 16903 315 df 0 4254 1 000 5 LogL 87 2249 S2 0 16594 315 df 0 5521 1 000 6 LogL 87 2398 S2 0 16532 315 df 0 5854 1 000 7 LogL 87 2398 S2 0 16530 315 df 0 5867 1 000 8 LogL 87 2398 S2 0 16530 315 df 0 5867 1 000 Final parameter values 0 58667 1 0000 Results from analysis of weight Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients dam 22 56 1 27762 11 5 1 0 Residual Variance 292 44 0 165300 0 0 1 0 Model_Term Gamma Sigma Sigma SE C dam 21 27 0 586674 0 969770E 01 2 02 QP 277 16 3 Unbalanced nested design Rats Variance 322 315 1 00000 0 165300 12 08 0 P Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P con b 7 mu 1 32 0 9049 48 1099 20 lt 001 3 littersize 1 21 5 27 99 46 25 B lt 001 1 dose 2 23 9 12 15 11 51 A lt 001 2 sex 1 299 8 57 96 57 96 A lt 001 8 dose sex 2 302 1 0 40 0 40 B 0 673 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives 4 dam 27 effects fitted SLOPES FOR LOG ABS RES on LOG PV for Section 1 ar 3 possible outliers see res file The iterative sequence has converged and the variance component parameter for dam hasn t changed for the last three iterations The incremental Wald F stat
164. 74 OP Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 8 mu 1 6 0 245 14 138 14 lt 001 4 variety 2 10 0 1 49 1 49 A 0 272 229 14 4 Other ASReml output files 7 linNitr 1 45 0 110 32 110 32 a lt 001 2 nitrogen 2 45 0 1 37 1 37 A 0 265 9 variety linNitr 2 45 0 0 48 0 48 b 0 625 10 variety nitrogen 4 45 0 O 22 0 22 B 0 928 The analysis shows that there is a significant linear response to nitrogen level but the lack of fit term and the interactions with variety are not significant In this example the conditional Wald F statistic is the same as the incremental one because the contrast must appear before the lack of fit and the main effect before the interaction and otherwise it is a balanced analysis The first part of the aov file the FMAP table only appears if the job is run in DEBUG mode There is a line for each model term showing the number of non singular effects in the terms before the current term is absorbed For example variety nitrogen initially has 12 degrees of freedom non singular effects mu takes 1 variety then takes 2 linNitr takes 1 nitrogen takes 2 variety linNitr takes 2 and there are four degrees of freedom left This information is used to make sure that the conditional Wald F statistic does not contradict marginality principles The next table indicates the details of the conditional Wald F statistic The conditional Wald F statistic is based in the reduction in Sums of Squares
165. 7551 4 70711 0 4 56648 8 86687 0 0 313123 4 10031 4 76546 8 76708 14 4 10 The vvp file The vvp file contains the inverse of the average information matrix on the components scale The file is formatted for reading back under the control of the pin file described in Chapter 13 The matrix is lower triangular row wise in the order the parameters are printed in the asr file This is nin89a vvp with the parameter estimates in the order error variance spatial row correlation spatial column correlation 241 14 4 Other ASReml output files Variance of Variance components 3 51 0852 0 217089 0 318058E 02 0 677748E 01 0 201181E 02 0 649355E 02 242 14 5 ASReml output objects and where to find them 14 5 ASReml output objects and where to find them Table 14 2 presents a list of objects produced with each ASReml run and where to find them in the output files Table 14 2 ASReml output objects and where to find them output object found in comment Wald F statistics asr file This table contains Wald F statistics for each term in the fixed table part of the model These provide for an incremental or option ally a conditional test of significance see Section 6 11 data summary asr file includes the number of records read and retained for analysis ass file the minimum mean maximum number of zeros number of missing values per data field factor variate field distinction An extended report of the data is
166. 77122E 03 0 472300E 01 0 326718E 01 0 126746E 01 0 00000 0 661114E 02 1 46479 1 51911 0 110770 3 55275 1 53980 2 55497 0 310141E 01 0 450851E 01 0 191030E 01 0 F 21026E 0 1 0 794020 0 417001E 01 0 897161 0 584748E 02 1 53000 0 163359E 01 0 422487 0 00000 528891E 02 181736 208097 218051E 01 416013 466606 811102 0 730000 0 609258E 01 0 786132E 02 0 220000 1 55000 0 760000 0 391773 O oD CD Oo o 16 11 Multivariate animal genetics data Sheep 90 1 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 Notice The parameter estimates are followed by Maternal Maternal Maternal Maternal Maternal Maternal residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG residWYG WWTh2 YWTh2 GFWh2 FDMh2 FATh2 GenCor GenCor GenCor GenCor GenCor GenCor GenCor GenCor GenCor GenCor MatCor MatCor MatCor w NANNA AF F WWD 3 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 T2 73 74 b2 mo po HS 02 b2 Fo 02 b2 F b2 me KH Direct Direct Direct Direct Direct Trait Trait Trait Trait Trait Trait Trait Trait Trait Trait Mater Mater Mater 1 5643 0 37542 1 5478 0 43280 0 75138 0 75145 0 13421 0 37 70E 01 0 16539 0 54770E 01 0 38619E 02 0 70075E 02 15 172 0 27 671 11 107 031755
167. 8 2409E 01 0 9948 0 2532 0 2358 0 3409 9 1921 0 000 1 0000 0 000 0 1016 0 4489 0 4567 0 5268 0 8428 0 000 0 000 1 0000 Note that the XFA matrix associated with tag has 8 rows and columns the first 5 relate to the five traits and the last three relate to the three factors 344 Bibliography Breslow N E 2003 Whither PQL Technical Report 192 UW Biostatistics Working Paper Series University of Washington URL http www bepress com uwbiostat paper192 Breslow N E and Clayton D G 1993 Approximate inference in generalized linear mixed models Journal of the American Statistical Association 88 9 25 Breslow N E and Lin X 1995 Bias correction in generalised linear mixed models with a single component of dispersion Biometrika 82 81 91 Cox D R and Hinkley D V 1974 Theoretical Statistics Chapman and Hall Cox D R and Snell E J 1981 Applied Statistics Principals and Examples Chapman and Hall Cressie N A C 1991 Statistics for spatial data John Wiley and Sons Cullis B R and Gleeson A C 1991 Spatial analysis of field experiments an extension to two dimensions Biometrics 47 1449 1460 Cullis B R Gleeson A C Lill W J Fisher J A and Read B J 1989 A new procedure for the analysis of early generation variety trials Applied Statistics 38 361 375 Cullis B R Gogel B J Verbyla A P and Thompson R 1998 Spatial analy
168. 8 1 44 1 44 B 0 234 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using empirical derivatives 129 mv_estimates 9 effects fitted 9 idsize 92 effects fitted 7 are zero 115 expt idsize 828 effects fitted 672 are zero 225 14 3 Key output files 127 at expt 6 type idsize meth 9 effects fitted 2199 singular 128 at expt 7 type idsize meth 10 effects fitted 2198 singular LINE REGRESSION RESIDUAL ADJUSTED FACTORS INCLUDED NO DF SUMSQUARES DF MEANSQU R SQUARED R SQUARED 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 1 3 0 1113D 02 452 0 2460 0 09098 0 08495 111000060000 000000 Ak kkk 2 3 0 1180D 02 452 0 2445 0 09648 0 09049 1 0110000000000000 Ak 2K 3 3 0 1843D 01 452 0 2666 0 01507 0 00853 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 3 0 1095D 02 452 0 2464 0 08957 0 08353 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 5 3 0 1271D 02 452 0 2425 0 10390 0 09795 1 0 0 1 40 0 6600 60 0 0 0 6 6 2K 2K 6 3 0 9291D 01 452 0 2501 0 07594 0 06981 0 10 1 1 0 0 0 0 0 0 0 0 0 0 0 0 7 3 0 9362D 01 452 0 2499 0 07652 0 07039 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 O 8 3 0 1357D402 452 0 2406 0 11091 0 10501 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 O Ak 2K 9 3 0 9404D 01 452 0 2498 0 07687 0 07074 0 1 10 1 0 0 0 0 0 0 0 0 0 0 0 0 10 3 0 1266D 02 452 0 2426 0 10350 0 09755 1 1 0 0 4 060 000 0 0 0 0 0 0 0 11 3 0 1261D 02 452 0 2427 0 10313 0 09717 1 0 0 0 1 10 0 6 6 06 6 6 0 6 6 6 12 3 0 9672D 01 452 0 2492 0 07906 0 07295 0 10
169. 8 27 A lt 001 Part 4 shows what happens if we wrongly drop dam from this model Even if a random term is not significant it should not be dropped from the model if it represents a strata of the design as in this case 278 16 4 Source of variability in unbalanced data Volts Rats example Residuals vs Fitted values Residuals Y 3 02 1 22 Fitted values X 5 04 7 63 8 o o o o o o 8 Cee o ge 8 he o o po 208 amp a 6 8 o o oo o s o 8 D Ore ae o 880 Foo o ooo go o 8 go 8 9 o 82 Bos o i i a a opoe oF E EN go 50 8 Sh amp go o 8 e 6 9 8 9 5 8 ego 8 Fo R Sa oo 000 8 o o o g bd o o j o o o o o o oo o o Figure 16 1 Residual plot for the rat data Model_Term Gamma Sigma Sigma SE C Variance 322 317 1 00000 0 253182 12 59 OP Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 7 mu 1 317 0 47077 31 3309 42 lt 001 3 littersize il 317 0 68 48 146 50 A lt 001 1 dose 2 317 0 60 99 58 43 A lt 001 2 sex 317 0 24 52 24 52 A lt 001 16 4 Source of variability in unbalanced data Volts In this example we illustrate an analysis of unbalanced data in which the main aim is to determine the sources of variation rather than assess the significance of imposed treatments The data are taken from Cox and Snell 1981 and involve an experiment to examine the variability in the production of car voltage regulators Standard production of regulators inv
170. 86 310 Residual CORRelat 5 0 558191 0 558191 000 000 000 000 000 000 1 0000 erererrrere Sigma SE C 2 11 0 P 4 90 o P 0 5000 0 5178 0 5400 0 5580 0 5582 0 55819 Sigma SE C 3 65 QP 4 28 O U A more realistic model for repeated measures data would allow the correlations to decrease as the lag increases such as occurs with the first order autoregressive model However since the heights are not measured at equally spaced time points we use the EXP model The correlation function is given by plu p where u is the time lag is weeks The coding for this is y1 y3 y5 y7 y10 Trait tmt Tr tmt 12 0 One error structure in two dimensions 14 Outer dimension 14 plants Tr Q EXP 5 136710 Time coordinates 284 16 5 Balanced repeated measures Height A portion of the output is LogL 183 734 S2 435 58 60 df 1 000 0 9500 LogL 183 255 82 370 40 60 df 1 000 0 9388 LogL 183 010 S2 321 50 60 df 1 000 0 9260 LogL 182 980 S2 298 84 60 df 1 000 0 9179 LogL 182 979 82 302 02 60 df 1 000 0 9192 Final parameter values 1 0000 UO 91897 Model_Term Sigma Sigma Sigma SE C Variance 70 60 1 00000 302 021 211 OP Residual POW EXP 5 0 918971 0 918971 29 53 OU When fitting power models be careful to ensure the scale of the defining variate here time does not result in an estimate of too close to 1 For example use of days in this example would result in an estimate for of about 993 Residual
171. 90 E 69 4817 13 6534 sqrt yc YRK3 13 3057 0 9549 E 177 0428 25 4106 sqrt ye YRK3 8 1133 0 8190 E 65 8264 13 2894 SED Overall Standard Error of Difference 1 219 Table 16 10 Estimated variance parameters from bivariate analysis of bloodworm data control treated source variance variance covariance us trait variety 3 84 1 96 2 33 us trait run 1 71 2 54 0 32 us trait pair 2 14 2 35 0 99 307 16 8 Paired Case Control study Rice exposed BLUP ang onuos Figure 16 9 BLUPs for treated for each variety plotted against BLUPs for control 16 8 3 Interpretation of results Recall that the researcher is interested in varietal tolerance to bloodworms This could be defined in various ways One option is to consider the regression implicit in the variance structure for the trait by variety effects The variance structure can arise from a regression of treated variety effects on control effects namely Uy Pty where the slope 6 0 0 Tolerance can be defined in terms of the deviations from regression Varieties with large positive deviations have greatest tolerance to bloodworms Note that this is similar to the researcher s original intentions except that the regression has been conducted at the genotypic rather than the phenotypic level In Figure 16 9 the BLUPs for treated have been plotted against the BLUPs for control for each variety and the fitted regression line slope 0 61 has b
172. 980 BRxP 1981 0 0 0180 0 0070 0 0430 0 0124 0 0748 0 0323 0 0281 0 0083 1 0 0151 0 0063 0 0373 0 0110 0 0592 0 0257 0 0401 0 0103 ASReml has an Analysis of Deviance option which we now demonstrate In a mixed model the variance components will change depending on which fixed terms are in the model This will invalidate the Analysis of Deviance unless the variance components are fixed at the full model solution So fitting the model line Rot bin TOT Total AODEV mu SEX GRP SEX GRP r SIRE 2632 GF produces the Analysis of Deviance Analysis of Deviance Table for Rot Source of Variation df Deviance Derived F SEX 1 0 02 0 021 GRP 3 4 35 1 833 SEX GRP B 1 16 0 487 Deviance from GLM fit 48 37 96 Variance heterogeneity factor Deviance DF 0 79 The Deviance is the deviance calculated from the binomial part of the log likelihood This is distinct from the log likelihood obtained by the REML algorithm which pertains to the working variable Since the working variable changes with the model fitted the LogL values are not comparable between models The heterogeneity factor is the Deviance df and gives some indication as to how well the discrete distribution fits the data A value greater than 1 suggests the data is over dispersed that is the data values are more variable than expected under the chosen distribution There is also a DISPERSION d qualifier If d is supplied it serves as a scaling factor for 322 1
173. A BA CBA OCBA site gen 2 G header line this example defines a structure for the genotype by site site 0 US 3 0A0AAO GPUPUUP interaction effects in a MET in which the genotypes are oy ar ee anes eee independent random effects within sites but are corre gen lated across sites with equal covariance 140 7 9 Constraining variance parameters Examples of constraining variance parameters in ASReml ASReml code action site 0 FA2 G4PZ3P4P 00000000VVVV a 2 factor Factor Analytic model for 4 sites with equal 49 initial values for 1st factor variance is specified using this syntax The first loading 0 3 1 initial values for 2nd factor in the second factor is constrained equal to 0 for iden first fixed at 0 tifiability P places restrictions on the magnitude of the 4 2 init values for site variances loadings and the variances to be positive xfa site 2 O XFA2 VVVVO 4P4PZ3P a 2 factor Factor analytic model in which the specific 4 2 sf initial specific variances variances are all equal 41 2 initial loadings for 1st factor 0 3 3 initial loadings for 2nd factor 7 9 Constraining variance parameters 7 9 1 Parameter constraints within a variance model Equality of parameters in a variance model can be specified using the s qualifier where s is a string of letters and or zeros see Table 7 4 Positions in the string correspond to the parameters of the variance model e all parameters with the same le
174. A R and Thompson R 2004 Predic tion in linear mixed models Australian and New Zealand Journal of Statistics 46 325 347 Wolfinger R D 1996 Heterogeneous variance covariance structures for repeated measures Journal of Agricultural Biological and Environmental Statistics 1 362 389 Wolfinger R and O Connell M 1993 Generalized linear mixed models A pseudo likelihood approach Journal of Statistical Computation and Simulation 48 233 243 Yates F 1935 Complex experiments Journal of the Royal Statistical Society Series B 2 181 247 348 Index ABORTASR NOW 68 FINALASR NOW 68 Access 42 accuracy genetic BLUP 226 advanced processing arguments 203 AI algorithm 14 AIC 17 ainverse bin 162 Akaike Information Criteria i7 aliassing 106 Analysis of Deviance 102 Analysis of Variance 20 Wald F statistics 107 animal breeding data 1 arguments 4 asrdata bin 81 ASReml symbols 85 41 41 41 42 I 88 1 88 88 88 88 88 88 25 88 Associated Factors 94 autoregressive 114 Average Information 1 balanced repeated measures 282 Bayesian Information Criteria BIC 17 binary files 43 Binomial divisor 102 BLUE 15 BLUP 15 16 case 86 combining variance models 12 command file 30 genetic analysis 159 multivariate 153 Command line option A ASK 199 B BRIEF 199 C CONTINUE 201 D DEBUG 200 F FINAL 201 Gg graphics 200
175. AC versions This option is usually set on the command line using the option letter N see Section 11 3 on graphics The text version of the graphics is still written to the res file is a mechanism for specifying the particular points to be predicted for covariates modelled using fac v leg v k spl v k and pol v k The points are specified here so that they can be included in the ap propriate design matrices v is the name of a data field p is the list of values at which prediction is required See GKRIGE for special conditions pertaining to fac x y prediction is used to read predict_points for several variables from a file f vlist is the names of the variables having values defined If the file contains unwanted fields put the pseudo variate label skip in the appropriate position in vlist to ignore them The file should only have numeric values predict_points cannot be specified for design factors is used with SECTION and COLUMNFACTOR to instruct ASReml to setup the R structures for multi environment spatial analysis and to insert extra data records to complete the grid of plots defined by the RowFactor and the ColumnFactor for each Section so that a two dimensional error structure can be defined vis the name of a factor or variate containing row numbers 1 n where n is the number of rows on which the data is to be sorted See SECTION for more detail 72 5 8 Job control qualifiers Table 5 4 List of occasiona
176. AY qualifier Table 5 4 By default the variogram and field plan are displayed The sample variogram is a plot of the semi variances of differences of residuals at particular distances The 0 0 position is zero because the difference is identically zero ASReml displays the plot for distances 0 1 2 8 9 10 11 14 15 20 The plot of residuals in field plan order Figure 14 3 contains in its top and right margins a diamond showing the minimum mean and maximum residual for that row or column Note that a gap identifies where the missing values occur 237 14 4 Other ASReml output files The plot of marginal means of residuals shows residuals for each row column as well as the trend in their means Fie IIA OPIS iiid phr Jul ZS 42 2 41 18 Y ang Figure 14 3 Plot of residuals in field plan order Finally we present a small example of the display produced when an XFA structure is fitted The output from a small example with 9 environments and 2 factors is DISPLAY of variance partitioning for XFA structure in xfa Env 2 Geno Lyl topo pon pon pod TotalVar fexpl PsiVar Loadings i i 0 3339 79 7 0 0679 0 5147 0 0335 2 12 0 1666 100 0 0 0000 0 4003 0 0797 3 1 2 0 2475 67 8 0 0798 0 3805 0 1514 4 4 2 0 1475 100 0 0 0000 0 3625 0 1269 5 1 2 0 4496 100 0 0 0000 0 6104 0 278 6 2 0 1210 100 0 0 0000 0 2287 0 2622 T 1 2 0 4106 54 4 0 1872 0 4152 0 226 8 1 2 0 0901 100
177. An image analysis technique for assessing resistance in rice cultivars to root feeding chironomid midge larvae diptera Chironomidae Field Crops Research 66 25 26 Stroup W W Baenziger P S and Mulitze D K 1994 Removing spatial variation from wheat yield trials a comparison of methods Crop Sci 86 62 66 Thompson R 1980 Maximum likelihood estimation of variance components Math Op erationsforsch Statistics Series Statistics 11 545 561 Thompson R Cullis B Smith A and Gilmour A 2003 A sparse implementation of the average information algorithm for factor analytic and reduced rank variance models Australian and New Zealand Journal of Statistics 45 445 459 Verbyla A P 1990 A conditional derivation of residual maximum likelihood Australian Journal of Statistics 32 227 230 Verbyla A P Cullis B R Kenward M G and Welham S J 1999 The analysis of designed experiments and longitudinal data by using smoothing splines with discussion Applied Statistics 48 269 311 Waddington D Welham S J Gilmour A R and Thompson R 1994 Comparisons of some glmm estimators for a simple binomial model Genstat Newsletter 30 13 24 Welham S J 2005 Glmm fits a generalized linear mixed model in R Payne and P Lane eds GenStat Reference Manual 3 Procedure Library PL17 VSN International Hemel Hempstead UK pp 260 265 Welham S J Cullis B R Gogel B J Gilmour
178. C is the dense portion of C71 This is the first 20 rows of nin89a vrb Note that the first element is the estimated error variance that is 48 6802 see the variance component estimates in the asr output 0 486802E 02 0 000000E 00 0 000000E 00 0 298660E 01 0 000000E 00 0 807551E 01 0 470711E 01 0 000000E 00 0 456648E 01 0 886687E 01 0 313123E 00 0 000000E 00 0 410031E 01 0 476546E 01 0 876708E 01 0 295404E 01 0 000000E 00 0 343331E 01 0 389620E 01 0 416124E 01 0 743616E 01 0 163302E 01 0 000000E 00 0 377176E 01 0 428109E 01 0 472519E 01 0 402696E 01 0 837281E 01 0 129013E 01 0 000000E 00 0 330076E 01 0 347471E 01 0 357605E 01 0 316915E 01 0 412130E 01 0 768275E 01 0 310018E 00 0 000000E 00 0 376637E 01 0 419780E 01 0 395693E 01 0 383429E 01 0 458492E 01 0 37 8585E 01 0 985202E 01 0 226478E 01 0 000000E 00 0 379286E 01 0 442457E 01 0 439485E 01 0 402503E 01 0 440539E 01 0 362391E 01 0 502071E 01 0 901191E 01 0 508553E 01 0 000000E 00 0 393626E 01 0 430512E 01 0 423753E 01 0 428826E 01 0 417864E 01 0 363341E 01 0 444776E 01 0 527289E 01 0 855241E 01 0 243687E 01 0 000000E 00 0 351386E 01 0 369983E 01 0 384055E 01 0 330171E 01 0 362019E 01 0 352370E 01 0 359516E 01 0 392097E 01 0 406762E 01 0 801579E 01 0 475935E 01 0 000000E 00 The first 5 rows of the lower triangular matrix in this case are 48 6802 0 0 2 98660 0 8 0
179. D 125 RENAME M125 Ir M35 M75 M125 The aim here is to generate the 3 MBF statements required to extract markers 35 75 and 125 from the marker file markers csv The names of model terms must begin with a letter hence the marker names are the letter M followed by the position number Alternatively RFIELDlettersinteger is interpreted as IRFIELD integer so the FOR statement can be written even more concisely as mbf Geno 1 markers csv key 1 RFIELD S RENAME M S without the need to assign Markern Now to add another marker to the model one can just add the marker integer to the ASSIGN statement Restriction list and command are both limited to 200 characters One form of the IF statement is IF string1 string2 ASSIGN M1 brt DamAge which makes the ASSIGN statement active if string1 is the same as string2 Note that there need to be spaces before and after to avoid confusion with the strings This has been used when performing a large number of bivariate analyses with trait specific fixed effects being fitted So IF 1 wwt ASSIGN M1 brt DamAge IIF 1 ywt ASSIGN M1 brt IF 1 fwt ASSIGN M1 DamAge LIF 2 wwt ASSIGN M2 brt DamAge IIF 2 ywt ASSIGN M2 brt IF 2 fwt ASSIGN M2 DamAge 1 2 Trait at Trait 1 M1 at Trait 2 M2 207 11 4 Advanced processing arguments High level qualifiers qualifier action IPATH pathlist The PATH or PART control statement may list multiple path
180. DF F_inc Prob 7 mu 1 41 7 6248 65 lt 001 3 weed 1 491 2 85 84 lt 001 The change in REML log likelihood is significant x 12 46 p lt 001 with the inclusion of the autoregressive parameter for columns Figure 16 6 presents the sample variogram of the residuals for the AR1xAR1 model There is an indication that a linear drift from column 1 to column 10 is present We include a linear regression coefficient pol column 1 in the model to account for this Note we use the 1 option in the pol term to exclude the overall constant in the regression as it is already fitted The linear regression of column number on yield is significant t 2 96 The sample variogram Figure 16 7 is more satisfactory though interpretation of variograms is often difficult particularly for unreplicated trials This is an issue for further research The abbreviated output for this model and the final model in which a nugget effect has been included is AR1xAR1 pol column 1 1 LogL 4270 99 S2 0 12730E 06 665 df 2 LogL 4258 95 o2 0 11961E 06 665 df 3 LogL 4245 27 S2 0 10545E 06 665 df 4 LogL 4229 50 S2 78387 665 df 5 LogL 4226 02 S2 75375 665 df 6 LogL 4225 64 52 77373 665 df 297 16 7 Unreplicated early generation variety trial Wheat Tullibigeal trial atts 26 Aug 2002 19 03 11 Outer displacement her displacement Figure 16 6 Sample variogram of the residuals from the AR1 x AR1 model for the Tullibigeal data
181. E 84 ISCREEN 81 ISECTION 73 ISED 185 ISEED 56 ISELECT 62 ISELF 164 ISEQ 57 ISETN 57 ISETU 57 ISET 57 ISIN 55 ISKIP 62 71 164 212 ISLNFORM 81 ISLOW 84 ISMX 81 ISORT 164 213 ISPARSE 71 ISPATIAL 82 ISPECIALCHAR 41 ISPLINE 73 ISQRT link 101 ISTEP 74 SUBGROUP 74 SUBSECTION 138 SUBSET 74 ISUB 57 INDEX ISUM 68 ITABFORM 82 ITARGET 51 57 ITHRESHOLD GLM 101 ITOLERANCE 84 ITOTAL 101 102 ITWOSTAGEWEIGHTS 186 ITWOWAY 82 ITXTFORM 82 UNIFORM 57 IUSE 138 143 IVCC 82 IVGSECTORS 82 IVPV 186 IVRB 84 IV 58 IWMF 74 IWORKSPACE 198 IWORK residuals 102 IXLINK 164 IX 68 IYHTFORM 82 IYSS 77 82 319 IYVAR 198 IY 68 ICENTRE 173 EXCEPT 181 IGSCALE 173 INOID 172 INONAMES 172 ONLYUSE 181 IPEV 173 IPSD 173 IRANGE 173 ISMODE 173 ISM 92 ITDIFF 185 qualifiers datafile line 62 genetic 159 job control 65 variance model 137 qualifier NSD 165 qualifier PRECISION 165 qualifier PSD 165 R structure 109 definition 120 definition lines 118 RAM 169 random effects 5 correlated 16 terms multivariate 154 random regressions 139 random terms 86 92 RCB 30 analysis 110 design 26 reading the data 31 46 Reduced animal model 169 relationships variance structure parameters 144 REML 1 12 16 REMLRT 16 repeated measures 1 282 reserved terms 88 Trait 88 98 a t r 95
182. E 01 1 000 5 LogL 20 8996 S2 50 213 5 df 0 7866E 01 1 000 Final parameter values O 78798E 01 1 0000 Degrees of Freedom and Stratum Variances 1 49 97 4813 12 0 1 0 3 51 50 1888 0 0 1 0 Model_Term Gamma Sigma Sigma SE C spl age 7 5 5 0 787457E 01 3 95215 0 40 OP Variance bd 5 1 00000 50 1888 Losa OP Wald F statistics Source of Variation NumDF DenDF F inc Prob 7 mu 1 3 5 1382 80 lt 001 3 age 1 oa 217 60 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives Estimate Standard Error T value T prey 3 age 1 0 814772E 01 0 552336E 02 14 75 7 mu il 24 4378 5 75429 4 25 6 spl age 7 5 effects fitted Finished 19 Aug 2005 10 08 11 980 LogL Converged The REML estimate of the smoothing constant indicates that there is some nonlinearity The fitted cubic smoothing spline is presented in Figure 16 13 The fitted values were obtained from the pvs file The four points below the line were the spring measurements We now consider the analysis of the full dataset Following Verbyla et al 1999 we con sider the analysis of variance decomposition see Table 16 11 which models the overall and individual curves An overall spline is fitted as well as tree deviation splines We note however that the intercept and slope for the tree deviation splines are assumed to be random effects This is consistent with Verbyla et al 1999 In this sense the tree deviati
183. ED AR1xAR1 700 32 3 13 04 59 0 AR1xAR1 units 696 82 4 10 22 60 5 IB 707 79 4 8 84 62 0 The predict statement included the qualifier TWOSTAGEWEIGHTS This generates an extra table in the pvs file which we now display for each model Predicted values with Effective Replication assuming Variance 38754 26 Heron 1 1257 98 22 1504 Heron 2 1501 45 20 6831 Heron 3 1404 99 22 5286 Heron 4 1412 57 22s T023 294 16 7 Unreplicated early generation variety trial Wheat Heron 5 1514 48 21 1830 Heron 25 1502 02 26 0990 Predicted values with Effective Replication assuming Variance 45796 58 Heron 1 1245 58 23 8842 Heron 2 1516 24 22 4423 Heron 3 1403 99 24 1931 Heron 4 1404 92 24 0811 Heron 5 1471 61 23 2995 Heron 25 1573 89 26 0505 Predicted values with Effective Replication assuming Variance 8061 808 Heron 1 1283 59 4 03145 Heron 2 1549 01 4 03145 Heron 3 1420 93 4 03145 Heron 4 1451 86 4 03145 Heron 5 1938 27 4 03145 Heron 25 1630 63 4 03145 The value of 4 for the IB analysis is clearly reasonable given there are 6 actual replicates but this analysis has used up 48 degrees of freedom for the rowblk and colblk effects The precision from the spatial analyses are similar 45796 58 23 8842 1917 442 c f 8061 808 4 03145 1999 729 but slightly lower reflecting the gain in accuracy from the spatial analysis For further reading see Smith et al 2001 2005 16 7 Unreplicated early generatio
184. EYENNE NE87522 REDLAND NE86501 NE87513 NE86482 BRULE SIOUXLAND LANCOTA HOMESTEAD juauniadxa pjay NIN t9siny 938358134 eyseaq N ZE 3 3 The ASReml data file 3 3 The ASReml data file The standard format of an ASReml data file is to have the data arranged in space TAB or comma separated columns fields with a line for each sampling unit The columns contain covariates factors response variates traits and weight variables in any convenient order This is the first 30 lines of the file nin89 asd containing the data for the NIN variety trial The data are in field order rows within columns and an optional heading first line of the file has been included to document the file In this case there are 11 space separated data fields variety column and the complete file has 224 data lines one for each variety in each replicate variety id pid raw repl nloc yield lat long row column optional field labels LANCER 1 1101 585 1 4 29 25 4 3 19 2 16 1 data for sampling unit 1 BRULE 2 1102 631 1 4 31 55 4 3 20 4 17 1 data for sampling unit 2 REDLAND 3 1103 791 1 4 35 05 4 3 21 6 18 1 CODY 4 1104 602 1 4 30 1 4 3 22 8 19 ARAPAHOE 5 1105 661 1 4 33 05 4 3 24 20 NE83404 6 1106 605 1 4 30 25 4 3 2 21 1 NE83406 7 1107 704 1 4 35 2 4 3 26 4 22 1 NE83407 8 1108 388 1 4 19 4 8 6 1 2 1 2 CENTURA 9 1109 487 1 4 24 35 8 6 2 4 2 2 1 2 i Se w w 2 Gs SCOUT66 10 1110 511 1 4 25 55 8 6 3 6 3 2 COLT 11 1111 502 1 4 25 1 8 6 4 8 4
185. Euclidean distance Setting A 1 provides the cityblock metric which together with y 0 5 models a separable AR1xAR1 process Cityblock metric may be appropriate when the dominant spatial processes are aligned with rows columns as occurs in field experiments Geometric anisotropy is discussed in most geostatistical books Webster and Oliver 2001 Diggle et al 2003 but rarely are the anisotropy angle or ratio estimated from the data Similarly the smoothness parameter v is often set a priori Kammann and Wand 2003 Diggle et al 2003 However Stein 1999 and Haskard 2006 demonstrate that y can be reliably estimated even for modest sized data sets subject to caveats regarding the sampling design The syntax for the Mat rn class in ASReml is given by MATk where k is the number of 130 7 5 Variance model description parameters to be specified the remaining parameters take their default values Use the G qualifier to control whether a specified parameter is estimated or fixed The order of the parameters in ASReml with their defaults is v 0 5 6 1 a 0 A 2 For example if we wish to fit a Mat rn model with only estimated and the other parameters set at their defaults then we use MAT1 MAT2 allows v to be estimated or fixed at some other value for example MAT2 2 1 GPF The parameters and y are highly correlated so it may be better to manually cover a grid of v values We note that there is non uniqueness in
186. LA R 1 A B R 1 A where the R operator denotes the residual sums of squares due to a model containing its argument and R denotes the difference between the residual sums of squares for any pair of nested models Thus R B 1 A represents the difference between the reduction in sums of squares between the so called maximal model yv1 A B and y 1l A Implicit in these calculations is that e we only compute Wald statistics for estimable functions Searle 1971 page 408 e all variance parameters are held fixed at the current REML estimates from the maximal model In this example it is clear that the incremental Wald statistics may not produce the desired test for the main effect of A as in many cases we would like to produce a Wald statistic for A based on R A 1 B R 1 A B R 1 B 20 2 5 Inference Fixed effects The issue is further complicated when we invoke marginality considerations The issue of marginality between terms in a linear mixed model has been discussed in much detail by Nelder 1977 In this paper Nelder defines marginality for terms in a factorial linear model with qualitative factors but later Nelder 1994 extended this concept to functional marginality for terms involving quantitative covariates and for mixed terms which involve an interaction between quantitative covariates and qualitative factors Referring to our simple illustrative example above with a full factoria
187. LUDE statements to specify which experiments were being combined If the subfiles have CSV format they should all have it and the CSV file should be declared on the primary datafile line This option is not available in combination with MERGE 5 8 Job control qualifiers The following tables list the job control qualifiers These change or control various aspects of the analysis Job control qualifiers may be placed on the datafile line and following lines They may also be defined using an environment variable called ASREML_QUAL The environment variable is processed immediately after the datafile line is processed All qual ifier settings are reported in the asr file Use the Index to check for examples or further discussion of these qualifiers Important Many of these are only required in very special circumstances and new users 65 5 8 Job control qualifiers should not attempt to understand all of them You do need to understand that all general qualifiers are specified here Many of these qualifiers are referenced in other chapters where their purpose will be more evident Table 5 3 List of commonly used job control qualifiers qualifier action ICONTINUE f New R4 These qualifiers are used to restart resume iterations from the IMSV f point reached in a previous run The qualifier CONTINUE f can alter ITSV f nately be set from the command line using the option letter C f see Section 11 3 on command line op
188. MMs PQL has been reported to perform adequately e g Breslow 2003 McCulloch and Searle 2001 also discuss the use of PQL for GLMMs The performance of PQL in other respects such as for hypothesis testing has received much less attention and most studies into PQL have examined only relatively simple GLMMs Anecdotal evidence suggests that this technique may give misleading results in certain situ ations Therefore we cannot recommend the use of this technique for general use and it is included in the current version of ASReml for advanced users If this technique is used we recommend the use of cross validatory assessment such as applying PQL to simulated data from the same design Millar and Willis 1999 The standard GLM Analysis of Deviance AOD should not be used when there are random terms in the model as the variance components are reestimated for each submodel 104 6 9 Missing values 6 9 Missing values 6 9 1 Missing values in the response It is sometimes computationally convenient to estimate NIN Alliance Trial 1989 missing values for example in spatial analysis of regular variety arrays see example 3a in Section 7 3 Missing values are estimated if the model term mv is included in the model row 22 Formally mv creates a factor with a covariate for each column 11 missing value The covariates are coded 0 except in the nin89 asd lskip 1 a ield iety record where the particular missing value occur
189. Model specification TERM LEVELS GAMMAS variety 56 mu 1 12 factors defined max 500 255 15 4 An example O variance parameters max1500 2 special structures Final parameter values 2 0 Last line read was IR Repl 0000 Finished 11 Apr 2008 16 21 43 968 Error in variance header line IR Repl Inserting a comma on the end of the first line of the model to give yield mu variety Ir Repl solves that problem but produces the error message Error reading model terms because Repl should have been spelt repl Portion of the output is displayed Since the model line is parsed before the data is read this run failed before reading the data Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 1 is active Reading nin asd FREE FORMAT skipping 1 lines Model term Repl is not valid recognised Fault Error reading model terms Last line read was Repl Currently defined structures COLS and LEVELS 1 variety 2 2 id 3 pid 4 raw 5 Pep PRP PP GBP PP FP F FE DD So CS O OG aor WN PO ao Oo a Oo SD 1 1 1 4 6 nloc 1 Finished 28 Jul 2005 10 06 49 173 Error reading model terms 256 15 4 An example 6 Misspelt factor name and 7 Wrong levels declaration in the G structure definition lines The next fault ASReml detects is Ain alliance ial G structure header Term not found E nin89 asd skip 1 indicating that there is something wrong in yield mu variety the G
190. R structures but there is one G structure 1 The next two lines define the G struc ture The first line a G structure header line links the structure that follows to a term in the linear model rep1 and indicates that it involves one variance model 1 a 2 would mean that the structure was the direct product of two variance models The second line tells ASReml that the variance model for replicates is IDV of order 4 o 1 The 0 1 is a starting value for y 02 07 a starting value must be specified Finally the second element 0 on the last line of the file indicates that the effects are in standard order There is almost always a O no sorting in this position for G structures The following points should be noted NIN Alliance Trial 1989 variety A id pid raw repl 4 row 22 column 11 nin89 asd skip 1 yield mu variety r repl 001 repl i 4 0 IDV 0 1 e the 4 on the final line could have been written as repl to give repl 0 IDV 0 1 This would tell ASReml that the order or dimension of the IDV variance model is equal to the number of levels in repl 4 in this case when specifying G structures the user should ensure that one scale parameter is present ASReml does not automatically include and estimate a scale parameter for a G structure when the explicit G structure does not include one For this reason the model supplied when the G structure involves just one variance model must not be
191. R1 AR1 If mv 120 11 column AR1 0 3 22 row AR1 0 3 yield mu variety units IDV column row AR1 AR1 lr units f mv 1 20 11 column AR1 0 3 22 row AR1 0 3 yield mu variety repl IDV column row AR1 AR1 lr repl f mv 121 11 column AR1 0 3 22 row AR1 0 3 repl 1 4 0 IDV 0 1 yield mu variety column row AR1 ARIV error ID lr column row 001 column row 2 column O AR1 5 row O AR1V 0 5 0 1 116 7 4 Variance structures 5 Two dimensional separable autoregressive spatial model defined as a G structure This model is equivalent to 3c but with the Win Alliance Trial 1989 spatial model defined as a G structure rather variety A than an R structure As discussed in 2b one id and only one of the component models must be a variance model and all others must be row 22 correlation models column 11 nin89 asd skip 1 i yield mu variety The V in AR1V converts the correlation model 1 row column AR1 to a variance model and the second initial 0 0 1 value 0 1 is for the variance ratio That row column 2 is V 02 Yodel Pc 6 Erlpr La row 0 ARIV O ete il column O AR1 0 5 Try starting this model with initial correla tions of 0 3 it fails to converge Use of row column as a G structure is a useful approach for analysing incomplete spatial arrays it will often run faster for large trials but requires more memory Note that we have used the original version of the
192. RAGE qualifier to set specific unequal weights for each level of a factor However sometimes the weights need to be defined with respect to two or more factors The simplest case is when there are missing cells and weighting is equal for those cells in a multiway table that are present achieved by using the PRESENT qualifier This is further generalized by allowing the user to supply the weights to be used by the PRESENT machinery via the PRWTS qualifier The user specifies the factors in the table of weights with the PRESENT statement and then gives the table of weights using the PRWTS qualifier There may only be one PRESENT qualifier on the predict line when PRWTS is specified The order of factors in the tables of weights must correspond to the order in the PRESENT list with later factors nested within preceding factors The weights may be given in a separate file if a filename in quotes is given as the argument to PRWTS Check the output to ensure that the values in the tables 191 10 3 Prediction of weights are applied in the correct order ASReml may transpose the table of weights to match the order it needs for processing When weights are supplied in a separate file two layouts are allowed The default is to read all values in the file regardless of layout Otherwise the weights must appear a single column field one weight per line where the field is specified by appending c to the filename Consider a rather co
193. Reml will arbitrarily fix one of the variance parameters leading to possible confusion for the user If you fix the variance parameter to a particular value then it is not free and does not count for the purposes of applying the principle that there be only one scaling variance parameter That is models 7 9 can be made identifiable by fixing all but one of the nonidentifiable scaling parameters in each of G and R to a particular value 2 2 Estimation Consider the sigma parameterization of Section 2 1 1 Estimation involves two processes that are closely linked They are performed within the engine of ASReml One process involves estimation of 7 and prediction of u although the latter may not always be of interest for given cr and a The other process involves estimation of these variance parameters 2 2 1 Estimation of the variance parameters Estimation of the variance parameters is carried out using residual or restricted maximum likelihood REML developed by Patterson and Thompson 1971 An historical develop ment of the theory can be found in Searle et al 1992 Note firstly that y N X7 H 2 10 12 2 2 Estimation Table 2 1 Combination of models for G and R structures model Gi G R Ry 0 comment 1 VO C C y valid 2 V C V C n valid 3 C C V C y valid but not recommended 4 n inappropriate as R is a correlation model 5 C C C C y inappropriate same scale for R and G 6 C V C n inappropriate no
194. S 3 USE 3 US_C 4 Vac 4 us amp 4 US_V 4 US_C 5 US_C 5 US_C 5 US_C 5 US_V 5 grp DIAG_V grp DIAG_V grp DIAG_V grp DIAG_V DIAG_V DIAG_V DIAG_V tag XFA_V 0 tag XFA_V 0 tag XFA_V 0 tag XFA_V 0 tag XFA_V 0 tag XFA_L 1 tag XFA_L 1 tag XFA_L 1 tag XFA_L 1 tag XFA_L 1 tag XFA_L 2 tag XFA_L 2 tag XFA_L 2 tag XFA_L 2 0 2 r CO GS C 9 52 mo 02 b2 po ds 02 52 po O1 ds 092 b2 F Ms 02 b2 F 02 52 F 52 ie KS ds s 03 b5 FF n Sigma effects 8 73764 7 28431 17 7518 0 247683 0 705206 0 109539 0 816826 2 03848 0 252672 3 31382 0 871460 2 531236 0 820500E 01 0 208757 1 54276 0 142095E 02 0 143902E 02 0 163766E 02 0 207278E 03 1 01249 15 2158 0 279183 0 00000 0 00000 0 00000 0 423561 0 00000 0 108621E 02 0 180299 0 219418 0 221424F 01 177555 1 17382 0 531936E 01 0 601790E 01 0 285498 343 43151 28 assuming 44 parameters restrained restrained restrained restrained Sigma Sigma SE C 8 73764 30 22 OP 7 28431 20 158 P 17 7518 26 87 OP 0 247683 5 82 OP 0 705206 14 30 OP 0 109539 11 15 vO P 0 816826 2 22 UP 2 03848 3 68 OP 0 252672 3 81 0 P 3 31382 7 50 OP 0 871460 6 23 OP 2 53136 19 24 OP 0 820500E 01 4 48 OP 0 208757 1 58 OP 1 54276 23 95 OP 0 142095E 02 2 04 OU 0 143902E 02 1 54 OU 0 163766E 02 11 guU 0 207278E 03 1 01 O U 1 01249 225 QU 15 2158 3 49 OU 0 279183 ir a O U 0 00000 0 00 OF 0 00000 0 00 OF 0 00000 0 00 OF 0 423561
195. Seb AA A Eee 2 1 4 How to use this A 3 1 5 Getting assistance and the ASReml forum svae ee 3 1 6 Typographic CONVENTIONS lt se ke HE GE EHR ain CEC RR ERK G 4 2 Some theory 5 2A The general linear mixed model 0 o 5 2 1 1 Sigma parameterization of the linear mixed model 5 2 1 2 Partitioning the fixed and random model terms 6 213 G structure for the random model terms 6 2 14 Partitioning the residual error term 2 020 T 2 1 5 R structure for the residual error term 7 2 1 6 Gamma parameterization for the linear mixed model f LLE Farameter Woes ec cede bei dundee dt e a r E e Son is 8 2 1 8 Variance structures for the random model terms 8 2 1 9 Variance models for terms with several factors 9 2 110 Direct product structures e so soes he eee Ee Re Ee we 9 2 1 11 Direct products in R structures v eee ee ee ee es 10 2 1 12 Direct products in G structures lt s oc cios ERE ESS 10 2 1 13 Range of variance models for R and G structures 11 2 1 14 Use of the gamma parameterization 4 12 2 1 15 Combining variance models 2 6506 ee ee ee ee ee 12 22 PMA i aen ch OR EMS AR ERE Oe RSE OES SEES EGY 12 2 2 1 Estimation of the variance parameters 12 2 2 2 Estimation prediction of the fixed and random effects 15 2 3 UI qe LUIS Dari
196. T TrLit1234 Trait 123 40 ISUBSET TrAG1245 Trait 12 4 5 ISUBSET TrSG123 Trait 12300 USING ASSIGN TO MAKE SPECIFICATION CLEARER ASSIGN SIRE DAM LITTER AND RESIDUAL INITIAL VALUES FROM UNIVARIATE ANALYSES ASSIGN SDIAGI 0 608 1 298 0 015 0 197 0 035 GP Initial sire variances ASSIGN DDIAGI 2 2 4 14 0 018 GP ASSIGN LDIAGI 3 74 0 97 0 019 0 941 GP ASSIGN RUSI lt 9 27 0 0 16 48 0 0 0 0 0 14 0 0 0 0 0 0 3 37 0 0 0 0 0 0 0 0 1 14 1 gt ASSIGN VARS lt TrAG1245 age grp TrSG123 sex grp 2 PART 1 DIAGONAL FOR SIRE DAM AND LITTER UNSTRUCTURED FOR RESIDUAL wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS Trait sire TrDam123 dam TrLit1234 lit lf Trait grp 125 1 R STRUCTURE WITH 2 COMPONENTS AND 5 G STRUCTURES O O O INDEPENDENT ACROSS ANIMALS Trait 0 US GP UNSTRUCTURED TRAIT MATRIX INITIAL VALUES FROM UNIVARIATE ANALYSES RUSI 330 16 11 Multivariate animal genetics data Sheep TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp O ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID Trait eire 2 Trait 0 DIAG SDIAGI sire 0 ID TrDam123 dam 2 TrDam123 0 DIAG DDIAGI dam O ID TrLit1234 1it 2 TrLit1234 0 DIAG LDIAGI 11 9 ID PART 2 CHANGE DIAGONAL TO XFA1 FOR SIRE DAM AND LITTER wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS xfa Trait 1 sire xfa TrDam123 1 dam xfa TrLit1234 1 1lit If
197. TASR NOW or FINALASR NOW must be upper case Note that the ABORTASR NOW file is deleted so nothing of importance should be in it If you perform a system level abort CTRL C or close the program win dow output files other than the rsv file will be incomplete The rsv file should still be functional for resuming iteration at the most recent parameter estimates see CONTINUE Use MAXIT 1 where you want estimates of fixed effects and predictions of random effects for the particular set of variance parameters supplied as initial values Otherwise the estimates and predictions will be for the updated variance parameters see the BLUP qualifier below If MAXIT 1 is used and an Unstructured Variance model is fitted AS Reml will perform a Score test of the US matrix Thus assume the variance structure is modelled with reduced parameters if that modelled structure is then processed as the initial values of a US structure ASReml tests the adequacy of the reduced parameterization causes ASReml to report a general description of the distribution of the data variables and factors and simple correlations among the variables for those records included in the analysis This summary will ignore data records for which the variable being analysed is missing unless a multivariate analysis is requested or missing values are being estimated The information is written to the ass file is used to plot the transformed data Use X to specify the zx
198. The offset is only included in binomial and Poisson models for Normal models just subtract the offset variable from the response variable for example count POIS OFFSET base DISP mu group The offset is included in the model as n X7 0 The offset will often be something like In n ITOTAL n is used especially with binomial and ordinal data where n is the field containing the total counts for each sample If omitted count is taken as 1 Residual qualifiers control the form of the residuals returned in the yht file The predicted values returned in the yht file will be on the linear predictor scale if the WORK or PVW qualifiers are used They will be on the observation scale if the DEVIANCE PEARSON RESPONSE or PVR qualifiers are used DEVIANCE produces deviance residuals the signed square root of d h from Table 6 4 where h is the dispersion parameter controlled by the DISP qualifier This is the default PEARSON writes Pearson residuals Te in the yht file PVR writes fitted values on the response scale in the yht file This is the default PVW writes fitted values on the linear predictor scale in the yht file RESPONSE produces simple residuals y y WORK produces residuals on the linear predictor scale ao 102 6 8 Generalized Linear Mixed Models A second dependent variable may be specified except with a multinomial response MULTINOMIAL if a bivariate analysis is required but it will always be
199. With this qualifier ASReml writes e Gu and G u diagy G G7C022G 7 to the sln file R e and R e diag R R WC W R to the yht file e and copies lines where the last ratio exceeds 3 in magnitude to the res file e and reports the number of such lines to the asr file e It has not been validated for multivariate models or XFA models with zero Vs The variogram has been suggested as a useful diagnostic for assisting with the identification of appropriate variance models for spatial data Cressie 1991 Gilmour et al 1997 demonstrate its usefulness for the identification of the sources of variation in the analysis of field experiments If the elements of the data vector and hence the residual vector are indexed by a vector of spatial coordinates s 2 1 n then the ordinates of the sample variogram are given by 1 tig 5 s E e ij l n 1 j The sample variogram reported by ASReml has two forms depending on whether the spatial coordinates represent a complete rectangular lattice as typical of a field trial or not In the lattice case the sample variogram is calculated from the triple l 1 lij2 vij where lij1 Si Sji and lija Sia Sj2 are the displacements As there will be many v with the same displacements ASReml calculates the means for each displacement pair l 1 lij2 either ignoring the signs default or separately for same sign and opposite sign TWOWAY after grouping t
200. Y and the female is XX This NRM inverse matrix is formed in addition to the usual A7 and can be accessed as GIV1 or as specified in the output The pedigree must include a fourth field which codes the SEX of the individual The actual code used is up to the user and deduced from the first line which is assumed to be a male Thus whatever string is found in the fourth field on the first line of the pedigree is taken to mean MALE and any other code found on other records is taken to mean FEMALE 9 5 Genetic groups If all individuals belong to one genetic group then use 0 as the identity of the parents of base individuals However if base individuals belong to various genetic groups this is indicated by the GROUPS qualifier and the pedigree file must begin by identifying these groups All base individuals should have group identifiers as parents In this case the identity O will 164 9 6 Reading a user defined inverse relationship matrix only appear on the group identity lines as in the following example where three sire lines are fitted as genetic groups Genetic group example Gl 0 0 animal P G2 0 0 sire 9 A G3 0 0 dam STRE 1 61 G1 lines 2 SIRE 2 Gi G1 damage SIRE_3 Gi Gi adailygain SIRE_4 G2 G2 harveyg ped ALPHA MAKE GROUP 3 SIRE 5 G2 G2 harvey dat SIRE 6 Ga G3 adailygain mu SIRE 7 G3 G3 lr animal 02 5 GU SIRE_8 G3 G3 SIRE_9 G3 G3 101 SIRE_1 G1 102 SIRE_1 G1 103 SIRE_1 G1 163 SIRE_9 G3 164 SIRE_9 G
201. a a a a e A ed 16 2 4 Inference Random effects ve 0 o e e eee 16 2 4 1 Tests of hypotheses variance parameters v o 16 24 2 Diagnostics lt lt cir dire ESE Re A AA 17 25 Inference Fixed effects oo oe 608 4 oe eka Se certi etr A 19 go WOOUWEIEN lt e so a Pa Se Se k eee eRe eee a Se IR 19 2 5 2 Incremental and conditional Wald F Statistics 20 2 5 3 Kenward and Roger adjustments 2 40 23 2 5 4 Approximate stratum variances osoo ee o 23 A guided tour 25 3 1 VARGO sc eoi adi e ee b enk on ele KOR Gie a Ee p Aee 25 3 2 Nebraska Intrastate Nursery NIN field experiment 26 3 3 The ASRemi data fil o coc 646 RRA AG RARER OR RR ERS a a 28 3 4 The ASReml command file 2 vs ee ee ee e e o 30 SALTA tide line casas dis ia SHADE hr wh OEE DE EG 30 3 4 2 Reading the data nd we hw ee eR ee ER AA 31 34 3 Thedatatileline koe ee cars ee eee eee ewe eee AR 31 IRA TaD IAHOR o s 64442444 4484650 64444444 444464 31 3 4 5 Specifying the terms in the mixed model 32 SE PRICE see dra A AO e SO eee 32 3 4 7 Variance structures hw ee eR REY ee ed 32 35 Running the JON lt s ase sra sa dda rd ee EE Yora be eS 33 3 5 1 Generating a template aaa a 34 3 6 Description Of OUTPUT oo ew ee eee See ee A 34 SEL The SEP ara is a a a Ee 35 302 Theal file ece ee ee O 36 3603 A ook eo RAE RHE EAE a o aa SEAR eS 37 3q
202. a correlationmodel all diagonal elements equal 1 all but one of the models supplied when the G structure involves more than one vari ance model must be correlation models the other must be either an homogeneous or a heterogeneous variance model see Section 7 5 for the distinction between these models see also 5 for an example an initial value can be supplied for all parameters in G structure definitions ASReml expects initial values immediately after the variance model identifier or on the next line 0 1 directly after IDV in this case 0 is ignored as an initial value on the model line if there is no initial value after the identifier ASReml will look on the next line New R4 If the user enters one instead of all the initial values then ASReml will supply initial 112 7 3 A sequence of structures for the NIN data values if ASReml does not find an initial value or it will stop and give an error message in the asr file e in this case V 0 Z Z 0 1 which is fitted as g yZ Z I1 where y is a variance ratio y 0 0 and 0 is the scale parameter Thus 0 1 is a reasonable initial value for y regardless of the scale of the data 3a Two dimensional spatial model with spatial correlation in one direc tion This code specifies a two dimensional spatial NIN Alliance Trial 1989 structure for error but with spatial correla variety A tion in the row direction only that is e id N
203. a on a scratch file rather than in memory In large jobs the system area where scratch files are held may not be large enough A Unix system may put this file in the tmp directory which may not have enough space to hold it affects the number of distinct points recognised by the pol model func tion Table 6 1 The default value of n is 1000 so that points closer than 0 1 of the range are regarded as the same point influences the number of points used when predicting splines and poly nomials The design matrix generated by the leg pol and sp1 Q functions are modified to include extra rows that are accessed by the PREDICT directive The default value of n is 21 if there is no PPOINTS qualifier The range of the data is divided by n 1 to give a step size For each point p in the list a predict point is inserted at p iif there is no data value in the interval p p 1 1x4 PPOINTS is ignored if PVAL is specified for the variable This process also effects the number of levels identified by the fac model term 83 5 8 Job control qualifiers Table 5 6 List of very rarely used job control qualifiers qualifier action REPORT ISCALE 1 SCORE ISLOW n TOLERANCE s1 s2 VRB forces ASReml to attempt to produce the standard output report when there is a failure of the iteration algorithm Usually no report is produced unless the algorithm has at least produced estimates for the fixed and ra
204. acters but should not begin with a number see command line arguments e Dollar substitution occurs before most other high level actions Consequently ASSIGN strings and commandline arguments may substitute into a CYCLE line e I J K and L are reserved as names refering to items in the CYCLE list and should therefore not be used as names of an ASSIGN string is a mechanism whereby ASReml can loop through a series of jobs The ICYCLE has a qualifier SAMEDATA that tells ASReml to use the same data for all cycles ie the data file is only read on the first cycle and is kept in memory for later cycles The CYCLE qualifier must appear on its own line starting in character 1 list is a series of values which are substituted into the job wherever the I string appears The list may spread over several lines if each incomplete line ends with a COMMA A series of sequential integer values can be given in the form i j no embedded spaces The output from the set of runs is concatenated into a single set of files 205 11 4 Advanced processing arguments High level qualifiers qualifier action DOPATH n For example ICYCLE 0 4 0 5 0 6 20 0 mat2 1 9 I GPF would result in three runs and the results would be appended to a single file Putting SAMEDATA on the leading CYCLE line makes ASReml read the data and grr file file in the first CYCLE and hold it in memory for use in subsequent cycles This is advantage
205. actor Trait i e nt analysis records ordered Trait within data record If the data is already in this long form use the ASMV t qualifier to indicate that a multivariate analysis is required 154 8 3 Variance structures 8 3 Variance structures Using the notation of Chapter 7 consider a multivariate analysis with traits and n units in which the data are ordered traits within units An algebraic expression for the variance matrix in this case is where E is an unstructured variance matrix This is the general form of variance struc I 6 52 tures required for multivariate analysis 8 3 1 Specifying multivariate variance structures in ASReml For a standard multivariate analysis the error structure for the residual must be specified as two dimensional with indepen dent records and an unstructured variance matrix across traits records may have ob servations missing in different patterns and these are handled internally during analy sis the R structure must be ordered traits within units that is the R structure defini tion line for units must be specified before the line for Trait variance parameters are variances not vari ance ratios the R structure definition line for units that is 1485 0 ID could be replaced by O or O 0 ID this tells ASReml to fill in the number of units and is a useful option when Orange Wether Trial 1984 8 SheepID I TRIAL BloodLine I TEAM YEAR GFW
206. actor in the averaging set is present and whether all cells in every fixed interaction is filled For example in the previous example no variety predictions would be obtained if site was declared as having 4 levels but only three were present in the data The message is also likely if any fixed model terms are IGNOREd The TABULATE command may be used to see which treatment combinations occur and in what order More formally there are often situations in which the fixed effects design matrix X is not of full column rank This aliasing has three main causes e linear dependencies among the model terms due to over parameterisation of the model e no data present for some factor combinations so that the corresponding effects cannot be estimated e linear dependencies due to other usually unexpected structure in the data The first type of aliasing is imposed by the parameterisation chosen and can be determined from the model The second type of aliasing can be detected when setting up the design matrix for parameter estimation which may require revision of imposed constraints All types are detected in ASReml during the absorption process used to obtain the predicted values ASReml doesn t print predictions of non estimable functions unless the PRINTALL qualifier is specified However using PRINTALL is rarely a satisfactory solution Failure to report predicted values normally means that the predict statement is averaging over some c
207. alifier which may only be associated with the second file causes the field contents for the nominated fields from the second file only be inserted once into the merged file For example assume we want to merge two files containing data from sheep The first file has several records per animal containing fleece data from various years The sec ond file has one record per animal containing birth and weaning weights Merging with NODUP bwt wwt will copy these traits only once into the merged file ISKIP fields is used to exclude fields from the merged file It may be specified with either or both input files 212 12 3 Examples List of MERGE qualifiers qualifier action SORT instructs ASReml to produce the merged file sorted on the key fields Otherwise the records are return in the order they appear in the primary file The merging algorithm is briefly as follows The secondary file is read in skip fields being omitted and the records are sorted on the key fields If sorted output is required the primary file is also read in and sorted The primary file or its sorted form is then processed line by line and the merged file is produced Matching of key fields is on a string basis not a value basis If there are no key fields the files are merged by interleaving If there are multiple records with the same key these are severally matched That is if 3 lines of file 1 match 4 lines of file 2 the merged file will contain al
208. alytic W contains specific variance covari ance form 126 7 5 Variance model description Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance XFA 1 1 k order y IT Y w w XFAk k extended T contains covariance factors kw w factor W contains specific variance analytic covari ance form Inverse relationship matrices AINV inverse relationship matrix derived from pedi 0 1 E gree NRM relationship matrix derived from pedigree 0 1 7 GIV1 generalized inverse number 1 0 1 GIV8 generalized inverse number 8 0 1 7 GRM1 generalized relationship number 1 0 1 GRM8 generalized relationship matrix 8 0 iL T This is the number of values the user must supply as initial values where w is the dimension of the matrix The homogeneous variance form is specified by appending V to the correlation basename the heterogeneous variance form is specified by appending H to the correlation basename These must be associated with 1 variance parameter unless used in direct product with another structure which provides the variance 127 7 5 Variance model description 7 5 1 Forming variance models from correlation models The base identifiers presented in the first part of Table 7 3 are used to specify the correlation models The corresponding homogeneous and heterogeneous variance models are specified
209. am 2 TrDam12 O DIAG DDIAGI dam O ID TrLit1234 1it 2 TrLit1234 0 DIAG LDIAGI lit O ID PATH 2 USING XFA1 FOR TAG DAM AND LIT US FOR RESIDUAL wwt ywt gfw fdm fat SIGMAP Trait Trait age Trait brr Trait sex Trait age sex r VARS xfa Trait 1 tag xfa TrDam12 1 dam xfa TrLit1234 1 1lit If Trait grp 125 000 Trait 0 US RUSI TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp O ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID xfa Trait 1 tag 2 xfa Trait 1 O XFA1 GP tag 0 AINV xfa TrDam12 1 dam 2 xfa TrDam12 1 O XFA1 IGP dam O ID xfa TrLit1234 1 1it 2 xfa TrLit1234 1 O XFA1 GP 146 9 ID PATH 3 wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS Trait tag xfa TrDam12 1 dam TrLit1234 1it If Trait grp 340 16 11 Multivariate animal genetics data Sheep 125 000 Trait 0 US GP TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp 0 ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID Trait tag 2 Trait 0 US GP tag 0 AINV xfa TrDam12 1 dam 2 xfa TrDam12 1 O XFA1 GP dam O ID TrLit1234 1it 2 TrLit1234 0 US GP 116 9 1D PATH 4 wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS xfa Trait 2 tag xfa TrDam12 1 dam TrLit1234 1lit If Trait grp 125 000 Trait 0 US GP TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0
210. am and lamb tag covariates such as age the age of the lamb at a set time brr the birth rearing rank 1 born single raised single 2 born twin raised single 3 born twin raised twin and 4 other sex M F and grp a factor indicating the flock year combination 16 11 1 Half sib analysis In the half sib analysis we include terms for the random effects of sires dams and litters In univariate analyses the variance component for sires is denoted by g 0 where g is the additive genetic variance the variance component for dams is denoted by 07 304 0 where o is the maternal variance component and the variance component for litters is denoted by g and represents variation attributable to the particular mating For a multivariate analysis these variance components for sires dams and litters are in theory replaced by unstructured matrices one for each term Additionally we assume the residuals for each trait may be correlated Thus for this example we would like to fit a total of 4 unstructured variance models For such a situation it is sensible to commence the modelling process with a series of univariate analyses These give starting values for the diagonals of the variance matrices but also indicate what variance components are estimable The ASReml job for the univariate analyses is IRENAME 1 ARG 1 2 3 4 5 Does 5 runs one for each trait Multivariate Sire amp Dam model DOPART 1 IF 1 1 ASSIGN YV wwt sets u
211. ameters The constraint lines occur after the G structures are defined The con straints are described in Section 7 9 4 The variance header line Section 7 4 must be present even if only 0 0 0 indicating there are no explicit R or G structures see Section 7 9 4 requests that the variogram formed with radial coordinates see page 18 be based on s 4 6 or 8 sectors of size 180 s degrees The default is 4 sectors if VGSECTORS is omitted and 6 sectors if it is specified without an argument The first sector is centred on the X direction Figure 5 1 is the variogram using radial coordinates obtained using pre dictors of random effects fitted as fac xsca ysca It shows low semi variance in xsca direction high semivariance in the ysca direction with intermediate values in the 45 and 135 degrees directions controls the form of the yht file YHTFORM 1 suppresses formation of the yht file YHTFORM 1 is TAB separated yht becomes _yht txt YHTFORM 2 is COMMA separated yht becomes _yht csv YHTFORM 3 is Ampersand separated yht becomes _yht tex adds r to the total Sum of Squares This might be used with DF to add some variance to the analysis when analysing summarised data 82 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action Table 5 6 List of very rarely used job control qualifiers qualifier action ICINV n prints the portion of the inverse of the coeffici
212. analysis of a field experiment Barley Table 16 5 Summary of Wald F statistics for fixed effects for variance models fitted to the plant data treatment treatment time model df 1 df 4 Uniform 9 41 5 10 Power 6 86 6 13 Heterogeneous power 0 00 4 81 Antedependence order 1 4 14 3 96 Unstructured 1 71 4 46 16 6 Spatial analysis of a field experiment Barley In this section we illustrate the ASReml syntax for performing spatial and incomplete block analysis of a field experiment There has been a large amount of interest in developing techniques for the analysis of spatial data both in the context of field experiments and geostatistical data see for example Cullis and Gleeson 1991 Cressie 1991 Gilmour et al 1997 This example illustrates the analysis of so called regular spatial data in which the data is observed on a lattice or regular grid This is typical of most small plot designed field experiments Spatial data is often irregularly spaced either by design or because of the observational nature of the study The techniques we present in the following can be extended for the analysis of irregularly spaced spatial data though larger spatial data sets may be computationally challenging depending on the degree of irregularity or models fitted The data we consider is taken from Gilmour et al 1995 and involves a field experiment designed to compare the performance of 25 varieties of barley The experiment
213. and has only been implemented for this specific case and the analagous region trial case The associated factors must occur together in this order for the prediction to give correct answers The ASSOCIATE effect with base averaging can usually be achieved with the PRESENT qualifier except when the factors have many levels so that the product of levels exceeds 2147 000 000 it fails in this case because the KEY for identifying the cells present is a simple combination of the levels and is stored as a normal 32bit integer However ASSOCIATE is preferred because it formally checks the association structure as well as allowing sequential averaging Two ASSOCIATE clauses may be specified for example PRED entry ASSOC family entry ASSOC reg loc trial ASAVE reg loc Only one member of an ASSOCIATE list may also appear in a PRESENT list If one member appears in the classify set only that member may appear in the PRESENT list For example yield region r region family entry PREDICT entry ASSOCIATE family entry PRESENT entry region Association averaging is used to form the cells in the PRESENT table and PRESENT averaging is then applied 10 3 5 Complicated weighting with PRESENT Generally when forming a prediction table it is necessary to average over or ignore some dimensions of the hyper table By default ASReml uses equal weights 1 f for a factor with f levels More complicated weighting is achieved by using the AVE
214. and use parameter constraints to equate the parameters If there are few parameters this can be done as follows xfa dTrial 1 Family 2 5 O XFA1 GPFPFP ABCDEFGH 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Family O GIV1 xfa dTrial 1 Entry 2 5 O XFA1 GPFPFP ABCDEFGH 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Entry 0 GIV2 However for a larger term there may not be enough letters in the alphabet and so VCC is required as in IVCC 1 143 7 9 Constraining variance parameters xfa dTrial 1 Family 2 5 O XFA1 GPFPFP 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Family O GIV1 xfa dTrial 1 Entry 2 5 XFA1 GPFPFP 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Entry 0 GIV2 21 29 BLOCKSIZE 8 parameters 21 28 are equal to parameters 29 36 pairwise Better still in this case we can use just one structure twice xfa dTrial 1 Family 2 5 O XFA1 GPFPFP NAME FIVE 0 72631 0 000 242713 0 000 882465 846305 04419 743393 Family O GIV1 xfa dTrial 1 Entry 2 USE FIVE Model and Initial parameters are given above Entry 0 GIV2 associates the model definition labeled FIVE with the second structure 7 9 4 Fitting linear relationships among variance structure parameters The user may wish to define relationships between particular variance parameters For example consider an experiment in which two or more separate trials are sown adjacent to on
215. ans that the covariance between two effects ab and ab in ab is constructed as the product of the covariance between a and a in model A i e its i element A and the covariance between bj and b in model B i e its k 1 element By ajo Example 2 3 A simple direct product structure If A has 3 levels and B has 2 levels then the term A B would have the 6 levels ab ab ab ab abs aba ab Using magenta and blue to highlight terms associated with A and B respectively in cov ab ab if Ay Ay Ais var A Ag A Aosa and var B As Aza Ass By Bi Ba Ba then COV ab ab Aos x Bi 2 1 10 Direct product structures Mathematically the result 2 9 is known as a direct product structure and is written in full as var ab A8 B 2 1 The general linear mixed model A B AB 11 A B gt A B ml mp Structures associated with direct product construction are known as separable variance struc tures and we call the assumption that a separable variance structure is plausible the assump tion of separability 2 1 11 Direct products in R structures Separable structures occur naturally in many practical situations Consider a vector of common errors associated with an experiment The usual least squares assumption and the default in ASReml is that these are independently and identically distributed IID However if e was from a field experiment laid out in a rectangular ar
216. art and end of a block are trimmed but empty rows in the middle of a block are kept Empty columns are ignored A single row of labels as the first non empty row in the block will be taken as column names Empty cells in this row will have default names C1 C2 etc assigned Missing values are commonly represented in ASReml data files by NA or ASReml will also recognise empty fields as missing values in csv x1s files 42 4 2 The data file 4 2 4 Binary format data files Conventions for binary files are as follows e binary files are read as unformatted Fortran binary in single precision if the filename has a bin or BIN extension Fortran binary data files are read in double precision if the filename has a dbl or DBL extension ASReml recognises the value 1e37 as a missing value in binary files Fortran binary in the above means all real bin or all double precision db1 vari ables mixed types that is integer and alphabetic binary representation of variables is not allowed in binary files binary files can only be used in conjunction with a pedigree file if the pedigree fields are coded in the binary file so that they correspond with the pedigree file this can be done using the SAVE option in ASReml to form the binary file see Table 5 5 or the identifiers are whole numbers less than 9 999 999 and the RECODE qualifier is specified see Table 5 5 43 5 Command file Reading the data 5 1 Introduction
217. ary vector performs the transformations in that vector and saves the values that relate to labelled variables to the internal data array Note that e there may be up to 10000 variables and these are internally labeled V1 V2 V10000 for transformation purposes Values from the data file ignoring any SKIPed fields are read into the leading variables e alpha A integer 1 pedigree P and date DATE fields are converted to real num bers level codes as they are read and before any transformations are applied 51 5 5 Transforming the data transformations may be applied to any variable since every variable is numeric but it may not be sensible to change factor level codes transformations operate on a single variable not a G group of variables unless it is explicitly stated otherwise transformations are performed in order for each record in turn variables that are created by transformation should be defined after below variables that are read from the data file unless it is the explicit intention to overwrite an input variable see below after completing the transformations for each record the values in the record for variables associated with a label are held for analysis or the record all values is discarded see ID transformation and Section 6 9 Thus variables form three classes those read from the data file possibly modified and labelled are available for subsequent use in analysis those c
218. ata field containing the coordinates for the second direction For example in the analysis of spatial data if the x coordinate was in field 3 and the y coordinate was in field 4 the second argument would be 304 For a G structure relating to the model term fac x y use fac x y For example y mu alr facia y fac x y 1 fac x y fac x y IEUCV 7 1 3 132 7 5 Variance model description 7 5 5 Notes on Factor Analytic models FAk FACVk and XFAk are different parameterizations of the factor analytic model in which Y is modelled as Y IT W where T is a matrix of loadings on the covariance scale and W is a diagonal vector of specific variances See Smith et al 2001 and Thompson et al 2003 for examples of factor analytic models in multi environment trials The general limitations are that W may not include zeros except in the XFAk formulation constraints are required in for k gt 1 for identifiability These are automatically set unless the user formally constrains one parameter in the second column two in the third column etc the total number of estimated parameters kw w k k 1 2 may not exceed w w 1 2 wxw In FAk models the variance covariance matrix 5 is modelled on the correlation scale as X DCD where D is diagonal such that DD diag X C is a correlation matrix of the form FF E where F is a matrix of loadings on the correlation scale and F is dia
219. ate analyses bivariate univariate effects model 16 10 model 16 7 trait variety Uy 1 8u u trait run ur 1 9 u u trait pair e 1 u e This unstructured form for trait variety in the bivariate analysis is equivalent to the variety main effect plus heterogeneous tmt variety interaction variance structure 16 8 in the univariate analysis Similarly the unstructured form for trait run is equivalent to the run main effect plus heterogeneous tmt run interaction variance structure The unstructured form for the errors trait pair in the bivariate analysis is equivalent to the pair plus heterogeneous error tmt pair variance in the univariate analysis This bivariate analysis is achieved in ASReml as follows noting that the tmt factor here is equivalent to traits this is for the paired data id pair 132 run 66 variety 44 A yc ye ricem asd skip 1 X syc Y sye sqrt yc sqrt ye Trait r Tr variety Tr run 12 2 132 S2 Tr 0 US 221 121 2 427 Tr variety 2 2 0 US 1 401 1 1 477 4400 Tr run 2 20 US 79 5 2 887 6600 predict variety A portion of the output from this analysis is 7 LogL 343 220 S2 1 0000 262 df 8 LogL 343 220 S2 1 0000 262 df Model_Term Sigma Sigma Sigma SE C Residual UnStruct 1 2 14373 2 14373 4 44 OU Residual UnStruct 1 0 987401 0 987401 2 59 OU Residual UnStruct 2 2 34751 2 34751 4 62 oU Tr variety UnStruct 1 3 83959 3 83959 3 47 OU Tr variety UnStruct 1 2 33394 2 33394 3 01 017 T
220. ate of the un derlying variance component matrix a rescaled version is also printed scaled according to the fitted variance parameters The primary purpose for this output is to provide reasonable start ing values for fitting more complex variance structure The cor relations may also be of interest After a multivariate analysis a similar matrix is also provided calculated from the residuals placed in the pvc file when postprocessing with a pin file these are residuals that are more than 3 5 standard deviations in magnitude these in the are printed in the second column given if a predict statement is supplied in the as file the REML log likelihood is given for each iteration The REML log likelihood should have converged and in binary form in dpr file these are printed in column 3 Furthermore for multivariate analyses the residuals will be in data order traits within records However in a univariate analysis with missing values that are not fitted there will be fewer residuals than data records there will be no residual where the data was missing so this can make it difficult to line up the values unless you can manipulate them in another program spreadsheet given if the DL command line option is used simple averages of cross classified data are produced by the tabulate directive to the tab file Adjusted means pre dicted from the fitted model are written to the pvs file by the predict directive base
221. ative y H IGAMMA INVERSE IDENTITY LOGARITHM PHI TOTAL n v u lon The inverse is the default link function n is defined with the TOTAL qualifier and ga 1n 1 would be degrees of freedom in the typical application to mean squares The default ae y value of is 1 101 6 8 Generalized Linear Mixed Models Table 6 4 GLM distribution qualifiers qualifier action INEGBIN LOGARITHM IDENTITY INVERSE PHI v u p 0 fits the Negative Binomial distribution Natural logarithms are the default link d 2 p y In function The default value of is 1 yln 4 General qualifiers AOD requests an Analysis of Deviance table be generated This is formed by fitting a series of sub models for terms in the DENSE part building up to the full model and comparing the deviances An example if its use is LS BIN TOT COUNT AOD mu SEX GROUP AOD may not be used in association with PREDICT IDISP A includes an overdispersion scaling parameter h in the weights If DISP is specified with no argument ASReml estimates it as the residual variance of the working variable Traditionally it is estimated from the deviance residuals reported by ASReml as Variance heterogeneity An example if its use is count POIS DISP mu group OFFSET o is used especially with binomial data to include an offset in the model where o is the number or name of a variable in the data
222. auses ASReml to print the transformed data file to basename asp If n lt 0 data fields 1 mod n are written to the file n 0 nothing is written n 1 all data fields are written to the file if it does not exist n 2 all data fields are written to the file overwriting any previous contents n gt 2 data fields n tare written to the file where tis the last defined column sets hardcopy graphics file type to png sets hardcopy graphics file type to ps modifies the format of the tables in the pvs file and changes the file extension of the file to reflect the format PVSFORM 1 is TAB separated pvs gt _pvs txt PVSFORM 2 is COMMA separated pvs gt _pvs csv PVSFORM 3 is Ampersand separated pvs gt _pvs tex See TXTFORM for more detail 80 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action IRESIDUALS 2 ISAVE n ISCREEN n SMX m SLNFORM n instructs ASReml to write the transformed data and the residuals to a binary file The residual is the last field The file basename srs is written in single precision unless the argument is 2 in which case basename drs is written in double precision Factor names are held in a v11 file see ISAVE below The file will not be written from a spatial analysis two dimensional error when the data records have been sorted into field order because the residuals are not in the same order t
223. aving an n x t n subjects with t traits each structure This will be a problem if the R structure model assumes n X t data structure the matrix may be OK but ASReml has not checked it this indicates that there are some lines on the end of the as file that were not used The first extra line is displayed This is only a problem if you intended ASReml to read these lines The RSKIP qualifier requested skipping header blocks which were not present 262 15 5 Information Warning and Error messages Table 15 2 List of warning messages and likely meaning s warning message likely meaning Warning Fewer levels found in term Warning FIELD DEFINITION lines should be INDENTED Warning Fixed levels for factor Warning Initial gamma value is zero Warning Invalid argument Warning It is usual to include Trait in the model Warning LogL Converged Parameters Not Converged Warning LogL not converged Notice LogL values are reported relative to a base of Warning Missing cells in table Warning More levels found in term Warning PREDICT LINE IGNORED TOO MANY Warning PREDICT statement is being ignored Warning Second occurrence of term dropped Warning Spatial mapping information for side Warning Standard errors Warning SYNTAX CHANGE text may be invalid Warning The A qualifier ignored when reading BINARY data Warning The SPLINE qualifier has been redefined
224. back to New ASReml users are advised to read Chapter 3 before attempting to code their first job It presents an overview of basic ASReml coding demonstrated on a real data example Chapter 16 presents a range of examples to assist users further When coding your first job look for an example to use as a model Data file preparationis described in Chapter 4 and Chapter 5 describes how to input data into ASReml Chapters 6 and 7 are key chapters which present the syntax for specify ing the linear model and the variance models for the random effects in the linear mixed model Variance modelling is a complex aspect of analysis We introduce variance modelling in ASReml by example in Chapter 16 Chapters 8 and 9 describe special commands for multivariate and genetic analyses respec tively Chapter 10 deals with prediction offixed and random effects from the linear mixed model and Chapter 13 presents the syntax for forming functions of variance components such as heritability Chapter 11 discusses the operating system level command for running an ASReml job Chap ter 12 describes a new data merging facility Chapter 14 gives a detailed explanationof the output files Chapter 15 gives an overview of the error messages generated in ASReml and some guidance as to their probable cause 1 5 Getting assistance and the ASReml forum The ASReml help accessable through ASReml W can also be linked to Con Text or accessed directly ASRem1 chm There
225. ble 15 2 Error messages with their probable cause s is pre sented in Table 15 3 Table 15 1 Some information messages and comments information message comment Logl converged BLUP run done JOB ABORTED by USER Logl converged parameters not converged Logl not converged the REML log likelihood last changed less than 0 002 iteration number and variance parameter values appear stable A full iteration has not been completed See discussion of BLUP See discussion of ABORTASR NOW the change in REML log likelihood was small and convergence was assumed but the parameters are in fact still changing the maximum number of iterations was reached before the REML log likelihood converged The user must decide whether to accept the results anyway to restart with the CONTINUE command line option see Section 11 3 on job control or to change the model and or initial values before proceding The sequence of estimates is reported in the res file It may be nec essary to simplify the model and estimate the dominant com ponents before estimating other terms if the LogL is oscilating Warning Only one iteration Parameter values are not at the REML solution performed Parameters appear to be at the REML solution in that the parameter values are stable Parameters unchanged after one iteration Messages beginning with the word Notice are not generally listed here They provide information the user sho
226. bs NY MA 1 1 order C 1 1 2 l w moving aver Cu 0 1 02 age C 0 j gt i 2 10 lt 1 MA2 2 order C 1 2 3 24w moving aver Ciria 0 1 0 1 8 02 age E Cias 0 1 0 02 Ci 0 j gt 1 2 0 0 lt 1 J lt 1 0 lt 1 ARMA autoregressive CE 1 2 3 2 w moving ave CC 0 64 1 age 02 20 Ci 0C i gt 1 1 lt 1 lo lt 1 CORU uniform C 1 C 0 1 1 2 l w correlation CORB banded C 1 w l w 2w 1 correlation Cir ilcjca l lp lt 1 CORG general C 1 weet ice Ee ww correlation C 0 1 j w CORGH US dig lt 1 One dimensional unequally spaced EXP exponential C 1 1 2 1 w Co lei eal 1 Fj xi are coordinates 0 lt lt 1 124 7 5 Variance model description Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance GAU gaussian C 1 1 2 l w C bis 145 ij xi are coordinates 0 lt lt 1 Two dimensional irregularly spaced x and y vectors of coordinates 65 min d 1 1 dij is euclidean distance IEXP isotropic C 1 1 2 l w exponential C plti ealtlyi usl ij 0 lt lt 1 IGAU isotropic C 1 1 2 1l w gaussian C pea Hu ij 0 lt lt 1 IEUC isotropic Ca 1 1 2 l w euclidean C p V Bs Hui i ij gt 0 lt lt 1 LVR linear variance C 1 045 1 2 l w 0 lt i 3 193 SPH spherica
227. by appending V and H to the base identifiers respectively and appending the corresponding variance parameters to the list of parameters This convention holds for most models How ever no V or H should be appended to the base identifiers for the heterogeneous variance models at the end of the table from DIAG on In summary to specify e a correlation model provide the base identifier given in Table 7 3 for example EXP 1 is an exponential correlation model an homogeneous variance model append a V to the base identifier and provide an addi tional initial value for the variance for example EXPY 1 3 is an exponential variance model a heterogeneous variance model append an H to the base identifier and provide additional initial values for the diagonal variances for example CORUH 1 3 4 2 is a 3 x 3 matrix with uniform correlations of 0 1 and heterogeneous variances 0 3 0 4 and 0 2 Important See Section 7 7 for rules on combining variance models and important notes regarding initial values The algebraic forms of the homogeneous and heterogeneous variance models are determined as follows Let C f Cy denote the correlation matrix for a particular correlation model If X is the corresponding homogeneous variance matrix then NS C It has just one more parameter than the correlation model For example the homogeneous variance model corresponding to the ID correlation model has variance matrix Y
228. ce ib few degrees of freedom In summary the following strategies are available e review starting values are they in the right order and of the right magnitude can ASReml generate better ones can you get better values from a simpler model hold some parameters fixed for the initial iterations review the model try a simpler structure and test where the variation is has something important been omitted review input structures is the GIV file positive definite and arranged in the right order review the summary of the data tabulate and plot the data check handling of missing values in response and in design review the iteration sequence 151 8 Command file Multivariate analysis 8 1 Introduction Multivariate analysis is used here in the narrow sense of a multivariate mixed model There are many other multivariate analysis techniques which are not covered by ASReml Multi variate analysis is used when we are interested in estimating the correlations between distinct traits for example fleece weight and fibre diameter in sheep and for repeated measures of a single trait 8 1 1 Repeated measures on rats Wolfinger 1996 summarises a range of vari Woifinger rat data ance structures that can be fitted to repeated treat A measures data and demonstrates the models wt0 wtl wt2 wt3 wt4 using five weights taken weekly on 27 rats sub rat dat jected to 3 treatments This command file 0 Wt wt2 wt3 wt4 Trait
229. ce models and hence direct product matrices involved in the G structure the following lines define the d variance models order is either the number of levels in the term or the name of a factor that has the same number of levels as the component key is usually zero but for power models EXP GAU provides the distance data needed to construct the model model is the ASReml variance model identifier acronym selected for the term variance models are listed in Table 7 3 these models have associated variance parameters initial_values are initial or starting values for the variance parameters the values for initial values are as described above for R structure definition lines qualifier tells ASReml to modify the variance model in some way the qualifiers are de scribed in Table 7 4 122 7 5 Variance model description 7 5 Variance model description Table 7 3 presents the full range of variance models that is correlation homogeneous vari ance and heterogeneous variance models available in ASReml The table contains the model identifier a brief description its algebraic form and the number of parameters The first section defines BASE correlation models and in the next section we show how to extend them to form variance models The second section defines some models parameterized as variance covariance matrices rather than as correlation matrices The third section covers some special cases where the covariance
230. ce parameters from bivariate analysis of bloodworm data 307 Orange data AOV decomposition 0020000 Fae 313 Sequence of models fitted to the Orange data 0 315 Response frequencies in a cheese tasting experiment 325 REML estimates of a subset of the variance parameters for each trait for the genetic example expressed as a ratio to their asymptotic s e 329 Wald F statistics of the fixed effects for each trait for the genetic example 329 Variance models fitted for each part of the ASReml job in the analysis of the Pantie example ssc ke ERK ER EE ew ee eS 332 xiii List 14 1 14 2 14 3 14 4 14 5 16 1 16 2 16 3 16 4 16 5 16 6 16 7 16 8 16 9 16 10 16 11 16 12 16 13 16 14 16 15 16 16 of Figures Residual versus Fitted values o ee ee ee eis 228 Variogram of residuals 2 occ rs ee ee ee eS 237 Plot of residuals in field plan order v v ve sa a 238 Plot of the marginal means of the residuals 239 Histogram of residuals lt lt sao orowan pu ada a ec a aa 239 Residual plot for the rat data s ss cereri ceric aetti tek 279 Residual plot for the voltage data a 281 Trellis plot of the height for each of 14 plants 282 Residual plots for the EXP variance model for the plant data 285 Sample variogram of the residuals from the AR1xAR1 model 292 Sample variogram
231. confidence intervals 2 standard error of predic tion Within this figure the data is adjusted to remove the estimated seasonal effect The conclusions from this analysis are quite different from those obtained by the nonlinear mixed effects analysis The individual curves for each tree are not convincingly modelled by a lo gistic function Figure 16 16 presents a plot of the residuals from the nonlinear model fitted on p340 of Pinheiro and Bates 2000 The distinct pattern in the residuals which is the same for all trees is taken up in our analysis by the season term Residual abe ooz 000L 008 009 oor 002 oorl 0091 Figure 16 16 Plot of the residuals from the nonlinear model of Pinheiro and Bates 318 16 10 Generalized Linear Mixed Models 16 10 Generalized Linear Mixed Models ASReml uses an approximate likelihood technique called penalized quasi likelihood PQL see section 6 8 to analyse data sampled from one of the common members of the exponential family In this section we present a few examples to demonstrate the coding in ASReml 16 10 1 Binomial analysis of Footrot score Mohommad Alwan pers comm for his Master thesis at Massey University scored the feet of 2513 lambs born in 1980 and 1981 The lambs were from 5 mating groups 7 Perendale rams over Perendale ewes in 1980 6 Booroola by Romney rams over Perendale ewes in 1980 3 Booroola rams over Romney ewes in 1980 6 Perendale rams over Perendale e
232. control group This reflects the fact that in the absence of bloodworms the potential maximum root area is greater Note that the tmt variety interaction variance for the treated group is negative The negative component 304 16 8 Paired Case Control study Rice is meaningful and in fact necessary and obtained by use of the GU option in this context since it should be considered as part of the variance structure for the combined variety main effects and treatment by variety interactions That is o 03 o var 12 69 444 U2 o ae o ge Q Lia 16 8 Using the estimates from table 16 8 this structure is estimated as 3 84 2 33 2 33 1 96 SL Thus the variance of the variety effects in the control group also known as the genetic variance for this group is 3 84 The genetic variance for the treated group is much lower 1 96 The genetic correlation is 2 33 v 3 84 1 96 0 85 which is strong supporting earlier indications of the dependence between the treated and control root area Figure 16 8 16 8 2 A multivariate approach In this simple case in which the variance heterogeneity is associated with the two level factor tmt the analysis is equivalent to a bivariate analysis in which the two traits correspond to the two levels of tmt namely sqrt rootwt for control and treated The model for each trait is given by Yi XTj Zw Zur e J 61 16 9 where y is a vector of length n 132 containing the sqrtroot
233. ctor BLUP of u for known cr and p We also note that aoi 15 2 4 Inference Random effects 2 3 What are BLUPs Consider a balanced one way classification For data records ordered r repeats within b treatments regarded as random effects the linear mixed model is y XT Zu e where X 1 9 1 is the design matrix for T the overall mean Z I 8 1 is the design matrix for the b random treatment effects u and e is the error vector Assuming that the treatment effects are random implies that u N Aw o7I for some design matrix A and parameter vector Y It can be shown that re o y 19 Av 2 19 U ro 0 ro 0 where y is the vector of treatment means y is the grand mean The differences of the treatment means and the grand mean are the estimates of treatment effects if treatment effects are fixed The BLUP is therefore a weighted mean of the data based estimate and the prior mean Ay If Y 0 the BLUP in 2 19 becomes 2 m rop u y 17 2 20 ro 0 y 19 2 20 and the BLUP is a so called shrinkage estimate As ro becomes large relative to c the BLUP tends to the fixed effect solution while for small ro relative to 0 the BLUP tends towards zero the assumed initial mean Thus 2 20 represents a weighted mean which involves the prior assumption that the u have zero mean Note also that the BLUPs in this simple case are constrained to sum to zero This i
234. d 2 1 0 388740 0 388740 2 60 0U Trait TEAM UnStructured 2 2 1 2002 1 36533 3 74 OU Trait TAG UnStructured 1 1 0 257159 0 257159 12 09 OU Trait TAG UnStructured 2 1 0 219557 0 219557 5 55 oU Trait TAG UnStructured 2 2 1 92082 1 92082 14 35 OU Covariance Variance Correlation Matrix UnStructured Residual 0 1984 0 4360 0 1289 0 4406 157 8 4 The output for a multivariate analysis Covariance Variance Correlation Matrix UnStructured Trait TEAM 0 3745 0 5436 0 3887 1 365 Covariance Variance Correlation Matrix UnStructured Trait TAG 0 2572 0 3124 0 2196 1 921 Wald F statistics Source of Variation NumDF DenDF F inc Prob 9 Trait 2 33 0 5761 58 lt 001 10 Trait YEAR 4 1162 2 1094 90 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using numerical derivatives Estimate Standard Error T value 1 prey 10 Trait YEAR 2 0 102262 0 290190E 01 3 52 3 1 06636 0 290831E 01 30 67 42 07 5 1 17407 0 433905E 01 27 06 6 2 53439 0 434880E 01 58 28 32 85 9 Trait N Tiar 0 107933 66 13 a 21 0569 0 209095 100 71 78 16 11 Trait TEAM 70 effects fitted 12 Trait TAG 1042 effects fitted SLOPES FOR LOG ABS RES on LOG PV for Section 1 1 00 1 54 10 possible outliers see res file Finished 08 Apr 2008 11 46 37 140 LogL Converged 158 9 Command file Genetic analysis 9 1 Introduction In an animal model or sire model genetic analysis we have data on a set of animals that are
235. d G structures are typically formed as a direct product of particular variance models the order of terms in a direct product must agree with the order of effects in the corre sponding model term variance models may be correlation matrices or variance matrices with equal or unequal variances on the diagonal A model for a correlation matrix eg AR1 can be converted to an equal variance form eg AR1V and to a heterogeneous variance form eg AR1H e variances are sometimes estimated as variance ratios relative to the residual variance These issues are fully discussed in Chapter 2 In this chapter we begin by considering an ordered sequence of variance structures for the NIN variety trial see Section 7 3 This is to introduce variance modelling in practice We then present the topics in detail 7 1 1 Non singular variance matrices When undertaking the REML estimation ASReml needs to invert each variance matrix For this it requires that the matrices be negative definite or positive definite They must not be singular Negative definite matrices will have negative elements on the diagonal of the matrix and or its inverse The exception is the XFA model which has been specifically designed to fit singular matrices Thompson et al 2003 109 7 3 A sequence of structures for the NIN data Let x Aa represent an arbitrary quadratic form for x 1 n The quadratic form is said to be nonnegative definite if Ar gt 0
236. d example 309 marginal distribution 13 Mat rn variance structure 131 measurement error 115 MERGE 211 MET 7 meta analysis 1 missing values 41 97 105 227 NA 41 in explanatory variables 105 in response 105 mixed effects 5 model 5 mixed model 5 equations 15 multivariate 154 specifying 32 model animal 159 338 correlation 11 covariance 11 formulae 85 sire 159 model building 147 moving average 96 multi environment trial 1 7 multivariate analysis 152 305 example 327 half sib analysis 328 Nebraska Intrastate Nursery 26 Negative binomial 102 non singular matrices 109 nonidentifiable 12 objective function 15 observed information matrix 14 operators 88 options command line 197 ordering of terms 106 351 INDEX Ordinal data 101 orthogonal polynomials 97 outliers 244 output files 34 multivariate analysis 156 objects 243 output file extension aov 221 228 apj 221 ask 222 asl 221 231 asp 222 asr 35 221 223 ass 222 dbr 222 dpr 222 231 msv 221 pvc 221 pvs 221 232 233 YES 221 233 rsv 221 238 sln 36 221 226 spr 222 tab 221 240 tsv 66 veo 222 VEL 222 vrb 240 Vvp 222 241 was 222 xml 222 yht 37 221 227 dgiv 165 grr 172 mef 173 sgiv 165 overspecified 12 own models 135 OWN variance structure 134 1F2 135 IT 135 Path DOPATH 206 PATH 208 PC environment 195 pedigree 159
237. d on the inverse of the average information matrix the values at each iteration are printed in the res file The final values are arranged in a table printed with labels and converted if necessary to variances 244 14 5 ASReml output objects and where to find them Table 14 2 Table of output objects and where to find them ASReml output object found in comment 245 15 Error messages 15 1 Introduction Identifying the reason ASReml does not run or does not produce the anticipated results can be a frustrating business This chapter aims to assist you by discussing four kinds of errors If ASReml does not run at all it is a setup or licensing issue which is not discussed in this chapter Coding errors can be classified as e typing errors these are difficult to resolve because we tend to read what we intended to type rather than what we actually typed Section 15 4 demonstrates the consequences of the common typographical errors that users make e wrong coding this arises often from misunderstanding the guide or making assumptions arising from past experience which are not valid for ASReml The best strategy here is to closely follow a worked example or to build up to the required model Sections 15 3 and 15 2 may help as well as reviewing all the relevant sections of this Guide It may be as simple as adding one more qualifier inappropriate model the variance model you propose may not be suited to the data in wh
238. d treatment contrast and u us correspond to random variety treatment by variety run treatment by run and variety by run effects The random effects and error are assumed to be independent Gaussian variables with zero means and variance structures var u o Iy where b is the length of u i 1 5 and var e g The ASReml code for this analysis is Bloodworm data Dr M Stevens pair 132 rootwt run 66 tmt 2 A id 302 16 8 Paired Case Control study Rice variety 44 A rice asd skip 1 DOPATH 1 IPATH 1 sqrt rootwt mu tmt r variety variety tmt run pair run tmt 000 PATH 2 sqrt rootwt mu tmt r variety tmt variety run pair tmt run uni tmt 2 002 tmt variety 2 20 DIAG 1 4 feu 4400 tmt run 2 20 DIAG 1 1 GU 6600 The two paths in the input file define the two univariate analyses we will conduct We consider the results from the analysis defined in PATH 1 first A portion of the output file is 5 LogL 345 306 s2 1 3216 262 d 6 LogL 345 267 Ss2 1 3155 262 df 7 LogL 345 264 s2 1 3149 262 df 8 LogL 345 263 s2 1 3149 262 df Model_Term Gamma Sigma Sigma SE C variety 44 44 1 80947 2 37920 3 01 0 P run 66 66 0 244243 0 321144 0 59 0 P variety tmt 88 88 0 374220 0 492047 1 78 0 P pair 132 132 0 742328 0 976057 2 51 0 P run tmt 132 132 1 32973 1 74841 3 65 0 P Variance 264 262 1 00000 1 31486 4 42 0 P Wald F statistics Source of Variation NumDF DenDF F_inc Prob 7 mu 1 53
239. d_Error Ecode LANCER 24 0894 2 4645 E predicted variety BRULE 21 0728 2 4944 E means REDLAND 28 7954 2 5064 E CODY 23 7728 2 4970 E ARAPAHOE 27 0431 2 4417 E NE83404 25 197 2 4424 E NE83406 25 3797 2 5028 E NE83407 24 3982 2 0882 E CENTURA 26 3532 2 4763 E SCOUT66 29 1743 2 4361 E NE87615 25 1238 2 4434 E NE87619 30 0267 2 4666 E NE87627 19 7126 2 4833 E SED Overall Standard Error of Difference 2 925 SED summary 14 4 6 The res file The res file contains miscellaneous supplementary information including e a list of unique values of x formed by using the fac model term e a list of unique z y combinations formed by using the fac x y model term e legandre polynomials produced by leg model term e orthogonal polynomials produced by pol model term e the design matrix formed for the sp1 model term e predicted values of the curvature component of cubic smoothing splines 233 14 4 Other ASReml output files the empirical variance covariance matrix based on the BLUPs when a J or 1 structure is used this may be used to obtain starting values for another run of ASReml a table showing the variance components for each iteration a figure and table showing the variance partitioning for any XFA structures fitted some statistics derived from the residuals from two dimensional data multivariate re peated measures or spatial the residuals from a spatial analysis will have the units part added to the
240. data and f mv is omitted from this analysis since row column is fitted as a G structure If we had used the augmented data nin89aug asd we would still omit f mv and ASReml would discard the records with missing yield 7 4 Variance structures The previous sections have introduced variance modelling in ASReml using the NIN data for demonstration In this and the remaining sections the syntax is described formally still using the example where appropriate Recall from Equation 2 2 on page 5 that the variance for the random effects in the linear mixed model was defined including an overall scale parameter 6 When this parameter is 1 0 R and G are defined in terms of variances Otherwise they are defined relative to this scale parameter Typically 0 is 1 if there are several residual variances as in the case of multivariate analysis a different residual variance for each trait or multienvironment trials a different residual variance for each trial However for simple analyses with a single residual variance 0 is modelled as the residual variance so that R becomes a correlation matrix 7 4 1 General syntax Variance model specification in ASReml has the following general form variance header line 117 7 4 Variance structures R structure definition lines G structure header and definition lines variance parameter constraints e variance header line specifies the number of R and G structures R structure definition
241. de 1 0000 1257 9763 64 6146 E 2 0000 1501 4483 64 9783 E 3 0000 1404 9874 64 6260 E 4 0000 1412 5674 64 9027 E 5 0000 1514 4764 65 5889 E 23 0000 1311 4888 64 0767 E 24 0000 1586 7840 64 7043 E 25 0000 1592 0204 63 5939 E SED Overall Standard Error of Difference 59 05 AR1 x AR1 units 293 16 6 Spatial analysis of a field experiment Barley variety Predicted_Value Standard_Error Ecode 1 0000 1245 5843 97 8591 E 2 0000 1516 2331 97 8473 E 3 0000 1403 9863 98 2398 E 4 0000 1404 9202 97 9875 E 5 0000 1471 6197 98 3607 E 23 0000 1316 8726 98 0402 E 24 0000 1557 5278 98 1272 E 25 0000 1573 8920 97 9803 E SED Overall Standard Error of Difference 60 51 IB Rep is ignored in the prediction RowBlk is ignored in the prediction Co1B1k is ignored in the prediction variety Predicted_Value Standard_Error Ecode 1 0000 1283 5870 60 1994 E 2 0000 1549 0133 60 1994 E 3 0000 1420 9307 60 1994 E 4 0000 1451 8554 60 1994 E 5 0000 1533 2749 60 1994 E 23 0000 1329 1088 60 1994 E 24 0000 1546 4699 60 1994 E 25 0000 1630 6285 60 1994 E SED Overall Standard Error of Difference 62 02 Notice the differences in SE and SED associated with the various models Choosing a model on the basis of smallest SE or SED is not recommended because the model is not necessarily fitting the variability present in the data Table 16 7 Summary of models for the Slate Hall data REML number of Wald model log likelihood parameters F statistic S
242. de the definition of the averaging set The fourth step is to choose the weights to use when averaging over dimensions in the hyper table The default is to simply average over the specified levels but the qualifier AVERAGE factor weights allows other weights to be specified PRESENT and ASSOCIATE ASAVERAGE generate more complicated averaging processes The basic prediction process is described in the following example yield site variety r site variety at site block predict variety puts variety in the classify set site in the averaging set and block in the ignore set Consequently ASReml implicitly forms the sitexvariety hyper table from model terms site variety and site variety but ignoring all terms in at site block and then averages across the sites to produce variety predictions This prediction will work even if some varieties were not grown at some sites because the site variety term was fitted as random If site variety was fitted as fixed variety predictions would be non estimable for those varieties which were not grown at every site 182 10 3 Prediction 10 3 3 Predict failure It is not uncommon for users to get the message Warning non estimable aliased cell s may be omitted because ASReml checks that predictions are of estimable functions in the sense defined by Searle 1971 p160 and are invariant to any constraint method used Immediate things to check include whether every level of every fixed f
243. ded for use with variety trials which will subseguently be combined in a meta analysis It forms the variance matrix for the predictions inverts it and writes the predicted variety means with the corresponding diagonal elements of this matrix to the pvs file These values are used in some variety testing programs in Australia for a subsequent second stage analysis across many trials Smith et al 2001 A data base is used to collect the results from the individual trials and write out the combined data set The diagonal elements scaled by the variance which is also reported and held in the data base are used as weights in the combined analysis requests that the variance matrix of predicted values be printed to the pvs file PLOT graphic control qualifiers This functionality was developed and this section was written by Damian Collins The PLOT qualifier produces a graphic of the predictions Where there is more than one prediction factor a multi panel trellis arrangement may be used Alternatively one or more factors can be superimposed on the one panel The data can be added to the plot to assist informal examination of the model fit With no plot options ASReml recognising any covariates and noting the size of factors customize how the predictions are plotted by either using options to the PLOT qualifier or by using the graphical interface The graphical interface is accessed by typing Esc when the figure is displayed
244. del showing the sums of squares degrees of freedom and terms in the model There is a limit of d 20 model terms in the screen ASReml will not allow interactions to be included in the screened terms For example to identify which three of my set of 12 covariates best explain my dependent variable given the other terms in the model specify SCREEN 3 SMX 3 The number of models evaluated quickly increases with d but ASReml has an arbitrary limit of 900 submodels evaluated Use the DENSE qualifier to control which terms are screened The screen is conditional on all other terms those in the SPARSE equations being present modifies the format of the s1n file SLNFORM 1 prevents the sln file from being written ISLNFORM 1 is TAB separated sln becomes s1n txt SLNFORM 2 is COMMA separated sln becomes _sln csv SLNFORM 3 is Ampersand separated sln becomes s1n tex See TXTFORM for more detail If SLNFORM is set expanded labelling of the levels in interactions is used because field width is no longer restricted 81 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action I SPATIAL TABFORM n TXTFORM n TWOWAY IVCC n VGSECTORS s YHTFORM f 1YSS r increases the amount of information reported on the residuals obtained from the analysis of a two dimensional regular grid field trial The infor mation is written to the res file con
245. del consisting of the I and C c terms Any c terms are ignored in calculating DenDF for F con using numerical derivatives for computational reasons The terms are ignored for both F inc and F con tests Consider now a nested model which might be represented symbolically by y 1 REGION REGION SITE For this model the incremental and conditional Wald F statistics will be the same However it is not uncommon for this model to be presented to ASReml as y 1 REGION SITE with SITE identified across REGION rather than within REGION Then the nested structure is hidden but ASReml will still detect the structure and produce a valid conditional Wald F statistic This situation will be flagged in the M code field by changing the letter to lower case Thus in the nested model the three M codes would be A and B because REGION SITE is obviously an interaction dependent on REGION In the second model REGION and SITE appear to be independent factors so the initial M codes are A and A However they are not independent because REGION removes additional degrees of freedom from SITE so the M codes are changed from A and Ato a and A When using the conditional Wald F statistic it is important to know what the maximal conditional model MCM is for that particular statistic It is given explicitly in the aov file The purpose of the conditional Wald F statistic is to facilitate inference for fixed effects It is not meant to be presc
246. dressed in this code e ASUV is required and if there had been any missing values in the data the fixed model term mv would also be required e ASReml constructs the R matrix by scaling the reported matrix by the binomial variance calculated from the fitted value of the binomial variate Consequently to avoid over under dispersion being also fitted the residual variance for the binomial trait is fixed at 1 0 by giving its initial value as 1 0 and using the qualifier GFPP e The response variables must be listed before the qualifiers If written as 323 16 10 Generalized Linear Mixed Models Score BIN YVar YVar would be parsed as an argument to BIN rather than as a response variable e Only one categorical response is permitted and it must be specified first Selected output follows Distribution and link Binomial Logit Mu P 1 1 exp XB Warning The LogL value is LogL 894 LogL 894 600 1 co 00 053 On BARUN p o LE LogL 890 LogL 884 159 413 969 941 962 962 961 LogL 885 LogL 892 LogL 896 LogL 897 LogL 897 LogL 897 LogL 897 Deviance from 974 554 431 GLM S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 S2 fit n a a s i PR 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 V Mu 1 Mu N unsuitable for comparing GLM models 5014 df Dev DF 0 6196 5014 df Dev DF 0 6194 50
247. ds KEEP NODUP SKIP fields ITO newfile CHECK SORT Warning Fields in the merged file will be arranged with key fields followed by other fields from the primary file and then fields from the secondary file Table 12 1 List of MERGE qualifiers qualifier action CHECK requests ASReml confirm that fields having a common name have the same contents Discrepancies are reported to the asr file If there are fields with common names which are not key fields and CHECK is omitted the fields will be assumed different and both versions will be copied IKEY keyfields names the fields which are to be used for matching records in the files If the fields have the same name in both file headers they need only be named in association with the primary input file If the key fields are the only fields with common names the KEY qualifier may be omitted altogether If key fields are not nominated and there are no common field names the files are interleaved KEEP instructs ASReml to include in the merged file records from the input file which are not matched in the other input file Missing values are inserted as the values from the other file Otherwise unmatched records are discarded KEEP may be specified with either or both input files INODUP fields Typically when a match occurs the field contents from the second file are combined with the field contents of the first file to produce the merged file The NODUP qu
248. ds when reading in a data file Use of CSKIP for skipping data fields is recommended to avoid confusion 5 5 Transforming the data Transformation is the process of modifying the data for example dividing all of the data values in a field by 10 forming new variables for example summing the data in two fields or creating temporary data for example a test variable used to discard some records from analysis and subsequently discarded Occasional users may find it easier to use a spreadsheet to calculate derived variables than to modify variables using ASReml transformations Transformation qualifiers are listed after data field labels and the field_type if present They define an operation e g often involving an argument a constant or another variable which is performed on a target variable By default the target is the current field but can be changed with the TARGET qualifier For a G group of variables the target is the first variable in the set Using transformations will be easier if you understand the process As ASReml parses the variable definitions it sequentially assigns them column positions in the internal data vector It notes which is the last variable which is not created by say the transformation and that determines how many fields are read from the data file unless overridden by READ qualifier in Table 5 2 ASReml actually reads the data file after parsing the model line It reads a line into a tempor
249. e character may not be included in the name of the level of an alphanumeric variable The qualifier SPECIALCHAR cancels the normal meaning of the character in an input file so that it can be included in the name of a level of an alphanumeric or pedigree variable If class names are being predefined the qualifier SPECIALCHAR must appear before the class names are read in 5 4 3 Ordering factor levels The default order for factor levels when factors are declared with I and A is the order the levels are encountered in the data file SORT declared after A or I on a field definition line will cause ASReml to fit the levels in numeric alphabetical order although they are defined in some other order To control the order levels are defined the level names must be prespecified using the L s qualifier applies only to factors declared A Thus for a variable SEX coded as Male and Female declared SEX A the user cannot know whether it will be coded 1 Male 2 Female or 1 Female 2 Male without looking to see which occurs first in the data file However declaring it as SEX A L Male Female will mean Male is coded 1 Female is coded 2 If it is declared as SEX A SORT the coding order is unspecified but ASReml creates a lookup table after reading the data to arrange levels in sorted order and uses this sorted order when forming the design matrices Consequentially with the SORT qualifier the order of fitted effects will be 1 Female 2 Male
250. e order 1 9 160 37 357 51 Unstructured 15 158 04 377 50 The split plot in time model can be fitted in two ways either by fitting a units term plus an independent residual as above or by specifying a CORU variance model for the R structure as follows yl ya y5 y7 y10 Trait tmt Tr tmt 120 14 Trait 0 CORU 5 283 16 5 Balanced repeated measures Height The two forms for are given by Y ofJ 031 E ol o p J 1 It follows that 2 a 2 2 g oi 05 o p oF 02 units CORU 16 3 16 4 Portions of the two outputs are given below The REML log likelihoods for the two models are the same and it is easy to verify that the REML estimates of the variance parameters satisfy 16 4 viz g 286 310 159 858 126 528 286 386 159 858 286 386 0 558191 lr units H LogL 204 593 S2 224 61 60 df 0 1000 LogL 201 233 52 186 52 60 df 0 2339 LogL 198 453 s2 155 09 60 df 0 4870 LogL 197 041 2 133 85 60 df 0 9339 LogL 196 881 s2 127 56 60 df 1 204 LogL 196 877 s2 126 53 60 df 1 261 Final parameter values 1 2634 Model_Term Gamma Sigma units 14 14 1 26342 159 858 Variance 70 60 1 00000 126 528 CORU LogL 196 975 S2 264 10 60 df 1 000 LogL 196 924 S2 270 14 60 df 1 000 LogL 196 886 S2 278 58 60 df 1 000 LogL 196 877 S2 286 23 60 df 1 000 LogL 196 877 s2 286 31 60 df 1 000 Final parameter values 1 0000 Model_Term Sigma Sigma Variance 70 60 1 00000 2
251. e 5 5 No more than 10 000 variables may be read or formed Data field definitions NIN Alliance Trial 1989 variety A e should be given for all fields in the data file id fields can be skipped and fields on the end pia of a data line without a field definition are raw ignored if there are not enough data fields repl 4 on a data line the remainder are taken from tioc E yield the next line s Jat long e must be presented in the order they appear row 22 in the data file column 11 nin89aug asd skip 1 F we ield mu variet can appear with other definitions on the y y same line data fields can be transformed see below additional variables can be created by transformation qualifiers 46 5 4 Specifying and reading the data 5 4 1 Data field definition syntax Data field definitions appear in the ASReml command file in the form SPACE label field_type transformations e SPACE is now optional e label is an alphanumeric string to identify the field has a maximum of 31 characters although only 20 are ever printed displayed must begin with a letter must not contain the special characters 4 or reserved words Table 6 1 must not be used CSKIP c can be used to skip c default 1 data fields e field_type defines how a variable is interpreted as it is read and whether it is regarded as a factor or variate if specified in the lin
252. e Chapter 2 are returned in nin89 yht see Section 14 3 Other files produced by this job include the aov pvs 34 3 6 Description of output files res tab vvp and veo files see Section 14 4 3 6 1 The asr file Below is nin89 asr with pointers to the main sections The first line gives the version of ASReml used in square brackets and the title of the job The second line gives the build date for the program and indicates whether it is a 32bit or 64bit version The third line gives the date and time that the job was run and reports the size of the workspace The general announcements box outlined in asterisks at the top of the file notifies the user of current release features The remaining lines report a data summary the iteration sequence the estimated variance parameters and a table of Wald F statistics The final line gives the date and time that the job was completed and a statement about convergence ASReml 3 01d 01 Apr 2008 NIN alliance trial 1989 job heading Build e 01 Apr 2008 32 bit 04 Apr 2008 17 00 47 453 32 Mbyte Windows nin89 Licensed to NSW Primary Industries permanent BEA ooo I ACI OK a A A IKK a A 11K kkk kkk kkk kkk kkk kkk k Contact support asreml co uk for licensing and support BECO COO ORK ARG Folder C data asr3 ug3 manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 1 is active Reading nin89 asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of
253. e Kenward and Roger adjustments 19 2 5 Inference Fixed effects 2 5 2 Incremental and conditional Wald F Statistics The basic tool for inference is the Wald statistic defined in equation 2 17 ASReml produces a test of fixed effects that reduces to an F statistic in special cases by dividing the Wald statistic constructed with l 0 by r the numerator degrees of freedom In this form it is possible to perform an approximate F test if we can deduce the denominator degrees of freedom However there are several ways L can be defined to construct a test for a particular model term two of which are available in ASReml These Wald F statistics are labelled F inc for incremental and F con for conditional respectively For balanced designs these Wald F statistics are numerically identical to the F statistics obtained from the standard analysis of variance The first method for computing Wald statistics for each term is the so called incremental form For this method Wald statistics are computed from an incremental sum of squares in the spirit of the approach used in classical regression analysis see Searle 1971 For example if we consider a very simple model with terms relating to the main effects of two qualitative factors A and B given symbolically by y1 A B where the 1 represents the constant term u then the incremental sums of squares for this model can be written as the sequence R 1 RAD R 1 A R 1 R BI
254. e SQRT option allows conversion of CORGH to US provided the dimension is moderate say lt 10 13 2 2 Convert CORUH and XFA to US e V label i where i j spans an XFA variance structure inserts the US matrix based on the XFA parameters e V label i j where i j spans an CORUH variance structure inserts the US matrix based on the CORUH parameters The variances and covariances are calculated using a Taylor series expansion Then for parameters vg and v derived from the a of parameters a with variance matrix V if Va falv and v filv then if dv Mato and if v 4 then cov u Ub OU Vous 13 2 3 Correlation Correlations are requested by lines beginning VPREDICT DEFINE with an R The specific form of the directive F phenvar 1 3 4 6 is F phenvar Sire Trait Residual R phencorr 7 8 9 phenvar R label a ab b R gencorr 4 6 Sire This calculates the correlation r o y 0207 and the associated standard error a b and ab are integers indicating the position of the components to be used Alternatively R label a n calculates the correlation r 0 p 020 for all correlations in the lower triangular row wise matrix represented by components a to n and the associated standard errors Note that covariances between ratios and other components are not generated so the corre lations are not numbered and cannot be used to derive other functions To avoid numbering confusion it is better to include
255. e a factor and the number of lev els in the new factor is set to the number of levels identified in this se quential process see Other exam ples below Missing values remain missing changes the focus of subsequent transformations to variable field v replaces the variate with uniform random variables having range 0 v 57 treat ILCA B CYR treat ISET 1 1 1 group treat ISET 1 2293 4 Anorm A SETN 2 5 10 Aeff A ISETU 5 10 year 3 SUB 66 67 68 plot V3 SEQ sqrtA meanAB A 2 TARGET sqrtA 70 5 Udat 1 0 UNIFORM 4 5 5 5 Transforming the data Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples Vtarget value assigns value to data field tar V3 2 5 get overwriting previous contents subsequent transformation qualifiers will operate on data field target Vfield assigns the contents of data field V10 V3 field to data field target overwriting V1i1 block previous contents subsequent trans V12 V0 formation qualifiers will operate on data field target If field is 0 the number of the data record is in serted 5 5 2 QTL marker transformations IMM s associates marker positions in the vector s based on the Haldane mapping function with marker variables and replaces missing values in a vector of marker states with expected values calculated using distances to non missing flankin
256. e and qualifiers gt nin89 asd skip 1 tabulate statement gt tabulate yield variety linear mixed model definition gt yield mu variety r repl predict statement gt predict variety variance model specification gt 00 1 repl i repl 0 IDV 0 1 3 4 1 The title line The first text non blank non control line in NIN Alliance trial 1989 an ASReml command file is taken as the title variety A for the job and is purely descriptive for future id reference 30 3 4 The ASReml command file 3 4 2 Reading the data The data fields are defined before the data file name is specified Field definitions must be given for all fields in the data file and in the order in which they appear in the data file Note that in previous releases data field definitions had to be indented but in Release 4 this condition has been relaxed and is not required In this case there are 11 data fields variety column in nin89 asd see Sec tion 3 3 The A after variety tells ASReml that the first field is an alphanumeric factor and the 4 after repl tells ASReml that the field called repl the fifth field read is a numeric factor with 4 levels coded 1 4 Similarly for row and NIN Alliance trial 1989 variety A id pid raw repl 4 nloc yield lat long row 22 column 11 nin89 asd skip 1 column The other fields include variates yield and various other variables 3 4
257. e another at the same trial site with trials sharing a common plot boundary In this case it might be sensible to fit the same spatial parameters and error variances for each trial In other situations it can be sensible to define the same variance structure over several model terms ASReml 3 catered for equality and multiplicative relationships among variance parameters In ASReml 4 linear relationships among variance structure parameters can be defined through a simple linear model and by supplying a design matrix for a set of parameters The design matrix is supplied as an ascii file containing a row for each parameter in a set of contiguous parameters and a column for each new parameter This design matrix is associated with the job through a statement after the residual model definition line s of the form VCM parameter_number_list new filename where parameter_number_list is a list of parameters in the set and can be abbreviated to first and last if all the intermediate parameters are in the set new is the number of new parameters and filename is the name of the file containing the design matrix For example the Wolfinger rats example involves modelling a 5x5 symmetric residual ma trix Wolfinger Rat data 144 7 9 Constraining variance parameters treat A wt0 wtl wt2 wt3 wt4 subject V0 wolfrat dat skip 1 wt0 wti wt2 wt3 wt4 Trait treat Trait treat 120 27 0 ID terror variance Trait 0 US indicates generates
258. e continuation symbol is used to indicate that some of the original code is omitted Data examples are displayed in larger boxes in the body of the text see for example page 40 Other conventions are as follows keyboard key names appear in SMALLCAPS for example TAB and ESC e example code within the body of the text is inthis size and font and is highlighted in bold type see pages 33 and 49 e in the presentation of general ASReml syntax for example path asrem1 basename l as arguments typewriter font is used for text that must be typed verbatim for example asreml and as after basename in the example italic font is used to name information to be supplied by the user for example basename stands for the name of a file with an as filename extension square brackets indicate that the enclosed text and or arguments are not always re quired Do not enter these square brackets e ASReml output is in this size and font see page 35 e this font is used for all other code 2 Some theory 2 1 The general linear mixed model If y n x 1 denotes the vector of observations the general linear mixed model can be written as y XT Zut e 2 1 where 7 p x 1 is a vector of fixed effects X n x p is the design matrix of full column rank that associates observations with the appropriate combination of fixed effects u q x 1 is a vector of random effects Z n x q is the design matrix that associates observa
259. e declared size of the error structures does not match the actual number of data records There is some problem on the SPLINE line It could be a wrong variable name or the wrong number of knot points Knot points should be in increasing order Try increasing workspace The problem may be due to the use of the SORT qualifier in the data definition section May be an unrecognised factor model term name or variance structure name or wrong count of initial values possible on an earlier line May be insufficient lines in the job Check your MYOWNGDG program and the gdg file Maybe increase WORKSPACE Messages may identify a prob lem with the pedigree This indicates the job needs more memory than was allocated or is available Try increasing the workspace or simplifying the model Likely causes are bad syntax or invalid characters in the variable labels vari able labels must not include any of these symbols and the data file name is misspelt there are too many variables declared or there is no valid value supplied with an arithmetic transformation option 266 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy G structure header Factor order G structure ORDER O MODEL GAMMAS G structure size does not match Getting Pedigree GLM Bounds failure Incr
260. e implication of the syntax However the target is reset for each transformation so that the transformations apply to the same set of variables Y1 Y2 Y3 Y4 Y5 Repeat 5 times incrementing just Ymean 0 D0 5 0 1 Y1 ENDDO 5 the argument is equivalent to Y1 Y2 Y3 Y4 Y5 Ymean 0 Y1 Y2 Y3 Y4 Y5 5 YO Y1 Y2 Y3 Y4 Y5 TARGET Y1 do 5 1 O YO ENDDO Take YO from rest Markers G 12 do D ENDDO Delete records with missing marker values The default arguments 12 1 0 are used The initial target is the first marker 5 5 3 Remarks concerning transformations Note the following e variables that are created should be listed after all variables that are read in unless the intention is to overwrite an input field e missing values are unaffected by arithmetic operations that is missing values in the current or target column remain missing after the transformation has been performed except in assignment 3 will leave missing values NA and as missing 3 will change missing values to 3 e multiple arithmetic operations cannot be expressed in a complex expression but must be given as separate operations that are performed in sequence as they appear for example yield 120 0 0333 would calculate 0 0333 yield 120 59 5 5 Transforming the data e Most transformations only operate on a single field and will not therefore be performed on all variables in a G factor set The only transf
261. e is all missing there must be at least 3 distinct data values for a spline term If ASReml has not obtained the maximum available workspace then use WORKSPACE to increase it The problem could be with the way the model is specified Try fitting a simpler model or using a reduced data set to discover where the workspace is being used The response variable nominated by the YVAR command line qualifier is not in the data The data values are out of the expected range for bi nary binomial data there is a problem with forming one of the generated fac tors The most probable cause is that an interaction cannot be formed You must either use the US error structure or use the ASUV qualifier and maybe include mv in the model a term in the model specification is not among the terms that have been defined Check the spelling there is a problem with the named variable 267 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy Invalid SOURCE in R structure definition Invalid weight filter column number Iteration aborted because of singularities Iteration failed Matern Maximum number of special structures exceeded Maximum number of variance parameters exceeded Missing faulty SKIP or A needed for Missing values in design variables factors Missing Value Miscount formin
262. e mode for the regressor data indicating whether it is marker data b 2 sets 2bit storage for strictly 0 1 2 marker data b 8 the default sets 8bit storage useful for marker data with imputed values having 2 digits after the decimal b 16 sets 16bit storage useful for marker data with imputation with more than 2 digits and b 32 sets 32bit real storage and should be used for non marker data IRANGE I h indicates the marker scores range l h and are to be transformed to have a range 0 2 IGSCALE s controls the scaling of the GRM matrix If unspecified s X2p 1 p is used for marker data s 1 for non marker data SMODE 32 Scaling is often used with centred marker data to scale the MM matrix so that it is a genomic matrix Example WORK 1 Nassau Clone Data Nfam 71 A Nfemale 26 A Nmale 37 A Clone A 860 rep 8 iblk 80 culture A DBH6 snpData grr Clone Marker nassau csv MAXIT 30 SKIP 1 DFF 1 DBH6 mu culture rep r grmi Clon 0 27 Clone 0 15 rep iblk 0 31 where snpData grr is first used to declare Clone identifiers taken from the first field in the correct order and then contains the marker scores it looks like Genotype 0 10024 01 114 0 10037 01 257 0 10040 02 394 140099 2 2 1 2 2 2 2 2 2 1 2 1 2 1 1 2 1 2 2 2 2 2 1 2 141099 2 2 0 0 2 2 1 2 2 1 2 1 2 2 0 2 2 2 2 1 2 2 1 1 173 9 8 Factor effects with large Random Regression models 547853 2 2 1 2 2 2 547966 2 2 1 1 1 2 548082
263. e not expected Normally when no TOLERANCE qualifier is specified a singularity is declared if the adjusted sum of squares of a covariable is less than a small constant 7 or less than the uncorrected sum of squares x7 where y is 1078 in the first iteration and 10 1 thereafter The qualifier scales 7 by 10 for the the first or subsequent iterations respectively so that it is more likely an equation will be declared singular Once a singularity is detected the corresponding equation is dropped forced to be zero in subsequent iterations If neither argument is supplied 2 is assumed If the second argument is omitted it is given the value of the first If the problem of later singularities arises because of the low coefficient of variation of a covariable it would be better to centre and rescale the covariable If the degrees of freedom are correct in the first iteration the problem will be with the variance parameters and a different variance model or variance constraints is required requests writing of vrb file Previously the default was to write the file 84 6 Command file Specifying the terms in the mixed model 6 1 Introduction The linear mixed model is specified in ASReml as a series of model terms and qualifiers In this chapter the model formula syntax is described 6 2 Specifying model formulae in ASReml The linear mixed model is specified in ASReml as a se NIN Alliance Trial 1989 ries of model te
264. e on page 327 1 A white paper downloadable from http www vsni co uk products asreml user PedigeeNotes pdf contains details of these options 162 9 4 Reading in the pedigree file Table 9 1 List of pedigree file qualifiers qualifier description ALPHA DIAG AIF IFGEN f IGIV GOFFSET o IGROUPS g INBRED indicates that the identities are alphanumeric with up to 225 characters otherwise by default they are numeric whole numbers lt 200 000 000 If using long alphabetic identities use SLNFORM to see the full identity in the s1n file causes the pedigree identifiers the diagonal elements of the Inverse of the Relationship and the inbreeding coefficients for the individuals calculated as the diagonal of A I to be written to basename aif indicates the pedigree file contains a fourth field indicating the level of selfing or the level of inbreeding in a base individual In the fourth field 0 indicates a simple cross 1 indicates selfed once 2 indicates selfed twice etc A value between 0 and 1 for a base individual is taken as its inbreeding value If the pedigree has implicit individuals they appear as parents but not in the first field of the pedigree file they will be assumed base non inbred individuals unless their inbreeding level is set with FGEN f where 0 lt f lt 1 is the inbreeding level of such individuals instructs ASReml to write out the A inverse in the format of g
265. e residuals from the current model This diagnostic and a summary of row and column residual trends are produced by default with graphical versions of ASReml when a spatial model has been fitted to the errors It can be suppressed by the use of the n option on the command line We have produced the following plots by use of the g22 option Table 16 6 Field layout of Slate Hall Farm experiment Column Replicate levels Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 2 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 5 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 6 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 7 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 8 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 9 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 10 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 Column Rowblk levels Row 1 2 3 4 5 6 T 8 9 10 11 12 13 14 15 1 1 1 1 1 1 11 11 11 11 11 21 21 21 21 21 2 2 2 2 2 2 12 12 12 12 12 22 22 22 22 22 3 3 3 3 3 3 13 13 13 13 13 23 23 23 23 23 4 4 4 4 4 4 14 14 14 14 14 24 24 24 24 24 5 5 5 5 5 5 15 15 15 15 15 25 25 25 25 25 6 6 6 6 6 6 16 16 16 16 16 26 26 26 26 26 7 7 iC 7 7 7 17 17 17 17 17 27 27 27 27 27 8 8 8 8 8 8 18 18 18 18 18 28 28 28 28 28 9 9 9 9 9 9 19 19 19 19 19 29 29 29 29 29 10 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 Column Colblk levels Row 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 2 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3 i 2 3 4 5 6 7 8 9
266. e zero at the first and last knot points Green and Silverman 1994 The ASReml job is this is the orange data for tree 1 seq record number is not used Tree 5 age 118 484 664 1004 1231 1372 1582 irg season L Spring Autumn orange asd skip 1 filter 2 select 1 ISPLINE spl age 7 118 484 664 1004 1231 1372 1582 IPVAL age 150 200 1500 circ mu age r spl age 7 predict age Note that the data for tree 1 has been selected by use of the filter and select qualifiers Also note the use of PVAL so that the spline curve is properly predicted at the additional nominated points These additional data points are required for ASReml to form the de 311 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges sign matrix to properly interpolate the cubic smoothing spline between knot points in the prediction process Since the spline knot points are specifically nominated in the SPLINE line these extra points have no effect on the analysis run time The SPLINE line does not modify the analysis in this example since it simply nominates the 7 ages in the data file The same analysis would result if the SPLINE line was omitted and spl age 7 in the model was replaced with spl age An extract of the output file is 1 LogL 20 9043 S2 48 470 5 df 0 1000 1 000 2 LogL 20 9017 S2 49 022 5 df 0 9266E 01 1 000 3 LogL 20 8999 S2 49 774 5 df 0 8356E 01 1 000 4 LogL 20 8996 S2 50 148 5 df 0 7937
267. ear model for a variate leave field_type blank or specify 1 for a model factor various qualifiers are required depending on the form of the factor coding where n is the number of levels of the factor and sis a list of labels or the name of a file containing the labels one per row to be assigned to the levels Or nN is used when the data field has values 1 n directly coding for the factor unless the levels are to be labelled see L Row 1 12 for example is used when the data field is numeric with values 1 n and labels are to be assigned to the n levels for example Sex L Male Female is required if the data field is alphanumeric for example Location A names Specify n if there are more than 1000 classes over all class factor variables indicating the expected number for this factor 47 5 4 Specifying and reading the data IA IL is used if the data field is alphanumeric and must be coded in a particular s order to set the order of the levels For example SNP A L C C C T T T defines the levels over riding the default data dependent order If there are many labels they may be written over several lines by using a trailing comma to indicate continuation of the list New R4 Alternatively the labels may be listed in a file If the filename includes embedded blanks or has no file extension it must be enclosed in quotes Genotype A L MyNames txt Genotype A L My Names txt Genotype A L MyNames
268. ease declared levels for factor Increase workspace Insufficient data read from file Insufficient points for Insufficient workspace invalid analysis trait number Invalid binary data Invalid Binomial Variable Invalid definition of factor Invalid error structure for Multivariate Analysis Invalid factor in model Invalid model factor there is a problem reading G structure header line An earlier error for example insufficient initial values may mean the ac tual line read is not actually a G header line at all A G header line must contain the name of a term in the linear model spelt exactly as it appears in the model a G structure line cannot be interpreted The size of the structure defined does not agree with the model term that it is associated with an error occurred processing the pedigree The pedigree file must be ascii free format with ANIMAL SIRE and DAM as the first three fields ASReml failed to calculate the GLM working variables or weights Check the data Either the field has alphanumeric values but has not been de clared using the A qualifier or there is not enough space to hold the levels of the factor To increase the levels insert the expected number of levels after the A or I qualifier in the field definition Use WORKSPACE s to increase the workspace available to AS Reml If the data set is not extremely big check the data summary Maybe the response variabl
269. ect product R structure does not match the multivariate data structure Maybe a trait name is repeated This is typically caused by negative variance parameters try changing the starting values or using the STEP option If the problem occurs after several iterations it is likely that the vari ance components are very small Try simplifying the model In multivariate analyses it arises if the error variance is becomes negative definite Try specifying GP on the structure line for the error variance too many terms are being defined Fix the argument to giv 268 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy No residual variation Dut of Out of memory Out of memory forming design Overflow structure table Pedigree coding errors Pedigree factor has wrong size Pedigree too big or in error POWER model setup error POWER Model Unique points disagree with size PROGRAM failed in PROGRAMMING error reading SELF option Reading distances for POWER structure after fitting the model the residual variation is essentially zero that is the model fully explains the data If this is intended use the BLUP 1 qualifier so that you can see the estimates Otherwise check that the dependent values are what you intend and then identify which variables explain it Again
270. ed Linear Mixed Models Wald F statistics Source of Variation NumDF F_inec 4 Trait 8 17 45 1 Cheese 3 38 38 Warning These Wald F statistics are based on the working variable and are not equivalent to an Analysis of Deviance Standard errors are scaled by the variance of the working variable not the residual deviance Finished 17 Jun 2008 13 19 51 484 LogL Converged 16 10 4 Multinomial Ordinal GLMM analysis of Footrot score Reverting to the collapsed lamb data the two response variables FS1 and FS2 contain counts of the lambs with all feet sound and with one foot deformed respectively The count for those with two or more deformed is given by difference from Total A threshold model analysis of this data is given by the model line FS1 FS2 mult 3 TOTAL Total Trait SEX GRP r SIRE with output Notice 1 singularities detected in design matrix 1 LogL 105 631 S2 1 0000 129 df Dev DF 1 082 2 LogL 105 632 S2 1 0000 129 df Dev DF 1 082 3 LogL 105 631 S2 1 0000 129 df Dev DF 1 081 4 LogL 105 628 S2 1 0000 129 df Dev DF 1 080 5 LogL 105 627 S2 1 0000 1239 di Dev DF 1 079 6 LogL 105 627 S2 1 0000 129 di Dev DF 1 078 Deviance from GLM fit 128 139 09 Variance heterogeneity factor Deviance DF 1 08 Results from analysis of FS1 FS2 Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed
271. ed and the SIRE variance is too large to represent purely genetic variance 324 16 10 Generalized Linear Mixed Models 16 10 3 Multinomial Ordinal GLM analysis of Cheese taste By way of introduction to ordinal analysis in ASReml consider the cheese data from page 175 of McCullagh and Nelder 1994 Four cheeses were scored on a nine point scale by 52 tasters giving Table 16 13 Response frequencies in a cheese tasting experiment Cheese I IT IH IV V VI VI VHI IX Total A 00 1 7 8 8 19 a 1 52 B 6 9 12 11 7 6 1 0 0 52 C 1 1 6 8 23 7 5 1 0 52 D 0 0 0 1 3 7 14 16 11 52 There are several ways of supplying the data for multinomial analysis In this case totals in the 9 classes are supplied in a single grouped response It is analysed using a multiple 8 threshold model as in McCullagh and Nelder 1994 with the ASReml code McCullagh and Nelder Cheese example p 175 Cheese A Rating G 9 Total Cheese txt Rating MULT 9 CUM Trait Cheese PREDICT Cheese where Cheese txt contains the data laid out as in Table 16 13 2 e 4 rows and 10 columns The model term Trait fits the thresholds and interpreting the model as a threshold model implies it should not be interacted with other terms Nevertheless sometimes an interaction is fitted Note that ASReml does not have a procedure for multinomial data which is not ordered except as fitted with a log linear model and fitting a bivariate analysis involving a multinomial trait is not poss
272. edict YEAR Trait SheepID Site Bloodline Team Year GFW Yield FD 0101 3 21 1 1 5 6 74 3 18 5 0101 321 1 2 6 0 711 2 19 6 0101 321 1 3 8 0 79 1 21 5 0102 3 21 1 1 5 3 70 9 20 8 0102 3 21 1 2 5 7 66 1 20 9 0102 3 21 1 3 6 8 70 3 22 1 0103 3 21 1 1 5 0 80 7 18 9 0103 3 21 126 5 75 5 19 9 0103 3 21 1 3 7 0 76 6 21 9 4013 3 43 35 1 7 9 75 9 22 6 4013 3 43 35 2 7 8 70 3 23 9 4013 3 43 35 3 9 0 76 2 25 4 4014 3 43 35 1 8 3 66 5 22 2 4014 3 43 35 2 7 8 63 9 23 3 4014 3 43 35 3 9 9 69 8 25 5 4015 3 43 35 1 6 9 75 1 20 0 4015 3 43 35 2 7 6 71 2 20 3 4015 3 43 35 3 8 5 78 1 21 7 153 8 2 Model specification 8 2 Model specification The syntax for specifying a multivariate linear model in ASReml is Y variates fixed r random f sparse_fized e Y variates is a list of up to 20 traits there may be more than 20 actual variates if the list includes sets of variates defined with G on page 49 e fired random and sparse_fixed are as in the univariate case see Chapter 6 but involve the special term Trait and interactions with Trait The design matrix for Trait has a level column for each trait Trait by itself fits the mean for each variate In an interaction Trait Fac fits the factor Fac for each variate and Trait Cov fits the covariate Cov for each variate ASReml internally rearranges the data so that n data records containing t traits each becomes n sets of t analysis records indexed by the internal f
273. edigree with the IGIV 2 qualifier will create a pedigree file just containing the parents and also the Q giv file for the non parent referred to below If we assume a heritability of 0 1111 so that the ratio of genetic variance to residual variance is 0 125 the following model will estimate the breeding values for the parents directly RAM BLUP model tree mum P V21 dad P V21 row column plot DBH Aldiag V21 NP A L Nonparent Parent parent P filter NP 1 create Nonparent filter mum filter dad filter Aldiag filter WT 0 125 Aldiag 1 Aldiag 1 filter ParentPed txt ramdbh txt DBH WT WT mu lr parent and mum 0 5 and dad 0 5 plot column row 007 parent 1 parent 0 NRM 0 125 column row 2 170 9 8 Factor effects with large Random Regression models column O AR V x row O ARi In this model e NP A L Nonparent Parent ensures the NP data field is coded 1 for non parents and 2 for parents filter NP 1 creates a variable that is 1 for non parents and zero for parents The filter transformations put mum dad and Aldiag information to zero for parents WT 0 125 Aldiag 1 Aldiag 1 V21 creates a weight variable which is 1 for parent records q q 7 for a non parent record with q the respective diagonal element of Aldiag with q 2 for non inbred non parents and y is the variance ratio g3 ca 0 125 in this case This weighting corresponds
274. een drawn Varieties with large positive deviations from the regression line include YRK3 Calrose HR19 and WC1403 An alternative definition of tolerance is the simple difference between treated and control BLUPs for each variety namely u Uy Unless 6 1 the two measures e and have very different interpretations The key difference is that is a measure which is independent of inherent vigour whereas is not To see this consider cov w cov ty Buy w Over 2 Ove T a Cue Laa Co 308 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges BLUP regression residual dnd onuos Figure 16 10 Estimated deviations from regression of treated on control for each variety plotted against estimate for control whereas COV ty Uy Y o7 m Tiss IE The independence of e and u and dependence between and w is clearly illustrated in Figures 16 10 and 16 11 In this example the two measures have provided very different rankings of the varieties The choice of tolerance measure depends on the aim of the experi ment In this experiment the aim was to identify tolerance which is independent of inherent vigour so the deviations from regression measure is preferred 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges We now illustrate the use of random coefficients and cubic smoothing splines for
275. el The model specified here for the NIN data is a simple random effects RCB model having fixed vari ety effects and random replicate effects The reserved word mu fits a constant term inter cept variety fits a fixed variety effect and repl fits a random replicate effect The r qualifier tells ASReml to fit the terms that follow as random effects 3 4 6 Prediction Prediction statements appear after the model statement and before any variance structure lines In this case the 56 variety means for yield as predicted from the fitted model would be formed and returned in the pvs output file See Chapter 10 for a detailed discussion of prediction in ASReml 3 4 7 Variance structures The last three lines are included for exposi tory purposes and are not actually needed for this particular analysis An extensive range of variance structures can be fitted in ASReml See Chapter 7 for a lengthy discussion of vari ance modelling in ASReml In this case in dependent and identically distributed random replicate effects are specified using the iden tifier IDV in a G structure G structures are described in Section 2 1 and the list of avail able variance structures models is presented NIN Alliance trial 1989 variety A column 11 nin89 asd skip 1 tabulate yield variety yield mu variety r repl predict variety 001 repl i rep 0 IDV 0 1 NIN Alliance trial 1989 variety A column 11 nin89 asd skip
276. eld lat long row column LANCER 1 NA NA 1 4 NA 4 3 1 2 1 1 LANCER 1 NA NA 1 4 NA 4 3 2 4 2 1 LANCER 1 NA NA 1 4 NA 4 3 3 6 3 1 LANCER 1 NA NA 1 4 NA 4 3 4 8 4 1 variety A id pid raw rep nloc x yield lat long row column Check Correct these field definitions nin89aug asd SKIP 1 column mu Specify fixed model ly Specify random model 120 column column AR1 0 1 row row AR1 0 1 This is a template in that it needs editing it has nominated an inappropriate response variable but it displays the first few lines of the data and infers whether fields are factors or variates as follows Missing fields and those with decimal points in the data value are taken as covariates integer fields are taken as simple factors and alphanumeric fields are taken as A factors 3 6 Description of output files A series of output files are produced with each ASReml run Nearly all files all that contain user information are ASCII files and can be viewed in any ASCII editor including ASReml W ConText and NotePad The primary output from the nin89 as job is written to nin89 asr This file contains a summary of the data the iteration sequence estimates of the variance parameters and an a table of Wald F statistics for testing fixed effects The estimates of all the fixed and random effects are written to nin89 sln The residuals predicted values of the observations and the diagonal elements of the hat matrix se
277. elihood of the restricted model that is the REML log likelihood under the null hypothesis then the REMLRT is given by D 2log p2 m 2 log Lo log Lz1 2 21 which is strictly positive If r is the number of parameters estimated in model then the asymptotic distribution of the REMLRT under the restricted model is eee The REMLRT is implicitly two sided and must be adjusted when the test involves an hy pothesis with the parameter on the boundary of the parameter space It can be shown that for a single variance component the theoretical asymptotic distribution of the REMLRT is a mixture of x variates where the mixing probabilities are 0 5 one with O degrees of free dom spike at 0 and the other with 1 degree of freedom The approximate P value for the REMLRT statistic D is 0 5 1 Pr x7 lt d where d is the observed value of D This has a 5 critical value of 2 71 in contrast to the 3 84 critical value for a x variate with 1 degree of freedom The distribution of the REMLRT for the test that k variance components are zero or tests involved in random regressions which involve both variance and covariance components involves a mixture of x variates from 0 to k degrees of freedom See Self and Liang 1987 for details Tests concerning variance components in generally balanced designs such as the balanced one way classification can be derived from the usual analysis of variance It can be shown that the REMLRT
278. ells of the hyper table that have no information and therefore cannot be averaged in a meaningful way Appropriate use of the AVERAGE and or PRESENT qualifiers will usually resolve the problem The PRESENT qualifier enables the construction of means by averaging only the estimable cells of the hyper table where this is appropriate Table 10 1 is a list of the prediction qualifiers with the following syntax e fis an explanatory variable which is a factor e tis a list of terms in the fitted model e nis an integer number e vis a list of explanatory variables 183 10 3 Prediction Table 10 1 List of prediction qualifiers qualifier action Controlling formation of tables ASSOCIATE Lu IAVERAGE f weights IAVERAGE f gt file n ASAVERAGE f weights ASAVERAGE f gt file n PARALLEL v PRESENT v IPRWTS v facilitates prediction when the levels of one factor are grouped by the levels of another in a hierarchical manner More details are given below Two independent associate lists may be specified is used to formally include a variable in the averaging set and to explicitly set the weights for averaging Variables that only appear in random model terms are not included in the averaging set unless specified with the AVERAGE ASSOCIATE or PRESENT qualifiers Explicit weights may be supplied directly or from a file The default is equal weights weights can be expressed l
279. emod asr and bsiremod vvp 1 error variance for ywt 2 error covariance for ywt and fat 3 error variance for fat 4 sire variance component for ywt 5 sire covariance for ywt and fat 6 sire variance for fat then F phenvar Residual Trait sire or F phenvar Residual sire or F phenvar 1 3 4 6 creates new components 7 1 4 8 2 5 and 9 3 6 F addvar sire Trait 4 or F addvar 4 6 4 creates new components 10 4 x 4 11 5 x 4and 12 6 x 4 218 13 3 VPREDICT PIN file processing H heritA addvar 1 phenvar 1 forms 10 7 to give the heritability for ywt H heritB addvar 3 phenvar 3 forms 12 9 to give the heritability for fat R phencorr phenvar forms 8 y7 x 9 that is the phenotypic correlation between ywt and fat R gencorr addvar forms 5 v4x6 that is the genetic correlation between ywt and fat The resulting pvc file contains Residual 1 0 4 0 Om amp 02 b2 9 10 11 12 13 14 15 16 Residual Residual Residual Residual Residual Residual Trait sire Trait sire Trait sire phenvar 1 phenvar 2 phenvar 3 addvar 4 addvar 5 addvar 6 heritA addvar heritB phenco 2 1 gencor 2 1 addvar 8140 effe 24 664 2 6343 1 6974 5 8328 0 52112 0 13775 10 phenvar 12 phenvar phenv 8 SQR phenv addva 11 SQR addva 10 addva 12 cts lt a lt lt Q Qa lt OF NM ND amp 2 0 64250 0 14763 0 52366E 01 1 5926 0 27170 0 67 799E 01 7 9 T phenv
280. ems vi and emacs are commonly used Under Windows there are several suitable program editors available such as ASReml W and ConText described in Section 1 3 3 2 Nebraska Intrastate Nursery NIN field experiment The yield data from an advanced Nebraska Intrastate Nursery NIN breeding trial conducted at Alliance in 1988 89 will be used for demonstration see Stroup et al 1994 for details Four replicates of 19 released cultivars 35 experimental wheat lines and 2 additional triticale lines were laid out in a 22 row by 11 column rectangular array of plots the varieties were allocated to the plots using a randomised complete block RCB design In field trials complete replicates are typically allocated to consecutive groups of whole columns or rows In this trial the replicates were not allocated to groups of whole columns but rather overlapped columns Table 3 1 gives the allocation of varieties to plots in field plan order with replicates 1 and 3 in rTALICS and replicates 2 and 4 in BOLD 26 Table 3 1 Trial layout and allocation of varieties to plots in the NIN field trial column row 1 2 3 4 5 6 7 8 9 10 11 1 NE83407 BUCKSKIN NE8S7612 VONA NE87512 NE87408 CODY BUCKSKIN NE87612 KS831374 2 CENTURA NE86527 NE87613 NE87463 NE83407 NE83407 NE8S7612 NE83406 BUCKSKIN NE86482 3 SCOUT66 NE86582 NE87615 NE86507 NE87403 NORKAN NE87457 NE87409 NE85556 NE85623 4 COLT NE86606 NE8S7619 BUCKSKIN NE87457 REDLAND NE84557 NE87499 BRULE NE8
281. ent matrix pertaining to FACPOINTS n IKNOTS n NOCHECK NOREORDER NOSCRATCH POLPOINTS n PPOINTS n the n term in the linear model Because the model has not been defined when ASReml reads this line it is up to the user to count the terms in the model to identify the portion of the inverse of the coefficient matrix to be printed The option is ignored if the portion is not wholly in the SPARSE stored equations The portion of the inverse is printed to a file with extension cii The sparse form of the matrix only is printed in the form i j CY that is elements of CY that were not needed in the estimation process are not included in the file affects the number of distinct points recognised by the fac model func tion Table 6 1 The default value of n is 1000 so that points closer than 0 1 of the range are regarded as the same point changes the default knot points used when fitting a spline to data with more than n different values of the spline variable When there are more than n default 50 points ASReml will default to using n equally spaced knot points forces ASReml to use any explicitly set spline knot points see SPLINE even if they do not appear to adequately cover the data values prevents the automatic reversal of the order of the fixed terms in the dense equations and possible reordering of terms in the sparse equations forces ASReml to hold the data in memory ASReml will usually hold the dat
282. er triangular with ones on the diagonal D is diagonal and k is the number of non zero off diagonals in U the CHOLk and ANTEk models are equivalent to the US structure that is the full variance structure when k is w 1 initial values for US CHOL and ANTE structures are given in the form of a US matrix which is specified lower triangle row wise viz co Fm Yo 3 932 O33 11 that is initial values are given in the order 1 o 2 0 3 0 the US model is associated with several special features of ASReml When used in the R structure for multivariate data ASReml automatically recognises patterns of missing values in the responses see Chapter 8 Also there is an option to update its values by EM rather than Al when its Al updates make the matrix non positive definite 129 7 5 Variance model description 7 5 3 Notes on Mat rn The Mat rn class of isotropic covariance models is now described ASReml uses an extended Mat rn class which accomodates geometric anisotropy and a choice of metrics for random fields observed in two dimensions This extension described in detail in Haskard 2006 is given by where h hz hy is the spatial separation vector 6 governs geometric anisotropy A specifies the choice of metric and v are the parameters of the Mat rn correlation function The function is pu d v Pras Ca ae 5 Ky 5 f 7 1 where gt 0 is a range parameter v gt 0 is a
283. ere is a missing parameter there are too many few initial values e there is an error in the predict statement e model term mv not included in the model when there are missing values in the data and the model fitted assumes all data is present The most common problem in running ASReml is that a variable label is misspelt The primary file to examine for diagnostic messages is the asr file When ASReml finds something atypical or inconsistent it prints an diagnostic message If it fails to successfully parse the input it dumps the current information to the asr file Below is the output for a job that has been terminated due to an coding error If a job has an error you should e read the whole asr file looking at all messages to see whether they identify the problem e focus particularly on any error message in the Fault line and the text of the Last line read this line appears twice in the file to make it easier to find e check that all labels have been defined and are in the correct case 247 15 2 Common problems e some errors arise from conflicting information the error may point to something that appears valid but is inconsistent with something earlier in the file e reduce to a simpler model and gradually build up to the desired analysis this should help to identify the exact location of the problem e check that lines which must start in column 1 like PREDICT TABULATE and the data filename line do start i
284. ernative of using MAXIT 1 rather than a tt BLUP n qualifier However MAXIT 1 does result in complete and correct output sets the number of equations solved densely up to a maximum of 5000 By default sparse matrix methods are applied to the random effects and any fixed effects listed after random factors or whose equation numbers exceed 800 Use DENSE nto apply sparse methods to effects listed before the r reducing the size of the DENSE block or if you have large fixed model terms and want Wald F statistics calculated for them Individual model terms will not be split so that only part is in the dense section n should be kept small lt 100 for faster processing 76 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action IDF n EMFLAG n PXEM n alters the error degrees of freedom from y to v n This qualifier might be used when analysing pre adjusted data to reduce the degrees of freedom n negative or when weights are used in lieu of actual data records to supply error information n positive The degrees of freedom is only used in the calculation of the residual variance in a univariate single site analysis The option will have no effect in analyses with multiple error variances for sites or traits other than in the reported degrees of freedom Use ADJUST r rather than DF n if ris not a whole number Use with YSS r to supply variance when data fully fitted
285. error For example a two factor interaction may have a variance model for each of the two factors involved in the interaction Variancemodels are listed in Table 7 3 As indicated in the discussion of 2b care must be taken with respect to 119 7 4 Variance structures scale parameters when combining variance models see also Section 7 7 7 4 3 R structure definition For each of the s sections there must be c R structure definitions Each definition may take several lines Each R structure definition specifies a variance model and has the form order field model initial_values qualifiers NIN Alliance Trial 1989 additional_initial_values variety A order is either the number of levels in the corresponding term or the name of a factor ect di that has the same number of levels as the ninggaug asd skip 1 row 22 term for example yield mu variety r repl f mv 11 column AR1 0 5 121 11 column AR1 0 3 22 row AR1 0 3 column column AR1 0 5 repl 1 repl 0 IDV 0 1 is equivalent to when column is a factor with 11 levels field is the name of the data field variate or factor that corresponds to the term and therefore indexes the levels of the term ASReml uses this field to sort the units so they match the R structure in the example the data will be sorted internally rows within columns for the analysis but the residuals will be printed in the yht file in the original order which is actually ro
286. es in the rsv file This is equivalent to setting CONTINUE on the datafile line see Table 5 4 for details F FINAL indicates that the job is to continue for one more iteration from the values in the rsv file This is useful when using predict see Chapter 10 0 ONERUN is used with the R option to make ASReml perform a single analysis when the R option would otherwise attempt multiple analyses The R option then builds some arguments into the output file name while other arguments are not For example ASReml nor2 mabphen 2 TWT out 621 out 929 results in one run with output files mabphen2_TWT R r RENAME r is used in conjunction with at least r argument s and does two things it modifies the output filename to include the first r arguments so the output is identified by these arguments and if there are more than r arguments the job is rerun moving the extra arguments up to position r unless ONERUN 0 is also set If r is not specified it is taken as 1 For example ASReml r2 job wwt gfw fd fat is equivalent to running three jobs ASReml r2 job wwt gfw jobwwt_gfw asr ASReml r2 job wwt fd jobwwt_fd asr ASReml r2 job wwt fat jobwwt_fat asr 201 11 3 Command line options Yy YVAR y overrides the value of response the variate to be analysed see Section 6 2 with the value y where y is the number of the data field containing the trait to be analysed This facilitates analysis of several trai
287. esent in the residuals the weights are applied as a matrix product If 2 is the structure and W is the diagonal matrix constructed from the square root of the values of the variate weight then R WD W Negative weights are treated as zeros 6 8 Generalized Linear Mixed Models Table 6 3 Link qualifiers and functions Qualifier Link Inverse Link Available with IDENTITY n p n All ISQRT n yH u Poisson Normal Poisson Negative Bino LOGARITHM n In p u exp n mial Gamma INVERSE n 1 p up 1 n Normal Gamma Negative Binomial LOGIT n pu 1 pu p E Binomial Multinomial Threshold PROBIT n p u O n Binomial Multinomial Threshold en COMPLOGLOG n In In l yp p 1 e Binomial Multinomial Threshold where p is the mean on the data scale and y XT is the linear predictor on the underlying scale ASReml includes facilities for fitting the family of Generalized Linear Models GLMs McCul lagh and Nelder 1994 A GLM is defined by a mean variance function and a link function In this context y is the observation n is the count for grouped data specified by the TOTAL qualifier is a parameter set with the PHI qualifier u is the mean on the data scale calculated using the inverse link function from the pre dicted value 7 on the underlying scale where yn XT v is the variance under some distributional assumption calculated as a function of u and n and d is the deviance twice the log likel
288. esign points Covariates grouped into a single term using G qualifier page 48 are treated as covariates Prediction at particular values of a covariate or particular levels of a factor is achieved by listing the levels values after the variate factor name Where there is a sequence of values use the notation ab n to represent the sequence of values from a to n with step size b a The default stepsize is 1 in which case b may be omitted A colon may replace the ellipsis An increasing sequence is assumed When giving particular values for factors the default is to use the coded level 1 n rather than the label alphabetical or integer To use the label precede it with a quote Where a large number of values must be given they can be supplied in a separate file and the filename specified in quotes The file form does not allow label coding or sequences See the discussion of PRWTS for an example Model terms mv and units are always ignored Model terms which are functions such as at and pol sin spl including those defined using CONTRAST GROUP SUBGROUP SUBSET and MBF are implicitly de fined through their base variables and can not be directly referenced in the classify and average sets For example GROUP Year YearLoc 1 112233344 forms a new factor Year with 4 levels from the existing factor YearLoc with 10 levels The prediction must be in terms of YearLoc not Year even if YearLoc does not fo
289. eters is not as easy Each variance structure parameter yi is allocated a number i internally These numbers are reported in the tsv file and some are reported in the structure input section of the asr file These numbers are used to specify which parameters are to be constrained using this method Warning Unfortunately the parameter numbers usually change if the model is changed e VCC c specifies that there are c lines defining parameter relationships e If VCC is used a residual line is required and the parameter relationship lines must occur after this residual line e each relationship is specified in a separate line of the form i ke Ok simple case i kxvuk px vp BLOCKSIZE n general case In this specification 1 and k p are the numbers of the specific variance model parameters and vm m k p are the associated scale coefficients such that ym x V m is equal in value to yi for example 5 7 1 indicates that y_7 x 1 y_5 ie parameter 7 is equal to parameter 5 5 7 1 indicates that parameter 7 is a tenth of parameter 5 indicates the presence of the scale coefficient v_m for the parameter m if the coefficient is 1 indicating parameter equality the 1 can be omitted for example 5 7 is asimplified coding of the first example if the coefficient is 1 i k x 1 can be simplified to i k for example 5 7 indicates that parameter 7 is has the same magnitude but opposite sign to parameter 5 t
290. f the publication may be reproduced by any process electronic or otherwise without specific written permission of the copyright owner Neither may information be stored electronically in any form whatever without such permission Published by VSN International Ltd 5 The Waterhouse Waterhouse Street Hemel Hempstead HP1 1ES UK email info asreml co uk website http www vsni co uk The correct bibliographical reference for this document is Gilmour A R Gogel B J Cullis B R Welham S J and Thompson R 2014 ASReml User Guide Release 4 1 Structural Specification VSN International Ltd Hemel Hempstead HP1 1ES UK www vsni co uk Preface ASReml is a statistical package that fits linear mixed models using Residual Maximum Like lihood REML It has been under development since 1993 and arose out of collaboration between Arthur Gilmour and Brian Cullis NSW Department of Primary Industries and Robin Thompson and Sue Welham Rothamsted Research to research into the analysis of mixed models and to develop appropriate software building on their wide expertise in relevant areas including the development of methods that are both statistically and compu tationally efficient the analysis of animal and plant breeding data the analysis of spatial and longitudinal data and the production of widely used statistical software More recently VSN International acquired the right to ASReml from these sponsoring organizati
291. f fixed and random effects REML log likelihood and residuals this is the default n 3 forming the estimates of the vector of fixed and random effects REML log likelihood residuals and inverse coefficient matrix For arguments 4 10 19 ASReml forms the mixed model equations and solves them iteratively to obtain solutions for the fixed and random ef fects The options are n 4 forming the estimates of the vector of fixed and random effects using the Preconditioned Conjugate Gradient PCG Method Mrode 2005 n 10 19 forming the estimates of the vector of fixed and random effects by Gauss Seidel iteration of the mixed model equations with relaxation factor n 10 The default maximum number of iterations is 12000 This can be re set by supplying a value greater than 100 with the MAXIT qualifier in conjunction with the BLUP qualifier Iteration stops when the average squared update divided by the average squared effect is less than le Gauss Seidel iteration is generally much slower than the PCG method ASReml prints its standard reports as if it had completed the iteration normally but since it has not completed it some of the information printed will be incorrect In particular variance information on the vari ance parameters will always be unavailable Standard errors on the es timates will be wrong unless n 3 Residuals are not available if n 1 Use of n 3 or n 2 will halve the processing time when compared to the alt
292. f pairwise prediction errors of variety differences 16 8 Paired Case Control study Rice This data is concerned with an experiment conducted to investigate the tolerance of rice varieties to attack by the larvae of bloodworms The data have been kindly provided by Dr Mark Stevens Yanco Agricultural Institute A full description of the experiment is given by Stevens et al 1999 Bloodworms are a significant pest of rice in the Murray and Murrumbidgee irrigation areas where they can cause poor establishment and substantial yield loss The experiment commenced with the transplanting of rice seedlings into trays Each tray contained 32 seedlings and the trays were paired so that a control tray no bloodworms and a treated tray bloodworms added were grown in a controlled environment room for the duration of the experiment At the end of this time rice plants were carefully extracted the root system washed and root area determined for the tray using an image analysis system described by Stevens et al 1999 Two pairs of trays each pair corresponding to a different variety were included in each run A new batch of bloodworm larvae was used for each run A total of 44 varieties was investigated with three replicates of each Unfortunately the variety concurrence within runs was less than optimal Eight varieties occurred with only one other variety 22 with two other varieties and the remaining 14 with three different varieties In the next th
293. f the experiment the treatment structure comprises variety and treat ment main effects and treatment by variety interactions In the traditional approach the terms in the block structure are regarded as random and the treatment terms as fixed The choice of treatment terms as fixed or random depends largely on the aims of the experi ment The aim of this example is to select the best varieties The definition of best is somewhat more complex since it does not involve the single trait sqrt rootwt but rather two traits namely sqrt rootwt in the presence absence of bloodworms Thus to minimise selection bias the variety main effects and thence the tmt variety interactions are taken as random The main effect of treatment is fitted as fixed to allow for the likely scenario that rather than a single population of treatment by variety effects there are in fact two populations control and treated with a different mean for each There is evidence of this prior to analysis with the large difference in mean sqrt rootwt for the two groups 14 93 and 8 23 for control and treated respectively The inclusion of tmt as a fixed effect ensures that BLUPs of tmt variety effects are shrunk to the correct mean treatment means rather than an overall mean The model for the data is given by y XT Ziu Zou L3U3 6 444 Z5us5 e 16 7 where y is a vector of length n 264 containing the sqrt rootwt values 7 corresponds to a constant term and the fixe
294. files and defining factor names and improved facilities for reading relationship matrices and better explanation of a simpler way of constructing variances of functions of parameters Among the developments associated with analysis are making it easier to specify functions of variance parameters using names rather than numbers fitting factor effects with large random regression models such as commonly used with marker data fitting linear rela tionships among variance structure parameters and calculating information criteria The developments associated with output include writing out design matrices A major devel opment in Release 4 is an alternative model specification using a functional approach Prior to Release 4 a structural specification was used in which variance models were applied by imposing variance structures on random model terms and or the residual error term after the mixed model had been specified In this case the variance models were presented in a separate part of the input file The functional specification offers an alternative to the struc i tural specfication in which the variance structures for random model terms and the residual error term are specified in the linear mixed model definition by wrapping terms with the required variance model function This approach is more concise less error prone and more automatic for specifying multi section residual variances The data sets and ASReml input used in this guide are avai
295. formance issues We have given Marker35 a new name because it is still also generated by the CYCLE unless it is modified to read ICYCLE 1 34 36 1000 After several cycles we might have Marker screen Genotype yield PhenData txt ASSIGN MSET R21 R35 R376 R645 R879 ICYCLE 1 1000 IMBF mbf Genotype MLIB Marker I csv rename Marker I IFOR MSET DO MBF mbf Genotype MLIB Marke S csv rename S yld mu r MSET Marker I 11 44 Order of Substitution The substitution order is ASSIGN FOR CYCLE TP command line arguments and finally the interactive prompt 11 5 Performance issues The following subsections raise several issues which affect the performance of ASReml 11 5 1 Multiple processors ASReml has not been configured for parallel processing Performance is downgraded if it tries to use two processors simultaneously as it wastes time swapping between processors 11 5 2 Slow processes The processing time is related to the size of the model the complexity of the variance model in particular the number of parameters the sparsity of the mixed model equations the amount of data being processed Typically the first iteration take longer than other iterations The extra work in the first iteration is to determine an optimum equation order for processing the model see EQORDER The extra processes in the last iteration are optional They include e calculation of predicted values see PREDICT statement e calculati
296. from dropping the particular term indicated by from the model also including the terms indicated by I C and c The next two tables based on incremental and conditional sums of squares report the model term the number of effects in the term the numerator degrees of freedom the Wald F statistic an adjusted Wald F statistic scaled by a constant reported in the next column and finally the computed denominator degrees of freedom The scaling constant is discussed by Kenward and Roger 1997 Table showing the reduction in the numerator degrees of freedom for each term as higher terms are absorbed variety LinNitr variety nitrogen Model Term 6 5 43 2 1 1 mu 123 413 1 2 variety i a 3 2 2 3 LinNitr 9 33 1 4 nitrogen 2 2 5 2 6 ds O 00 Marginality pattern for F con calculation Model terms Model Term DF 12 3 4 5 6 1 mu LE Los e 2 variety 2 1 3 LinNitr 1 L L 4 nitrogen 2 L 1 I 5 variety LinNitr a Lidl 6 variety nitrogen 4 I I I I I amp 230 14 4 Other ASReml output files Model codes b A a A bB F inc tests the additional variation explained when the term is added to a model consisting of the 1 terms F con tests the additional variation explained when the term is added to a model consisting of the I and C c terms The terms are ignored for both F inc and F con tests Incremental F statistics calculation of Denominator degrees of freedom Source Size NumDF F value Lambda
297. from experiment which meant that one dose had only 7 dams The analysis must account for the presence of between dam variation but must also recognise the stratification of the experimental units pups within litters and that doses and littersize belong to the dam stratum Table 16 2 presents an indicative AOV decomposition for this experiment The dose and littersize effects are tested against the residual dam variation while the re maining effects are tested against the residual within litter variation The ASReml input to achieve this analysis is presented below Rats example dose 3 A sex 2 A littersize dam 27 pup 18 weight 276 16 3 Unbalanced nested design Rats Table 16 2 Rat data AOV decomposition stratum decomposition type df or ne constant 1 F 1 dams dose F 2 littersize F 1 dam R 27 dams pups sex F 1 dose sex F 2 error R rats asd DOPATH 1 Change DOPATH argument to select each PATH PATH 1 weight PATH 2 weight mu out 66 littersize dose sex dose sex r dam PATH 3 weight mu littersize dose sex r dam PATH 4 weight mu littersize dose sex mu littersize dose sex dose sex r dam The input file contains an example of the use of the DOPATH qualifier Its argument specifies which part to execute We will discuss the models in the two parts It also includes the FCON qualifier to request conditional Wald F statistics Abbreviated output from part 1 is presented below 1 LogL
298. g design Missing values not allowed here Multiple trait mapping problem Negative Sum of Squares NFACT out of range No giv file for The second field in the R structure line does not refer to a variate in the data the weight and filter columns must be data fields Check the data summary See the discussion of AISINGULARITIES Maybe increase workspace or restructure simplify the model Numerical problems calculating the Mat rn function If rescal ing the X Y cordinates so that the step size is closer to 1 0 does not resolve the issue try AEXP instead special structures are weights the Ainverse and GIV structures The limit is 98 and so no more than 96 GIV structures can be defined The limit is 1500 It may be possible to restructure the job so the limit is not exceeded assuming that the actual number of parameters to be estimated is less ASReml failed to read the first data record Maybe it is a head ing line which should be skipped by using the SKIP qualifier or maybe the field is an alphanumeric field but has not been declared so with the A qualifier You need to identify which design terms contain missing values and decide whether to delete the records containing the missing values in these variables or if it is reasonable to treat the missing values as zero by using MVINCLUDE More missing values in the response were found than expected missing observations have been dropped so that dir
299. g markers This transformation will normally be used on a G n factor where the n variables are the marker states for n markers in a linkage group in map order and coded 1 1 backcross or 1 0 1 F2 design s length n 1 should be the n marker positions relative to a left telomere position of zero and an extra value being the length of the linkage group the position of the right telomere The length right telomere may be omitted in which case the last marker is taken as the end of the linkage group The positions may be given in Morgans or centiMorgans if the length is greater than 10 it will be divided by 100 to convert to Morgans The recombination rate between markers at sz and sp L is left and R is right of some putative QTL at Q is OLR 1 e 2 n sr 2 Consequently for 3 markers L Q R OLR 010 Par 20 o0on The expected value of a missing marker at Q between L and R depends on the marker states at L and R E q 1 1 1 010 O0r 1 OLR E ql1 1 os 910 01r Elql 1 1 010 00r Lr and E q 1 1 1 810 608 1 Oza Let Az E g 1 1 E g 1 1 2 er ura OLR L OLR and AR E q 1 1 E q 1 1 2 OQ 1 01 9 1 200R OLR L OLR Then E qlx 2g Apt AR R Where there is no marker on one side E qlur 1 Oor Tr dor TR trR 1 20on This qualifier facilitates the QTL method discussed in Gilmour 2007
300. g user specified variance matrices 2 1 14 Use of the gamma parameterization ASReml uses either the gamma or sigma parameterization for estimation depending on the residual specification The default for univariate single section data sets is the gamma parameterization In this case all scale parameters are estimated as a ratio with respect to the residual variance c and any parameters that measure only correlation are unchanged See Chapter 7 for more detail 2 1 15 Combining variance models The combination of variance models within G structures and R structures and between G structures and R structures is a difficult and important concept The underlying principle is that each R and G variance model can only have a single free not fixed scaling variance parameter associated with it If there is more than one scaling variance parameter for any R or G then the variance model is overspecified or nonidentifiable Some variance models are presented in Table 2 1 to illustrate this principle While all 9 forms of model in Table 2 1 can be specified within ASReml only models of forms 1 and 2 are recommended Models 4 6 have too few variance parameters and are likely to cause serious estimation problems For model 3 where the scale parameter g has been fitted univariate single site analysis it becomes the scale for G This parameterisation is bizarre and is not recommended Models 7 9 each have one inestimable variance parameter and AS
301. ge of alphabetic factor labels with a default allocation being 2000 labels of 16 characters long If there are large A factors so that the total across all factors will exceed 2000 you must specify the anticipated size within say 5 of the larger factors If some labels are longer then 16 characters and the extra characters are significant you must lengthen the space for each label by specifying LL c e g cross A 2300 LL 48 indicates the factor cross has about 2300 levels and needs 48 characters to hold the level names only the first 20 characters of the names are ever printed PRUNE on a field definition line means that if fewer levels are actually present in the factor than were declared ASReml will reduce the factor size to the actual number of levels Use PRUNEALL for this action to be taken on the current and subsequent factors up to but 49 5 4 Specifying and reading the data not including a factor with the PRUNEOFF qualifier The user may overestimate the size for large ALPHA and INTEGER coded factors so that ASReml reserves enough space for the list Using PRUNE will mean the extra undefined levels will not appear in the sln file Since it is sometimes necessary that factors not be pruned in this way for example in pedigree GIV factors pruning is only done if requested Normally a character in the data file will have the effect of eliminating whatever text follows on the line This means that ordinarily th
302. gn and the allocation of variety to whole plots In this balanced case it is straightforward to derive the ANOVA estimates of the stratum variances from the REML estimates of the variance components That is blocks 1267 40 6 3175 1 blocks wplots 462 6 601 3 residual 6 177 1 The default output for testing fixed effects used by ASReml is a table of so called incremental Wald F statistics These Wald F statistics are described in Section 6 11 The statistics are simply the appropriate Wald test statistics divided by the number of estimable effects for that term In this example there are four terms included in the summary The overall mean denoted by mu is of no interest for these data The tests are sequential that is the effect of each term is assessed by the change in sums of squares achieved by adding the term to the current model defined by the model which includes those terms appearing above the current term given the variance parameters For example the test of nitrogen is calculated from the change in sums of squares for the two models mu variety nitrogen and mu variety No refitting occurs that is the variance parameters are held constant at the REML estimates obtained from the currently specified fixed model The incremental Wald statistics have an asymptotic x distribution with degrees of freedom df given by the number of estimable effects the number in the DF column In this example the incremental Wald F stati
303. gonal and is defined by difference the parameters are specified in the order loadings for each factor F followed by the variances diag when k is greater than 1 constraints on the elements of F are required see Table 7 5 FACVk models CV for covariance are an alternative formulation of FA models in which gt is modelled as Y PT W where FT is a matrix of loadings on the covariance scale and W is diagonal The parameters in FACV are specified in the order loadings T followed by variances W when k is greater than 1 constraints on the elements of I are required see Table 7 5 are related to those in FA by F DF and Y DED XFAk X for extended is the third form of the factor analytic model and has the same parameterisation as for FACV that is TT W However XFA models have parameters specified in the order diag W and vec T when k is greater than 1 constraints on the elements of I are required see Table 7 5 may not be used in R structures are used in G structures in combination with the xfa f k model term return the factors as well as the effects permit some elements of Y to be fixed to zero 133 7 5 Variance model description are computationally faster than the FACV formulation for large problems when k is much smaller than w Special consideration is required when using the XFAk model The SSP must be expanded to have room to hold the k factors This
304. h the residual effect for the residual We consider the case when there is data on parents and non parents and some individuals are inbred An example tree model for a single trait and a single site might be DBH mu r nrmv tree plot row column 001 row column row 0 AR V column O ARI 169 9 7 The reduced animal model RAM since trees are often planted in plots of say 5 trees This is a spatial analysis the idv units term is required so that error variance is not transferred to the nrmv tree term since trees are unreplicated This analysis requires a pedigree file say TreePed csv and if the DIAG qualifier is specified on the pedigree line the resulting aif file will contain the inbreeding level for every tree in the pedigree the diagonal of the A7 matrix and a N P code distinguishing parents with progeny from non parents without progeny To analyse the data using the RAM we need to incorporate these last two columns into the data file which can be done with the MERGE statement If there is data on parents further processing of the data file is required create a copy of the tree field call it say parent and change it to 0 for the progeny records Assume our data file ramdbh txt has fields tree mum dad row column plot DBH Aldiag OP parent and we have deleted the non parent rows from the full pedigree file to form ParentPed txt If you have a pedigree file for all trees processing that p
305. hapter 3 for an introduction to these data This is to give a feel for variance modelling in ASReml and some of the models that are possible Before proceeding it is useful to link this section to the algebra of Chapter 2 In this case the mixed linear model is y XT Zut e where y is the vector of yield data T is a vector of fixed variety effects but would also include fixed replicate effects in a simple RCB analysis and might also include fixed missing value effects when spatial models are considered u N 0 G is a vector of random effects for example random replicate effects and the errors are in e N 0 R The focus of this discussion is on e changes to u and e and the assumptions about these terms e the impact this has on the specification of the G structures for u and the R structures for e 110 7 3 A sequence of structures for the NIN data 1 Traditional randomised complete block RCB analysis The only random term in a traditional RCB analysis of these data is the residual error term e N 0 o2I The model therefore involves just one R structure and no G struc tures u 0 In ASReml e the error term is implicit in the model and is not formally specified on the model line e the IID variance structure R 0 1 is the default for error Important The error term is always present in the model but its variance structure does not NIN Alliance Trial 1989 variety A id pid raw repl
306. hat the data is stored The residual from a spatial analysis will have the units part added to it when units is also fitted The drs file could be renamed with extension db1 and used for input in a subsequent run instructs ASReml to write the data to a binary file The file asrdata bin is written in single precision if the argument n is 1 or 3 asrdata dbl is written in double precision if the argument n is 2 or 4 the data values are written before transformation if the argument is 1 or 2 and after transformation if the argument is 3 or 4 The default is single precision after transformation see Section 4 2 When either SAVE or RESIDUALS is specified ASReml saves the factor level labels to a basename v1l and attempts to read them back when data input is from a binary file Note that if the job basename changes between runs the v11 file will need to be copied to the new basename If the v11 file does not match the factor structure i e the same factors in the same order reading the v11 file is aborted performs a Regression Screen a form of all subsets regression For d model terms in the DENSE equations there are 27 1 possible submodels Since for d gt 8 24 1 is large the submodels explored are reduced by the parameters n and m so that only models with at least n default 1 terms but no more than m default 6 terms are considered The output see page 225 is a report to the asr file with a line for every submo
307. he BLOCKSIZE n qualifier is used when constraints of the same form are required on blocks of n contiguous parameters for example 21 29 BLOCKSIZE 8 equates parameters 29 with 21 30 with 22 36 with 28 a variance structure parameter may only be included in one relationship line to equate 142 7 9 Constraining variance parameters several components put them all in one list on one line where the relationship applies among simple model terms those without an explicit variance structure for example units the model term name may be given rather than the parameter number These examples are summarized in the following table ASReml code action 57 gt 1 parameter 7 equals parameter 5 ST simple coding for 5 7 1 57 1 parameter 7 is a tenth of parameter 5 a F parameter 7 is the negative of parameter 5 32 34 as 37 26 39 for a 4 x 4 US matrix given by parameters 31 40 the covari ances parameters 32 39 are forced to be equal 21 29 BLOCKSIZE 8 equates parameters 29 with 21 30 with 22 36 with 28 units uni check parameter associated with model term uni check has the same magnitude but opposite sign to the parameter associated with model term units 7 9 3 Equating variance structures In some plant breeding applications it is sometimes convenient to define a variance structure as the sum of two simpler terms Then it is necessary to give the same variance model to each term
308. he 1 B C and A B C terms would be the same as the incremental Wald statistics produced using the linear model y x1 A B C A B A C B C A B C The preceeding table includes a so called M marginality code reported by ASReml when conditional Wald statistics are presented All terms with the highest M code letter are tested conditionally on all other terms in the model i e by dropping the term from the maximum model All terms with the preceeding M code letter are marginal to at least one term in a higher group and so forth For example in the table model term A B has M code B because it is marginal to model term A B C and model term A has M code A because it is marginal to A B A C and A B C Model term mu M code is a special case in that its test is conditional on all covariates but no factors Following is some ASReml output from the aov file which reports the terms in the conditional statistics Marginality pattern for F con calculation 21 2 5 Inference Fixed effects Model terms Model Term DF 12 3 4 5 6 7 8 1 mu 1 Eo 2 water 1 I C C c 3 variety 7 I I GC 6 4 sow 2 I I I CO 5 water variety 7 I I I 1 C C 6 water sow 2 1 1 1 1 1 7 variety sow 14 I 1 1 1 1 1 8 water variety sow 14 I I I I I I I x F inc tests the additional variation explained when the term is added to a model con sisting of the I terms F con tests the additional variation explained when the term is added to a mo
309. he DENSE partition conditional on the order the terms were nominated in the model Note that probability values are only available when the denominator degrees of freedom is calculated and this must be explicitly requested with the DDF qualifier in larger jobs Users should study Section 2 5 to understand the contents of this table The conditional maximum model used as the basis for the conditional F statistic is spelt out in the aov file described in section 14 4 The numerator degrees of freedom NumDF for each term is easily determined as the number of non singular equations involved in the term However in general calculation of the denominator degrees of freedom DDF is not trivial ASReml will by default attempt the calculation for small analyses by one of two methods In larger analyses users can request the calculation be attempted using the DDF qualifier page 67 Use DDF 1 to prevent the calculation to save processing time when significance testing is not required 108 7 Command file Specifying the variance structures 7 1 Introduction The subject of this chapter is variance model specification in ASReml ASReml allows a wide range of models to be fitted The key concepts you need to understand are the mixed linear model y XT Zu e has a residual term e N O R and random effects u N 0 G we use the terms R structure and G structure to refer to the independent blocks of R and G respectively R an
310. he data record containing them see Table 5 1 comma delimited files whose file name ends in csv or for which the CSV qualifier is set recognise empty fields as missing values a line beginning with a comma implies a preceding missing value consecutive commas imply a missing value a line ending with a comma implies a trailing missing value if the filename does not end in csv and the CSV qualifier is not set commas are treated as white space e TAB delimited files recognise empty fields as missing values e characters following on a line are ignored so this character may not be used except to flag trailing comments on the ends of lines or to comment out data records unless SPECIALCHAR is specified see see Section 5 4 2 adjacent lines can be concatenated and written on one line using For example line_1 line_2 linen 41 4 2 The data file can be written on one line as line 1 line 2 linen This can aid legibility of the input file Note that everything including after the first on a line is intepreted as a comment blank spaces tabs and commas must not be used embedded in alphanumeric fields unless the label is enclosed in quotes for example the name Willow Creek would need to be appear in the data file as Willow Creek to avoid an error the symbol must not be used in the data file alphanumeric factor level labels have a default size of 16 characters Use the LL s
311. he highest between plot correlation relates to the larger spatial distance then this may suggest the presence of extraneous variation see Gilmour et al 1997 for example Figure 16 5 presents a plot of the sample variogram of the residuals from this model The plot appears in reasonable agreement with the model The next model includes a measurement error or nugget effect component That is the variance model for the plot errors is now given by Y 0 X 8 Dr 1150 16 6 where 1 is the ratio of nugget variance to error variance o The abbreviated output for this model is given below There is a significant improvement in the REML log likelihood with the inclusion of the nugget effect see Table 16 7 AR1 x AR1 1 LogL 739 681 S2 36034 125 df 1 000 0 1000 0 1000 2 LogL 714 340 s2 28109 125 df 1 000 0 4049 0 1870 3 LogL 703 338 82 29914 125 dE 1 000 0 5737 0 3122 4 LogL 700 371 S2 37464 125 df 1 000 0 6789 0 4320 5 LogL 700 324 S2 38602 125 dr 1 000 0 6838 0 4542 6 LogL 700 322 S2 38735 125 af 1 000 0 6838 0 4579 7 LogL 700 322 S2 38754 125 dE 1 000 0 6838 0 4585 8 LogL 700 322 S2 38757 125 df 1 000 0 6838 0 4586 Final parameter values 1 0000 0 68377 0 45861 Model_Term Gamma Sigma Sigma SE C Variance 150 125 1 00000 38756 6 5 00 0 P Residual AR AutoR 15 0 683767 0 683767 10 80 OU Residual AR AutoR 10 0 458607 0 458607 5 55 OU Wald F statistics Source of Variation NumDF DenDF F_ine Prob 8 mu il 12 8 850 88
312. he larger displacements 9 10 11 14 15 20 The result is displayed as a perspective plot see page 237 of the one or two surfaces indexed by absolute displacement group In this case the two directions may be on different scales Otherwise ASReml forms a variogram based on polar coordinates It calculates the distance between points dij 1 2 and an angle 0 180 lt 0 lt 180 subtended by the line 18 2 5 Inference Fixed effects from 0 0 to lu li 2 with the x axis The angle can be calculated as 0 tan7 1ij1 li 2 choosing 0 lt 6 lt 180 if l 2 gt 0 and 180 lt 0 lt 0 if li j2 lt 0 Note that the variogram has angular symmetry in that vj Vi dij d and 6 180 The variogram presented averages the v within 12 distance classes and 4 6 or 8 sectors selected using a VGSECTORS qualifier centred on an angle of 1 180 s i 1 s A figure is produced which reports the trends in u with increasing distance for each sector ASReml also computes the variogram from predictors of random effects which appear to have a variance structures defined in terms of distance The variogram details are reported in the res file 2 5 Inference Fixed effects 2 5 1 Introduction Inference for fixed effects in linear mixed models introduces some difficulties In general the methods used to construct F tests in analysis of variance and regression cannot be used for the diversit
313. he model 6 3 2 Sparse fixed terms The f sparse_fixed terms in model formula NIN Alliance Trial 1989 variety e are the fixed covariates for example the fixed lin row covariate now included in the model for oe BD mula factors and interactions including special func column 11 tions and reserved words for example mv see Table nin89 asd skip 1 6 1 for which Wald F statistics are not required yield mu variety r e include large gt 100 levels terms huain If mv lin row 12 11 column AR1 424 22 row AR1 904 6 4 Random terms in the model The r random terms in the model formula NIN Alliance Trial 1989 variety e comprise random covariates factors and interactions including special functions and reserved words see Ta eee ble 6 1 column 11 e involve an initial non zero variance component or ra nin89 asd skip 1 tio relative to the residual variance default 0 1 the yield mu variety r initial value can be specified after the model term or if pl th i tructure is not scaled identity by syntax oe A TT Y DY Sy 11 column AR1 424 described in detail in Chapter 7 22 row AR1 904 an initial value of its variance ratio may be followed by a GP keep positive the default GU unrestricted or GF fixed qualifier see Table 7 4 use and to group model terms that may not be reordered Normally ASReml will reorder the model terms in the sparse equations putting smaller terms
314. he suggested power is approximately 1 b where b is the slope A slope of 1 suggests a log transformation This is indicative only and should not be blindly applied Weighted analysis or identifying the cause of the heterogeneity should also be considered This statistic is not reliable in genetic animal models or when units is included in the linear model because then the predicted value includes some of the residual 243 14 5 ASReml output objects and where to find them Table 14 2 Table of output objects and where to find them ASReml output object found in comment observed variance covariance matrix formed from BLUPs and residuals phenotypic vari ance plot of residu als against field position possible outliers predicted fitted values at the data points predicted values REML log likelihood residuals score tables of means variance of variance parameters variance ters parame variogram res file pvc file graphics file res file yht file pvs file asr file yht file asl file tab file pvs file vvp file asr file res file graphics file for an interaction fitted as random effects when the first outer dimension is smaller than the inner dimension less 10 ASReml prints an observed variance matrix calculated from the BLUPs The observed correlations are printed in the upper triangle Since this matrix is not well scaled as an estim
315. hich an R structure or a G structure has been associated a variogram and spatial correlations for spatial analysis the spatial correlations are based on distance between data points see Gilmour et al 1997 the slope of the log absolute residual on log predicted value for assessing possible mean variance relationships and the location of large residuals For example SLOPES FOR LOG ABS RES ON LOG PV for section 1 0 99 2 01 4 34 produced from a trivariate analysis reports the slopes A slope of b suggests that y might have less mean variance relationship If there is no mean variance relation a slope of zero is expected A slope of z suggests a SQRT transformation might resolve the dependence a 234 14 4 Other ASReml output files slope of 1 means a LOG transformation might be appropriate So for the 3 traits log y1 Yo and yz are indicated This diagnostic strategy works better when based on grouped data regressing log standard deviation on log mean Also SIND RES 16 2 39 6 58 5 64 indicates that for the 16th data record the residuals are 2 35 6 58 and 5 64 times the respective standard deviations The standard deviation used in this test is calculated directly from the residuals rather than from the analysis They are intended to flag the records with large residuals rather than to precisely quantify their relative size They are not studentised residuals and are generally not relevant when the user has f
316. hip matrix and store the result in a GIV file So 2 relationship matrices based on two separate pedigrees may be used by generating a GIV file from one pedigree and then using that GIV file and the other pedigree in a subsequent run To process the GIV file properly we must also generate a file with identities as required for the GIV matrix An example of this is if the file Hybrid as includes IPART 1 Mline P 167 9 6 Reading a user defined inverse relationship matrix Fline A Mline ped GIV DIAG GIV generates the file HybridiA giv and DIAG generates Hybrid1 aif which contains the identifier names PART 2 reads in inverse additive relationship matrix generated in PART 1 Mline A L Hybridi aif SKIP 1 associates identifier names with levels of Mline used in giv file Fline P Fline ped GIV DIAG Hybridi_A giv formed in part 1 from Mline ped Hybrid asd SKIP 1 grmi Mline nrm Fline using new synonyms and functions 9 6 1 New model names In previous releases of ASReml a pedigree file could be associated with a factor and a numer ator relationship matrix was generated and could be used as a variance structure Slightly illogically this structure was specified in models using AINV Additive Inverse Matrix Sim ilarly generalised relationship matrices grm or their inverses giv could be read in and givO and GIV could be used in the model specification In Release 4 ASReml allows the use of NRM as a synonym fo
317. his crude measure then the conclusions would have been inconsistent with the conclusions obtained from the REML log likelihood ratio see Table 16 3 Model_Term Gamma Sigma Sigma SE C setstat 10 10 0 233417 Q 119370E 01 1 35 0 P setstat regulatr 80 64 0 601817 0 307771E 01 3 64 0 P teststat 4 4 0 642752E 01 0 328705E 02 0 98 0 P Variance 256 255 1 00000 0 511402E 01 Sta O P 281 16 5 Balanced repeated measures Height Table 16 3 REML log likelihood ratio for the variance components in the voltage data REML 2x terms log likelihood difference P value setstat 200 31 5 864 0077 setstat regulatr 184 15 38 19 0000 teststat 199 71 7 064 0039 16 5 Balanced repeated measures Height The data for this example is taken from the GENSTAT manual It consists of a total of 5 measurements of height cm taken on 14 plants The 14 plants were either diseased or healthy and were arranged in a glasshouse in a completely random design The heights were measured 1 3 5 7 and 10 weeks after the plants were placed in the glasshouse There were 7 plants in each treatment The data are depicted in Figure 16 3 obtained by qualifier line ly y1 G tmt JOIN in the following multivariate ASReml job Y y1 This is plant data multivariate Y axis 21 0000 13025000 x axfs 0 5000 5 5000 1 2 Figure 16 3 Trellis plot of the height for each of 14 plants In the following we illustrate how various repeated measures ana
318. ible The output is Univariate analysis of Rating Summary of 4 records retained of 4 read Model term Size miss zero MinNon0 Mean MaxNon0 StndDevn 1 Cheese 4 0 0 1 2 5000 4 2 Rating Variate 0 2 1 000 1 750 6 000 2 872 2 Rating Variate 0 2 1 000 2 500 9 000 4 359 2 Rating Variate 0 1 1 000 4 750 12 00 5 500 2 Rating Variate 0 O 1 000 6 750 11 00 4 193 2 Rating Variate 0 0 3 000 10 25 23 00 TTO 2 Rating Variate 0 O 6 000 7 000 8 000 0 8165 2 Rating Variate 0 O 1 000 9 750 19 00 8 221 2 Rating Variate 0 1 1 000 6 250 16 00 7 411 2 Rating Variate 0 2 1 000 3 000 11 00 5 354 3 Total 0 06 52 00 52 00 52 00 0 000 4 Trait 8 Forming 12 equations 12 dense 325 16 10 Generalized Linear Mixed Models Initial updates will be shrunk by factor 0 010 Distribution and link Cum Multinomial Logit P 1 1 exp XB Warning The LogL value is unsuitable for comparing GLM models Notice 1 singularities detected in design matrix 1 LogL 26 4243 s2 1 0000 21 df Dev DF 0 3356 2 LogL 26 4503 s2 1 0000 21 df Dev DF 0 3376 3 LogL 26 4506 s2 1 0000 21 df Dev DF 0 3376 4 LogL 26 4506 s2 1 0000 21 d Dev DF 0 3376 5 LogL 26 4506 s2 1 0000 21 df Dev DF 0 3376 Deviance from GLM fit 21 20 31 Variance heterogeneity factor Deviance DF 0 97 Results from analysis of Rating Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generaliz
319. ic is i th i is ba 2 2759 gt gt oy amp 8 2 gt gt O l e xx 236 OoOO 18 zeros 38 0 28 32 0 26 24 0 19 91 86 65 49 131 20 68 141 69 109 63 57 119 181 101 0 50 66 16 57 30 45 92 70 62 48 27 57 15 24 116 27 2 141 40 25 104 sit 70 198 29 73 64 14 4 Other ASReml output files Residual section 1 column 8 11 row 4 22 is 3 32 SD Residual section 1 column 9 11 row 2 22 is 3 33 SD Residual section 1 column 9 11 row 3 22 is 3 52 SD Residual section 1 column 10 11 row 3 22 is 3 56 SD Residual section 1 column 10 11 row 4 22 is 3 35 SD Residual section 1 column 11 11 row 3 22 is 3 52 SD 6 possible outliers in section 1 test value 23 0311757288330 varidguait of Pesiduats 1d Jul 2005 12 41 18 aes ne Ae Outer displacement uu Inner displacement Figure 14 2 Variogram of residuals Figures 14 2 to 14 5 show the graphics derived from the residuals when the DISPLAY 15 qualifier is specified and which are written to eps files by running ASReml g22 nin89a as The graphs are a variogram of the residuals from the spatial analysis for site 1 Figure 14 2 a plot of the residuals in field plan order Figure 14 3 plots of the marginal means of the residuals Figure 14 4 and a histogram of the residuals Figure 14 5 The selection of which plots are displayed is controlled by the DISPL
320. ich case ASReml may fail to produce a solution You can verify the model is appropriate by closer examination of the structure of the data and by fitting simpler models software problems There are many options in ASReml and some combinations have not been tested Some jobs are too big When all else fails send for support to support vsni cu uk There are over 6000 one line diagnostic messages that ASReml may print in the asr file Hopefully most are self explanatory but it will always be helpful to recognise whether they relate to parsing the input file or raise some other issue See Section 15 5 for more information on these messages 246 15 2 Common problems 15 2 Common problems Common problems in coding ASReml are as follows e a variable name has been misspelt variable names are case sensitive a model term has been misspelt model term functions and reserved words mu Trait mv units are case sensitive the data file name is misspelt or the wrong path has been given enclose the pathname in quotes if it includes embedded blanks a qualifier has been misspelt or is in the wrong place e there is an inconsistency between the variance header line and the structure definition lines presented failure to use commas appropriately in model definition lines e there is an error in the R structure definition lines e there is an error in the G structure definition lines there is a factor name error th
321. idea is to use Z4 4 in place of the expected information matrix in 2 16 to update 14 2 2 Estimation The elements of Z4 are 1 La Ki Kj zY PHiPH Py 2 17 The Z4 matrix is the scaled residual sums of squares and products matrix of y Vi Yel where y is the working variate for k and is given by y H Py H R e R R ki E Cr ZG G ta Ky Og where y X7 Zu 7 and w are solutions to 2 18 In this form the Al matrix is relatively straightforward to calculate The combination of the Al algorithm with sparse matrix methods in which only non zero values are stored gives an efficient algorithm in terms of both computing time and workspace 2 2 2 Estimation prediction of the fixed and random effects To estimate 7 and predict u the objective function log fy y u T R log fulu G is used This is the log joint distribution of Y u Differentiating with respect to 7 and u leads to the mixed model equations Henderson et al 1959 Robinson 1991 which are given by X BR X X R Z TXR y Z R X ZR Z G a ZR y These can be written as 2 18 C W R l where C W R W G B r u and 0 0 0G The solution of 2 18 requires values for cr and o In practice we replace o and a by their REML estimates dy and er a Note that 7 is the best linear unbiased estimator BLUE of 7 while w is the best linear unbiased predi
322. ided The data file may need to be rewritten with some factors re coded as sequential integers This is an internal limit Reduce the number of response vari ables Response variables may be grouped using the G factor definition qualifier so that more than 20 actual variables can be analysed this message occurs when there is an error forming the inverse of a variance structure The probable cause is a non positive definite initial variance structure US CHOL and ANTE mod els It may also occur if an identity by unstructured ID US error variance model is not specified in a multivariate analysis including ASMV see Chapter 8 If the failure is on the first iteration the problem is with the starting values If on a sub sequent iteration the updates have caused the problem You can specify GP to force the matrix positive definite and try reducing the updates by using the STEP qualifier Otherwise you could try fitting an alternative parameterisation generally refers to a problem setting up the mixed model equa tions Most commonly it is caused by a non positive definite matrix Use better initial values or a structured variance matricx that is positive definite You may use FA or FACV The R structure must be positive definite 271 16 Examples 16 1 Introduction In this chapter we present the analysis of a variety of examples The primary aim is to illustrate the capabilities of ASReml in the context of analys
323. ied operations The results are reported in the pvc file In Section 13 2 the syntax for these instructions are discussed Direct use of the pin file as was required in ASReml 2 is discussed in Section 13 3 13 2 Syntax Instructions to calculate functions are headed by a line VPREDICT DEFINE This line and the following instructions can occur anywhere in the as file but the logical place is at the end of the file The instructions are processed after the job part cycle has been completed ASReml recognises a blank line or end of file as termination of the functional instructions Functions of the variance components are specified by lines of the form letter label coefficients e letter either F H R S V or X must occur in column 1 F forms linear combinations of variance components 214 13 2 Syntax His for forming heritabilities the ratio of two components Ris for forming the correlation from a covariance component Sis a square root function Vis for converting components related to a CORUH or an XFA structure into compo nents related to a US structure X is a multiply function e label names the result e coefficients is the list of arguments coefficients for the linear function When ASReml reads back the variance parameters from the asr file the parameters are given a name based on the random linear model term The parameters in the R structures are effectively given a name Residual The
324. ied from that point Unfortunately the prompt may not appear on the top screen under some windows operating systems in which case it may not be obvious that ASReml is waiting for a keyboard response 11 43 Paths and Loops ASReml is designed to analyse just one model per run However the analysis of a data set typically requires many runs fitting different models to different traits It is often convenient to have all these runs coded into a single as file and control the details from the command line or top job control line using arguments The highlevel qualifiers CYCLE and DOPATH enable multiple analyses to be defined and run in one execution of ASReml 204 11 4 Advanced processing arguments Table 11 3 High level qualifiers qualifier action ASSIGN list ICYCLE SAMEDATA list An ASSIGN string qualifier has been added to extend coding options It is a high level qualifier command which may appear anywhere in the job Each occurrence of ASSIGN must start on its own input line The syntax is beginning in position 1 ASSIGN name string and the defined string is substituted into the job where name appears string is the rest of the line and may include blanks For example ASSIGN TRT xfa Treat 1 TRT geno TRT geno 2 TRT O XFA1 geno Restrictions e A maximum of 50 assign strings may be defined e The combined length of all strings is 5000 characters e name may consist of 1 4 char
325. ignal on background In this example signal is a multivariate set of 93 variates and background is a set of 93 covariates The signal values relate to either the Red or Green channels So for each slide and channel we need to fit a simple regression of signal mu background But the data for the 93 slides is presented in parallel If it were presented in series with a factor slide indexing the slides the equivalent model would be signal slide slide background Factor analytic models are discussed in Chapter 7 There are three forms FAk FACVk and XFAk where k is the number of factors The XFAk form is a sparse formulation that requires an extra k levels to be inserted into the mixed model equations for the k factors This is achieved by the xfa f k model function which defines a design matrix based on the design matrix for f augmented with k columns of zeros for the k factors 99 6 8 Generalized Linear Mixed Models 6 7 Weights Weighted analyses are achieved by using WT weight as a qualifier to the response variable An example of this is y WT wt mu A X where y is the name of the response variable and wt is the name of a variate in the data containing weights If these are relative weights to be scaled by the units variance then this is all that is required If they are absolute weights that is the reciprocal of known variances use the S2 1 qualifier described in Table 7 4 to fix the unit variance When a structure is pr
326. ihood for that distribution GLMs are specified by qualifiers after the name of the dependent variable but before the character Table 6 3 lists the link function qualifiers which relate the linear predictor n scale to the observation w E y scale Table 6 4 lists the distribution and other qualifiers 100 6 8 Generalized Linear Mixed Models Table 6 4 GLM distribution qualifiers The default link is listed first followed by permitted alternatives qualifiers action INORMAL IDENTITY LOGARITHM INVERSE allows the model to be fitted on the log inverse scale but with the residuals on the natural scale NORMAL IDENTITY is the default BINOMIAL LOGIT IDENTITY PROBIT COMPLOGLOG TOTAL n v u 1 u n Proportions or counts r ny are indicated if TOTAL specifies the variate con d 2n yln y t taining the binomial totals Proportions are assumed if no response value exceeds 1 y n 4 1 A binary variate 0 1 is indicated if TOTAL is unspecified The expression for d on the left applies when y is proportions or binary The logit is the default link function The variance on the underlying scale is 77 3 3 3 underlying logistic distribution for the logit link IMULTINOMIAL k CUMULATIVE LOGIT PROBIT COMPLOGLOG TOTAL n fits a multiple threshold model with t k 1 thresholds to polytomous ordinal vij pill p3 n data with k categories assuming a
327. ike 3 1 0 2 1 5 to represent the sequence 0 2 0 2 0 2 0 0 2 0 2 The string inside the curly brace is expanded first and the expression n c means n occurrences of c When there are a large number of weights it may be convenient to prepare them in a file and retrieve them All values in the file are taken unless n is specified in which case they are taken from field column n is used to control averaging over associated factors The default is to simply average at the base level Hierarchal averaging is achieved by listing the associated factors to average in f Explicit weights may be supplied directly or from a file as for AVERAGE without arguments means all classify variables are expanded in parallel Oth erwise list the variables from the classify set whose levels are to be taken in parallel is used when averaging is to be based only on cells with data v is a list of variables and may include variables in the classify set v may not include variables with an explicit AVERAGE qualifier The variable names in v may optionally be followed by a list of levels for inclusion if such a list has not been supplied in the specification of the classify set ASReml works out what combinations are present from the design matrix It may have trouble with complicated models such as those involving and terms A second PRESENT qualifier is allowed on a predict statement but not with PRWTS The two lists must not overlap is used in c
328. in the analysis regardless of which appears first in the file It will generally be preferable to presepecify the levels than to use SORT because most other references to particular levels of factors will refer to the unsorted levels Therefore users should verify that ASReml has made the correct interpretation when nominating specific levels of SORTed factors In particular any transformations are performed as the data is read in and before the sorting occurs SORTALL means that the levels of this and subsequent factors are to be sorted 5 4 4 Skipping input fields This is particularly useful in large files with alphabetic fields that are not needed as it saves ASReml the time required to classify the alphabetic labels New R4 CSKIP f can be used to skip f fields Thus ICSKIP 1 AB 50 5 5 Transforming the data skips the first data field and reads the second and third fields into variables A and B and ICSKIP Sire I CSKIP 2 Y will define two variables Sire taken from the second data field and Y taken from the fifth data field Also SKIP f will skip f data fields BEFORE reading this field Thus Sire I SKIP 1 Y SKIP 2 achieves the same result but in a less obvious way These qualifiers are ignored when reading binary data Important Using the SKIP qualifier in association with the specification of a file to be read in allows initial lines of the file to be skipped SKIP can also be used to skip columns or data fiel
329. ince there is error in both variables We seek to determine an index of tolerance from the joint analysis of treated and control root area this is for the paired data e Y sye 5yc i e aa Q 5 A 992 eri a Q 7 2 Y axis 1 8957 14 8835 X axis 8 2675 23 5051 o o o o o o o0 o o o o a 2 o o o f o 9 i o i o 8 a 6 o o ia ot o o o o o o o o Go o o 9 o o o e ae sr oo o o o o o o o o o o o o 2 o e gt o gt o e o o o gp e o a oo o o0 o o i o 9 0 Figure 16 8 Rice bloodworm data Plot of square root of root weight for treated versus control 16 8 1 Standard analysis The allocation of bloodworm treatments within varieties and varieties within runs defines a nested block structure of the form 301 16 8 Paired Case Control study Rice run variety tmt run run variety run variety tmt run pair pair tmt run run variety units There is an additional blocking term however due to the fact that the bloodworms within a run are derived from the same batch of larvae whereas between runs the bloodworms come from different sources This defines a block structure of the form run tmt variety run run tmt run tmt variety run run tmt pair tmt Combining the two provides the full block structure for the design namely run run variety run tmt run tmt variety run run variety run tmt units run pair run tmt pair tmt In line with the aims o
330. ing real data sets We also discuss the output produced by ASReml and indicate when problems may occur Statistical concepts and issues are discussed as necessary but we stress that the analyses are illustrative not prescriptive 16 2 Split plot design Oats The first example involves the analysis of a split plot design originally presented by Yates 1935 The experiment was conducted to assess the effects on yield of three oat varieties Golden Rain Marvellous and Victory with four levels of nitrogen application 0 0 2 0 4 and 0 6 cwt acre The field layout consisted of six blocks labelled II HI IV V and VI with three whole plots per block each split into four sub plots The three varieties were randomly allocated to the three whole plots while the four levels of nitrogen application were randomly assigned to the four sub plots within each whole plot The data is presented in Table 16 1 A standard analysis of these data recognises the two basic elements inherent in the ex periment These two aspects are firstly the stratification of the experiment units that is the blocks whole plots and sub plots and secondly the treatment structure that is super imposed on the experimental material The latter is of prime interest in the presence of stratification Thus the aim of the analysis is to examine the importance of the treatment effects while accounting for the stratification and restricted randomisation of the treatments to the e
331. initial values uses 15 parameters numbered 5 19 generating symmetric matrix 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Wolfinger 1996 reports the fitting of the HuynhFeldt variance structure to this data This structure is of the form Oii Oni Oj 1 2 Oni 0Onj Ono j lt i lt p In the rats example the relationship between the original and new parameters is o Mo where cr and On are 15 x 1 and 6 x 1 vectors respectively and M is a 15 x 6 matrix 1 0 0 o 0 0 0 5 0 5 O o 0 i 0 1 0 Q Q 0 0 5 0 0 5 Y si 0 0 5 0 5 0 0 1 0 0 1 o o 0 0 5 0 0 0 5 0 1 0 0 5 0 0 5 0 1 0 0 0 5 0 50 1 0 0 0 1 0 0 0 5 0 0 0 Q i 0 0 5 0 O Ges SL 0 0 Oe GS f 0 0 0 0 5 0 5 0 0 0 0 i Q A way of fitting this model would be to put the matrix values in a file HuynhFeldt vcm and replace the G Trait specification by Trait 0 US LGU 45 20 45 20 20 45 20 20 20 45 20 20 20 20 45 Supply start values because raw SSP generates bad initial values 145 7 9 Constraining variance parameters for HuynhFeldt structure because it does not fit well VCM 5 19 6 HuynhFeldt vcm parameters 5 to 19 explained in terms of 6 parameters Note that if the user fits another model with differing numbers of variance structure param eters so that the variance structure parameters are renumbered then all the user needs to do to continue with the same relationships is to change the parameter_number_list parameters on the VCM line Important
332. ion Used EMFLAG O Single standard EM update when AI update unacceptable You could try GU negative definite US or use XFA instead Notice Akaike Information Criterion 43065 77 assuming 52 parameters Bayesian Information Criterion 43471 52 Model_Term Sigma Sigma Sigma SE C Residual 35200 effects Residual US V 1 1 9 46109 9 46109 33 29 0 P Residual US 2 1 7 34181 7 34181 20 55 0 P Residual US V 2 2 17 6050 17 6050 27 09 0 P Residual US CC 3 1 0 272536 0 272536 8 38 0 P Residual US_C 3 2 0 668009 0 668009 13 99 0 P Residual US V 3 3 0 141595 0 141595 23 70 oF Residual US_C 4 1 0 963017 0 963017 2 89 0 P Residual US cC 4 2 1 99771 L977 1 3 64 0 P Residual US_C 4 3 0 286984 0 286984 5 08 0 P Residual US V 4 4 3 64374 3 64374 9 00 ae Residual US_C 5 1 0 850282 0 850282 8 48 0 P Residual USC 5 2 2 48313 2 48313 19 33 0 P Residual US_C 5 3 0 786089E 01 0 786089E 01 7 04 0 P Residual US C 5 4 0 115894 0 115894 11r 0 P Residual UE amp 5 1 63179 1 63175 32 90 0 P TrAG1245 age grp DIAG_V 1 Q 132755E 02 0 132 55 02 2 01 o y TrAG1245 age grp DIAG_V 2 0 976533E 03 0 976533E 03 1 21 OU TrAG1245 age grp DIAG_V 3 0 176684E 02 0 176684E 02 1 13 OU TrAG1245 age grp DIAG_V 4 0 208076E 03 0 208076E 03 1 62 OU TrSG123 sex grp DIAG_V 1 1 01106 1 01106 297 OU TrSG123 sex grp DIAG_V 2 16 0229 16 0229 a 51 OU TrSG123 sex grp DIAG_V 3 0 280259 0 280259 3 41 OU Trait sire US_V 1 1 0 593942 0 593942 3 68 0 P Trait sire US C 2 1 0 677334 0 677334 3
333. ion with the OWN structure as ASReml knows the type in other cases The valid type codes are as follows 135 7 5 Variance model description code description action if GP is set V variance forced positive G variance ratio forced positive R correlation 1I lt r lt 1 C covariance P positive correlation 0 lt r lt 1 L loading This coding also affects whether the parameter is scaled by g in the output 136 7 6 Variance structure qualifiers 7 6 Variance structure qualifiers Table 7 4 describes the R and G structure line qualifiers Table 7 4 List of R and G structure qualifiers qualifier action l s IGP GU GF IGZ INAME f 1S2 r 1S2 1S2 r used to constrain parameters within variance structures see Section 7 9 4 modify the updating of the variance parameters The exact action of these codes in setting bounds for parameters depends on the particular model GP the default in most cases attempts to keep the parameter in the theoretical parameter space and is activated when the update of a parameter would take it outside its space For example if an update would make a variance negative the negative value is replaced by a small positive value Under the GP condition repeated attempts to make a variance negative are detected and the value is then fired at a small positive value This is shown in the output in that the parameter will have the code B rather than P appended to the va
334. ionship matrix J inv u r forms reciprocal of v r lt le f condition on factor variable f lt r lt leg v n forms n 1 Legendre polynomials of order 0 in y tercept 1 linear n from the values in v the intercept polynomial is omitted if v is preceded by the negative sign lt f condition on factor variable f lt r lt log v r forms natural logarithm of v r mal f constructs MA1 design matrix for factor f y mal forms an MA1 design matrix from plot numbers J mbf v r is a factor derived from data factor v by using the y y IMBF qualifier out n condition on observation n y out n t condition on record n trait t y y pol v n forms n 1 orthogonal polynomials of order 0 in tercept 1 linear nm from the values in v the intercept polynomial is omitted if n is preceded by the negative sign pow x p o defines the covariable x 0 for use in the model y where x is a variable in the data p is a power and o is an offset qtl f p impute a covariable from marker map information vy at position p sin u r forms sine from v with period r SS sqrt u r forms square root of v r uni f forms a factor with a level for each record where y factor fis non zero 89 6 2 Specifying model formulae in ASReml Table 6 1 Summary of reserved words operators and functions model term brief description common usage fixed random uni f n vec
335. ired before the model can be fitted This extra step involves defining the G structure for each term In Release 4 this is achieved by using functions to directly apply variance models to the individual component factors in a random model term to define G This produces a consolidated model term that simultaneously defines both the design matrix Z and variance model G This process is described in detail in Chapter 7 with examples 2 1 The general linear mixed model 2 1 9 Variance models for terms with several factors A random model term may comprise either a single factor or several component factors to give a compound model term Consider a compound model term represented by A B where the component factors A and B have m and n levels respectively and the operator forms a term with levels corresponding to the combinations of all levels of A with all levels of B The effects ab for A B are generated with the levels of B nested in the levels of A ie the levels of B cycling fastest ab ab ab ab ab ab ab ab ab A ab in an m1 Now consider the variance model for the term A B If we specify our variance model generi cally as vmodeli A vmodel2 B where vmodel1 is a variance model function with variance matrix A A and vmodel2 is a variance model function with variance matrix B Bw then the G structure for this term is defined by cov ab abji Aj X Bri 2 9 This me
336. is confusing When the A matrix incorporates fixed effects the number of DF involved may not be obvious especially if there is also a sparsely fitted fixed HYS factor The number of Fixed effects degrees of freedom associated with GROUPS is taken as the declared number less twice the number of constraints applied This assumes all groups are represented in the data and that degrees of freedom associated with group constraints will be fitted elsewhere in the model generates pedigree for inbred lines Each cross is assumed to be selfed several times to stabilize as an inbred line as is usual for cereals such as wheat before being evaluated or crossed with another line Since inbreeding is usually associated with strong selection it is not obvious that a pedigree assumption of covariance of 0 5 between parent and offspring actually holds Do not use the INBRED qualifier with the MGS or SELF qualifiers 163 9 5 Genetic groups List of pedigree file qualifiers qualifier description LONGINTEGER MAKE MEUWISSEN MGS QUAAS IREPEAT SARGOLZAEI ISELF s ISKIP n SORT IXLINK indicates the identifiers are numeric integer with less than 16 digits The default is integer values with less than 9 digits The alternative is alphanumeric identifiers with up to 255 character indicated by ALPHA tells ASReml to make the A inverse rather than trying to retrieve it from the ainverse bin file The
337. is a User Area on the website http www VSNi co uk select ASReml and then User Area which contains contributed material that may be of assistance Users with a support contract with VSN should email support asreml co uk for assistance with installation and running ASReml When requesting help please send the input com mand file the data file and the corresponding primary output file along with a description of the problem All ASReml users including unsupported users are encouraged to join the ASReml forum register now at http www vsni co uk forum 1 6 Typographic conventions If ASReml appears to be failing then please send details of the problem to support vsni co uk 1 6 Typographic conventions A hands on approach is the best way to develop a working understanding of a new computing package We therefore begin by presenting a guided tour of ASReml using a sample data set for demonstration see Chapter 3 Throughout the guide new concepts are demonstrated by example wherever possible In this guide you will find framed sample boxes to the right of the page as shown here These contain ASReml command file sample code Note that the code under discussion is highlighted in bold type for easy identification s AS that some of the original code is omitted from the display An example ASReml code box bold type highlights sections of code currently under discussion remaining code is not highlighted th
338. is achieved by using the xfa f k model term in place of fin the model For example y site r geno xfa site 2 0 0 1 geno xfa site 2 2 geno xfa site 2 O XFA2 With multiple factors some constraints are required to maintain identifiablity Traditionally this has simply been to set the leading loadings of new factors to zero Loadings then need to be rotated to orthogonality In ASReml 3 if no loadings are fixed i e GP ASReml will rotate the loadings to orthogonality and hold the leading loadings of lower factors fixed They are however updated in the orthogonalization process which occurs at the beginning of each iteration so the final returned values have not been formally rotated Finding the REML solutions for multifactor Factor Analytic models can be difficult The first problem is specifying initial values When using CONTINUE and progressing XFA k to XFA k 1 ASReml3 initialises the factor k 1 at W x 0 2 changing the sign of the relatively largest loading to negative One strategy which sometimes works in this context is to hold the previously estimated factor loadings fixed for one a few iterations so that the factor k 1 initally aims to explain variation previously incorporated in w Then allow all loadings to be updated in the remaining rounds A second problem at present unresolved is that sometimes the LogL rises to a relatively high value and then drifts away In an attempt to make the process easier
339. ist of values functions at f forms conditioning covariables for all levels of fac y J tor f fac v forms a factor from v with a level for each unique y value in v fac v y forms a factor with a level for each combination of J values in v and y lin f forms a variable from the factor fwith values equal y to 1 n corresponding to level 1 level n of the factor spl v k forms the design matrix for the random component J of a cubic spline for variable v other t n fits variable n from the G set of variables t This y y functions is a special case of the SUBGROUP qualifier func tion applied to G variables Note that the square parentheses are permitted alternative syntax and t r adds r times the design matrix for model term t to the previous design matrix r has a default value of 1 If tis complex it may be necessary to predefine it by saying t and t r c f factor fis fitted with sum to zero constraints J 88 6 2 Specifying model formulae in ASReml Table 6 1 Summary of reserved words operators and functions model brief description common usage term fixed random cos u Tr forms cosine from v with period r y ge f condition on factor variable f gt r y giv f n associates the nth giv G inverse with the factor J f grm f n associates the nth grm G with the factor f J gt f condition on factor variable f gt r J h f factor fis fitted Helmert constraints J ide f fits pedigree factor f without relat
340. istics indicate that the interaction between dose and sex is not significant The F_con column helps us to assess the significance of the other terms in the model It confirms littersize is significant after the other terms that dose is significant when adjusted for littersize and sex but ignoring dose sex and that sex is significant when adjusted for littersize and dose but ignoring dose sex These tests respect marginality to the dose sex interaction We also note the comment 3 possible outliers see res file Checking the res file we discover unit 66 has a standardised residual of 8 80 see Figure 16 1 The weight of this female rat within litter 9 is only 3 68 compared to weights of 7 26 and 6 58 for two other female sibling pups This weight appears erroneous but without knowledge of the actual experiment we retain the observation in the following However part 2 shows one way of dropping unit 66 by fitting an effect for it with out 66 We refit the model without the dose sex term Note that the variance parameters are re estimated though there is little change from the previous analysis Model_Term Gamma Sigma Sigma SE 7 C dam ar 27 0 595157 0 87 S179E 01 2 93 0 P Variance 322 317 1 00000 0 164524 12 13 0 P Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 7 mu 1 32 0 8981 48 1093 05 lt 001 3 littersize 1 31 4 27 85 46 43 A lt 001 1 dose 2 24 0 12 05 11 42 A lt 001 2 sex 1 301 7 58 27 5
341. itional_initial_values are read from the following lines if there are not enough initial values on the model line Each variance model has a certain number of parameters If insufficient non zero values are found on the model line ASReml expects to find them on the following line s initial values of 0 0 will be ignored if they are on the model line but are accepted on subsequent lines the notation n v for example 5 0 1 is permitted on subsequent lines but not the model line when there are n repeats of a particular initial value v only in a few specified cases is O permitted as an initial value of a non zero parameter 7 4 4 G structure header and definition lines There are g sets of G structure definition lines and each set is of the form model_term d order key model initial_values qualifier additional_initial_values order key model initial values qualifier additional initial values order key model initial_values qualifier additional_initial_values e model_term is the term from the linear model to which the variance structure ap plies the variance structure may cover ad ditional terms in the linear model see Sec tion 7 8 NIN Alliance Trial 1989 variety A id row 22 column 11 nin89aug asd skip 1 yield mu variety r repl If mv 121 22 row AR1 0 3 11 column AR1 0 3 repl i repl O IDV 0 1 121 7 4 Variance structures e dis the number of varian
342. itted hetero geneous variances This is nin89a res Convergence sequence of variance parameters Iteration 1 2 3 4 5 6 LogL 401 827 400 780 399 807 399 353 399 326 399 324 Change 59 80 83 21 5 1 Adjusted 0 0 0 0 0 0 StepSz 0 316 0 562 1 000 1 000 1 000 1 000 5 0 500000 0 538787 0 589519 0 639457 0 651397 0 654445 Dab 6 0 500000 0 487564 0 469768 0 448895 0 440861 0 438406 0 6 Plot of Residuals 24 8730 15 9145 vs Fitted values 16 7724 35 9355 RvE SA A a ene ee enn en erie en eh ee enone en anes 1 T 1 1 1 12 2 1211 1211 i 1 i 112 15 1 311 121 4 1 i 312 111 2291 3 a 1 1 1 4 1 4 1 22121 41121 2 2 1 1 11 1112 23 11 1 2 1 12 4 TZ Tis E 2 UL ace a aa eae aa A a a 1 1 11 1 1 412 12 1 2 1 1 11 1 3 2 1 if 1 11 11 i 1 111 4 2 1i 1 1 1 1 12 1 1 1 1 1 SLOPES FOR LOG ABS RES on LOG PV for Section 1 0 15 SLOPES FOR LOG SDi on LOG PVBari for Section I 4 37 xk kkk ES xk kkk kkk kkk OK 2K KK KK OK OK KOK kkk KOK 235 14 4 Other ASReml output files o o T 29 87 A 44 1i 18 18 40 29 ab 75 99 114 257 333 227 167 183 277 EEES ok A Rd k kk kkk k kk a OK OR ORR kk k Min Mean Max 24 873 0 27954 15 915 omitting Spatial diagnostic statistics of Residuals 22 1 Residual Plot and Autocorrelations lt LOo xXH gt se 0 077 ttr O x x x gt X lo
343. iv files If GROUPS is also specified this giv file will include the GROUPSDF qualifier on its first line An alternative to group constraints see GROUP below is to shrink the group effects by adding the constant o gt 0 to the diagonal elements of A pertaining to groups When a constant is added no adjustment of the degrees of freedom is made for genetic groups Use GOFFSET 1 to add no offset but to suppress insertion of constraints where empty groups appear The empty groups are then not counted in the DF adjustment includes genetic groups in the pedigree The first g lines of the pedigree identify genetic groups with zero in both the sire and dam fields All other lines must specify one of the genetic groups as sire or dam if the actual parent is unknown You may insert Groups with no members to define constraints on groups that is to associate groups into supergroups where the supergroup fixed effect is formally fitted separately in the model A constraint is added to the inverse which causes the preceding set of groups which have members to have effects which sum to zero The issue is to get the degrees of freedom correct and to get the correct calculation of the Likelihood especially in bivariate cases where DF associated with groups may differ between traits The LAST qualifier see page 80 is designed to help as without it reordering may associate singularities in the A matrix with random effects which at the very least
344. ize qualifier to extend the size of factor labels stored extra data fields on a line are ignored if there are fewer data items on a line than ASReml expects the remainder are taken from the following line s except in csv files were they are taken as missing If you end up with half the number of records you expected this is probably the reason e all lines beginning with followed by a blank are copied to the asr file as comments for the output their contents are ignored 4 2 2 Fixed format data files The format must be supplied with the FORMAT qualifier which is described in Table 5 5 However if all fields are present and are separated the file can be read free format 4 2 3 Preparing data files in Excel Many users find it convenient to prepare their data in EXCEL ACCESS or some other database Such data must be exported from these programs into either csv Comma separated values or txt TAB separated values form for ASReml to read it ASReml can convert an x1s file to a csv file When ASReml is invoked with an x1s file as the filename argument and there is no csv file or as with the same basename it exports the first sheet as a csv file and then generates a template as command file from any column headings it finds see page 196 It will also convert a Genstat gsh spreadsheet file to csv format The data extracted from the x1s file are labels numerical values and the results from formulae Empty rows at the st
345. k a treat Trait treat demonstrates a multivariate analysis of the 5 9 five repeated measures Note that the two di 97 0 Ip terror variance mensional structure for common error meets Trait 0 US the requirement of independent units and is ASReml generates initial values correctly ordered traits with units 152 8 1 Introduction 8 1 2 Wether trial data Three key traits for the Australian wool industry are the weight of wool grown per year the cleanness and the diame ter of that wool Much of the wool is produced from wethers and most ma jor producers have traditionally used a particular strain or bloodline To as sess the importance of bloodline differences many wether trials were conducted One trial was conducted from 1984 to 1988 at Borenore near Orange It involved 35 teams of wethers representing 27 blood lines The file wether dat shown below con tains greasy fleece weight kg yield per centage of clean fleece weight to greasy fleece weight and fibre diameter microns The code wether as to the right per forms a basic bivariate analysis of this data Orange Wether Trial 1984 8 SheepID I TRIAL BloodLine I TEAM YEAR GFW YLD FDIAM wether dat skip 1 GFW FDIAM Trait Trait YEAR lr Trait TEAM Trait SheepID 122 1485 O ID Trait 0 US IGP 2 2 4 Trait TEAM 2 Trait 0 US 0 4 03 1 3 TEAM O ID Trait SheepID 2 Trait 0 US GP 0 2 0 2 2 SheepID O ID pr
346. k on the following lines They are then listed again with identifying information in a form that the user may edit 0 000000 0 000000 0 000000 1 0000000 0 4374436 0 6555482 RSTRUCTURE 1 2 3 VARIANCE 1 1 0 4 V P 1 00000000 0 Q STRUCTURE 11 1 1 Ss By U 0 43744360 o 0 STRUCTURE 22 1 1 6 RE U 0 65554814 O 0 14 4 8 The tab file The tab file contains the simple variety means and cell frequencies Below is a cut down version of nin89 tab nin alliance trial 10 Sep 2002 04 20 15 Simple tabulation of yield variety LANCER 28 56 4 BRULE 26 07 4 REDLAND 30 50 4 CODY 21 21 4 ARAPAHOE 29 44 4 NE83404 27 39 4 NE83406 24 28 4 NE83407 22 69 4 CENTURA 21 65 4 SCOUT66 27 52 4 COLT 27 00 4 NE87615 25 69 4 NE87619 31 26 4 NE87627 23 23 4 14 4 9 The vrb file 240 14 4 Other ASReml output files The vrb file contains the estimates of the effects together with their approximate prediction variance matrix corresponding to the dense portion It is only written if the VRB qualifier is specified The file is formatted for reading back for post processing The number of equations in the dense portion can be increased to a maximum of 800 using the DENSE option Table 5 5 but not to include random effects The matrix is lower triangular row wise in the order that the parameters are printed in the sln file It can be thought of as a partitioned lower triangular matrix q a ec where B is the dense portion of 8 and
347. kelihood 345 256 343 22 we expect more variation for the exposed treatment and thus the extra variance component for this term should be positive Had we mistakenly specified level 1 then ASReml would have estimated a negative component by setting the GU option for this term The portion of the ASReml output for this analysis is 6 LogL 343 428 s2 1 1498 262 df i 1 components constrained 7 LogL 343 234 S2 1 1531 262 df 8 LogL 343 228 s2 1 1572 262 df 9 LogL 343 228 S2 1 1563 262 df Model_Term Gamma Sigma Sigma SE C variety 44 44 2 01903 2 33451 3 01 QP run 66 66 0 276045 0 319178 0 59 OP pair 132 132 0 853941 0 987372 2 59 UFP uni tmt 2 264 264 0 176158 0 203684 0 32 OP Variance 264 262 1 00000 1 15625 2 37 OP tmt variety DIAGonal 1 1 30142 1 50477 2 26 OU tmt variety DIAGonal 2 0 321901 0 372199 0 62 4D tmt run DIAGonal 1 1 20098 1 38864 218 QU tmt run DIAGonal 2 1 92457 2 22530 207 GU Wald F statistics Source of Variation NumDF DenDF F inc Prob 7 mu 1 56 5 1276 73 lt 001 4 tmt 1 60 6 448 83 lt 001 The estimated variance components from this analysis are given in column b of table 16 8 There is no significant variance heterogeneity at the residual or tmt run level This indicates that the square root transformation of the data has successfully stabilised the error variance There is however significant variance heterogeneity for tmt variety interactions with the variance being much greater for the
348. king the estimates from the univariate analyses and using them in the diagonal analysis The Log likelihood from this run is 20000 1566 45 Once the model from PATH 1 has run we can rerun the analysis changing ARG 1 to ARG 2 332 16 11 Multivariate animal genetics data Sheep to obtain the next analysis With the statement CONTINUE coopmf1 rsv ASReml generates initial values from the coopmf1 rsv file if no filename is given ASRem1 will look for the previous rsv file to generate initial values In analysis 2 we get estimates of the sire dam and litter matrices based on a factor analysis parameterization This can give better initial values for unstructured matrices and indicate if the estimated matrices are near singularity The log likelihood from this run is 20000 1488 11 In this case the dam variance parameters are Model_Term Sigma Sigma Sigma SE C xfa TrDam123 1 dam XFAV O 1 0 405222 0 405222 1 30 o P xfa TrDam123 1 dam XFAV O 2 0 00000 0 00000 0 00 0 F xfa TrDam123 1 dam AFA V 0 3 0 616 12 02 0 616712E 02 1 14 0 P xfa TrDam123 1 dam AFA_L 1 1 1 29793 1 29793 9 05 0 P xfa TrDam123 1 dam AFA L 1 2 1 68814 1 68814 9 90 OP xfa TrDam123 1 dam XFA_L 1 3 0 124492 0 124492 6 02 iP And one of the dam specific variances is zero The resulting dam matrix is Covariance Variance Correlation Matrix XFA xfa TrDam123 1 dam 2 090 0 8981 0 7590 0 8981 2 190 2 845 0 8451 1 0000 0 1613 0 2096 0 2162E 01 0 8451 1 298 1 687 0 1243 1
349. l 12 combinations 12 3 Examples Key fields have different names IMERGE filel KEY keyla keylb WITH file2 KEY key2a key2b TO newfile Key fields have common name and other fields are also duplicated IMERGE filel KEY keya keyb WITH file TO newfile CHECK IMERGE filel Key key KEEP WITH file2 to newfile will discard records from file2 that do not match records in filel but all records in file1 are retained Omitting fields from the merged file IMERGE filel KEY key skip slaslb WITH file SKIP s2a s2b TO newfile Single insertion merging IMERGE adult txt KEY ewe KEEP WITH birth txt KEEP TO newfile NODUP but 213 13 Functions of variance components 13 1 Introduction ASReml includes a procedure to calculate cer YEREDICT DEFINE tain functions of variance components either F PhenVar Sire Residual as a final stage of an analysis or as a post F GenVar Sire 4 analysis procedure These functions enable H herit GenVar PhenVar the calculation of heritabilities and correla tions from simple variance components and when US CORUH and XFA structures are used in the model fitting A simple example is shown in the code box The instructions to per form the required operations are listed after the VPREDICT DEFINE line and terminated by a blank line ASReml holds the instructions in a pin until the end of the job when it retrieves the relevant information from the asr and vvp files and performs the specif
350. l C 1 304 30 1 2 l uw 0 lt CIR circular Web C 1 1 2 l w ster amp Oliver 2 2 o 1 j 6 1 07 sin ij 2001 p 113 1 bis 7 i 0 lt AEXP anisotropic ex Ca 1 2 3 2 w ponential C gliz plyi ys 0 lt lt 1 0 lt lt 1 AGAU anisotropic C 1 2 3 2 w gaussian C pra piri 0 lt lt 10 lt lt 1 125 7 5 Variance model description Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance MATk Mat rn with C Mat rn see text k k 1 hi first 1 lt k lt 5 gt 0 range v shape 0 5 o is gt 0 anisotropy ratio 1 the user a anisotropy angle 0 A 1 2 metric 2 Additional heterogeneous variance models DIAG diagonal IDH 0 X 0 1 J Ww ii US unstructured Xij Q E Ww w 1 general covari ance matrix OWNk user explicitly k forms V and OV ANTE 1 1 k order Y UDU wrt ANTE k see D 4 De 0 i4j pendence me 1 U u 1 lt 7 t lt 1 lt k lt w l U De DER J lt k Us 0 1 gt CHOL 1 1 k order X LDI sieti th CHOLk cholesky D d D 0 143 1 lt k lt w 1 L 1 Lsi 151 j lt k FA 1 1 korder x DCD w w th FAk k factor C FF E kw w analytic F contains k correlation factors E diagonal DD diag 2 FACV 1 IS k order X IT w w FACVk k factor T contains covariance factors kw w an
351. l linear model given symbolically by yo 1 A B AB then A and B are said to be marginal to A B and 1 is marginal to A and B In a three way factorial model given by yv 1 A B C AB AC B C A B C the terms A B C A B A C and B C are marginal to A B C Nelder 1977 1994 argues that meaningful and interesting tests for terms in such models can only be conducted for those tests which respect marginality relations This philosophy underpins the following description of the second Wald statistic available in ASReml the so called conditional Wald statistic This method is invoked by placing FCON on the datafile line ASReml attempts to construct conditional Wald statistics for each term in the fixed dense linear model so that marginality relations are respected As a simple example for the three way factorial model the conditional Wald statistics would be computed as Term Sums of Squares M code 1 R 1 A R A 1 B C B C R 1 A B C B C R 1 B C B C A B R B 1 A C A C R 1 A B C A C R 1 A C A C A C R C 1 A B A B R 1 A B C A B R 1 A B A B A A B R A B 1 A B C A C B C R 1 A B C A B A C B C R 1 A B C A C B C B A C R A C 1 A B C A B B C R 1 A B C A B A C B C R 1 A B C A B B C B B C R B C 1 A B C A B A C R 1 A B C A B A C B C R 1 A B C A B A C B A B C R A B C 1 A B C A B A C B C R 1 A B C A B A C B C A B C R 1 A B C A B A C B C Q Of these the conditional Wald statistic for t
352. l qualifiers lt lt ocos cosas eee Ee Command file Specifying the terms in the mixed model 6 1 6 2 6 3 e oe Ree ee Se Se EERE ER EER EEE Specifying model formulae in ASReml 2 22004 GAl General rules ee AER SRR ADEE ERE ES amp APA oe ee Pe ee Se CES SS Ee eee Se woke Fixed terms in the model 2000 ee ee ee ee vi GaL Primary Ed TENN o ie yoy Bo od BREN SHE SOS HERS 91 032 Sie tiked terms o oos ee we EEG REG ES 92 6 4 Random terms in the model 2 2266 ies eso ee ee 92 6 5 Interactions and conditional factors v v ve ee ee ee ee ee 93 051 Interactions o co o Rk eee ew he oe eh ee ee ah og 93 ORF Epes ss ala oda res eee eh ee ee bee a TE 93 653 Conditional factos occu oe Sw be ee See Ee Re Sew ed 94 6 5 4 Associated Factors o 0 000022 eee eee 94 6 6 Alphabetic list of model functions o ee eee 95 6 7 WEEDS ds e no a a A eS 100 6 8 Generalized Linear Mixed Models o 100 6 8 1 Generalized Linear Mixed Models o 104 6 9 Missing valties e te we hae ee RE go GB eS ee Ee eS ee 105 6 9 1 Missing values in the response 2 2 20004 105 6 9 2 Missing values in the explanatory variables 105 6 10 Some technical details about model fitting in ASReml 106 6 10 1 Sparse versus deise see ei ek ke ara ew 106 6 10 2 Ordering of terms in ASReml 0 0 000004 106
353. lable from http www vsni co uk products asreml as well as in the examples directory created under the standard installation They remain the property of the authors or of the origi nal source but may be freely distributed provided the source is acknowledged The authors would appreciate feedback and suggestions for improvements to the program and this guide Proceeds from the licensing of ASReml are used to support continued development to im plement new developments in the application of linear mixed models The developmental version is available to supported licensees via a website upon request to VSN Most users will not need to access the developmental version unless they are actively involved in testing a new development Acknowledgements We gratefully acknowledge the Grains Research and Development Corporation of Australia for their financial support for our research since 1988 Brian Cullis and Arthur Gilmour wish to thank the NSW Department of Primary Industries and more recently the University of Wollongong for providing a stimulating and exciting environment for applied biometrical re search and consulting Rothamsted Research receives grant aided support from the Biotech nology and Biological Sciences Research Council of the United Kingdom We sincerely thank Ari Verbyla Dave Butler and Alison Smith the other members of the ASReml team Ari contributed the cubic smoothing splines technology information for the Marker map impu
354. lements in the model may also be separated by which is ignored except at the end of a line when it implies the model is continued on the next line the character separates the response variables s from the explanatory variables in the model data fields are identified in the model by their labels labels are case sensitive labels may be abbreviated truncated when used in the model line but care must be taken that the truncated form is not ambiguous If the truncated form matches more than one label the term associated with the first match is assumed For example dens is an abbeviation for density but spl dens 7 is a different model term to spl density 7 because it does not represent a simple truncation model terms may only appear once in the model line repeated occurrences are ignored model terms other than the original data fields are defined the first time they appear on the model line They may be abbreviated truncated if they are referred to again provided no ambiguity is introduced Important It is often clearer if labels are not abbreviated If abbreviations are used then they need to be chosen to avoid confusion e if the model is written over several lines all but the final line must end with a comma or sign to indicate that the list is continued In Tables 6 1 and 6 2 the arguments in model term functions are represented by the following symbols f the label of a data variable defined as a model fac
355. lled the growth curves by a three parameter logistic function of age given by Q 1 exp z 2 93 where y is the trunk circumference x is the tree age in days since December 31 1968 is the asymptotic height Ha is the inflection point or the time at which the tree reaches 0 5 3 is the time elapsed between trees reaching half and about 3 4 of q y 16 11 The datafile consists of 5 columns viz Tree a factor with 5 levels age tree age in days since 31st December 1968 circ the trunk circumference and season The last column season was added after noting that tree age spans several years and if converted to day of year 310 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges this is the orange data circ age Tree Figure 16 12 Trellis plot of trunk circumference for each tree measurements were taken in either Spring April May or Autumn September October First we demonstrate the fitting of a cubic spline in ASReml by restricting the dataset to tree 1 only The model includes the intercept and linear regression of trunk circumference on age and an additional random term spl age 7 which instructs ASReml to include a random term with a special design matrix with 7 2 5 columns which relate to the vector whose elements 6 27 2 6 are the second differentials of the cubic spline at the knot points The second differentials of a natural cubic spline ar
356. lly used job control qualifiers qualifier action ISECTION v ISPLINE spl v n p specifies the factor in the data that defines the data sections This qual ifier enables ASReml to check that sections have been correctly dimen sioned but does not cause ASReml to sort the data unless ROWFACTOR and COLUMNFACTOR are also specified Data is assumed to be presorted by section but will be sorted on row and column within section Further more when the model term mv is included in the model and ROWFACTOR and COLUMNFACTOR are defined ASRem1 will check that the observations in each section form a complete grid if not the grid will be completed by adding the appropriate extra data records The following is a basic example assuming 5 sites sections When ROWFACTOR vu and COLUMNFACTOR v are both specified ASReml generates the R structures for a standard AR1 ARI spatial analysis However if the number of rows or columns is five see IDLIMIT or less an ID rather than AR1 structure is applied The R structure lines that a user would normally be required to work out and type into the as file see the example of Section 16 6 are written to the res file The user may then cut and paste them into the as file for a later run if the structures need to be modified Basic multi environment trial analysis site 5 sites coded 1 5 column columns coded 1 row rows coded 1 variety A variety names yield met dat
357. lt args gt is any argument strings built into the output names by use of the RENAME qual ifier lt type gt indicates the contents of the figure as given in the following table lt pass gt is inserted when the job is repeated RENAME or CYCLE to ensure filenames are unique across repeats lt section gt is inserted to distinquish files produced from different sections of data for example from multisite spatial analysis and lt ext gt indicates the file graphics format lt type gt file contents R marginal means of residuals from spatial analysis of a section V variogram of residuals from spatial analysis for a section S residuals in field plan for a section H histogram of residuals for a section _RvE residuals plotted against expected values XYGi figure produced by X Y and G qualifiers PV_i Predicted values plotted for PREDICT directive 2 The graphics file format is specified by following the G or H option by a number g or specifying the appropriate qualifier on the top job control line as follows 200 11 3 Command line options g qualifier description lt ert gt 1 HPGL HP GL pgl 2 IPS Postscript default ps 6 BMP BMP bmp 10 WPM Windows Print Manager 11 WMF Windows Meta File wmf 12 HPGL 2 HP GL2 hgl 21 PNG PNG png 22 1EPS EncapsulatedPostScript eps 11 3 5 Job control command line options C F O R C CONTINUE indicates that the job is to continue iterating from the valu
358. lt message ERROR Reading the data The warning does not cause the job to terminate immediately but arises because slip is not a recognised data file line qualifier the correct qualifier is skip The job terminates when reading the header line of the nin asd file which is alphabetic when it is expecting numeric values The following output displays the error message produced Folder C data ex manex QUALIFIERS SLIP 1 Warning Unrecognised qualifier at character 9 SLIP 1 QUALIFIER DOPART 1 is active Reading nin asd FREE FORMAT skipping O lines Univariate analysis of yield Error at field 1 variety of record 1 line 1 error Since this is the first data record you may need to skip some header lines hint see SKIP or append the A qualifier to the definition of factor variety Fault Missing faulty SKIP or A needed for variety Last line read was variety id pid raw rep nloc yield lat long row column give away Currently defined structures COLS and LEVELS 1 variety a 56 56 0 0 0 2 id L 1 1 0 1 3 pid i il 1 0 2 15 4 An example raw repl nloc yield lat long oO 0 4 On Re RR PP BR e e e re re BR 0 MOAN OT DAOU 22 22 11 11 10 row 11 column 10 12 mu ninerr2 nin asd Model specification TERM LEVELS GAMMAS mu 0 ORRR RFP PR PP oo Oo O SS O O O YO SO a K amp 2 a a a amp variety 0 12 factors defined max 500 O variance parameters max1500 2 special structures Last line read was variety id
359. lue in the variance component table GU unrestricted does not limit the updates to the parameter This allows variance parameters to go negative and correlation parameters to exceed 1 Negative variance components may lead to problems the mixed model coefficient matrix may become non positive definite In this case the sequence of REML log likelihoods may be erratic and you may need to experiment with starting values IGF fixes the parameter at its starting value IGZ only applies to FA and FACV models and fixes the corresponding parameter in to zero 0 00 For multiple parameters the form GXXXX can be used to specify F P U or Z for the parameters individually A shorthand notation allows a repeat count before a code letter Thus GPPPPPPPPPPPPPPZPPPZP could be written as G14PZ3PZP For a US model GP makes ASReml attempt to keep the matrix positive definite After each AI update it extracts the eigenvalues of the updated matrix If any are negative or zero the AI update is discarded and an EM update is performed Notice that the EM update is applied to all of the variance parameters in the particular US model and cannot be applied to only a subset of them is used to associate a label f with a variance structure so that the same structure can be used elsewhere in the variance model via the USE f qualifier see page 143 The variance model see Section 2 2 is 2 530 Ri i ZG y Z e For multivariate models c and 0
360. lumns containing the outlier statistics described on page 18 Model Term Level Effect seEffect variety LANCER 0 000 0 000 variety estimates variety BRULE 2 987 2 842 variety REDLAND 4 707 2 978 variety CODY 0 3131 2 961 variety ARAPAHOE 2 954 2 727 variety NE87615 1 035 2 934 variety NE87619 5 939 2 850 variety NE87627 4 376 2 998 mu 1 24 09 2 465 intercept mv_estimates 1 21 81 6 729 missing value mv_estimates 2 23 22 6 721 estimates mv_estimates 3 22 52 6 708 mv_estimates 23 49 6 676 mv_estimates 5 22 20 6 698 mv_estimates 6 24 47 6 107 mv_estimates 7 20 14 6 697 mv_estimates 8 25 01 6 691 mv_estimates 9 24 29 6 676 mv_estimates 10 26 30 6 658 14 3 3 The yht file The yht file contains the predicted values of the data in the original order this is not changed by supplying row column order in spatial analyses the residuals and the diagonal elements of the hat matrix Figure 14 1 shows the residuals plotted against the fitted values Yhat and a line printer version of this figure is written to the res file Where an observa tion is missing the residual missing values predicted value and Hat value are also declared missing The missing value estimates with standard errors are reported in the sln file This is the first 20 lines of nin89a yht Note that the values corresponding to the missing data first 15 records are all 0 1000E 36 which is the internal value used for missing values Record Yhat Residual
361. ly used job control qualifiers qualifier action MVINCLUDE MVREMOVE NODISPLAY IPVAL v p IPVAL f ulist ROWFACTOR v ROWFAC v Restrictions The key field MUST be numeric In particular if the data field it relates to is either an A or I encoded factor the original uncoded level labels may not specified in the MBF file Rather the coded levels must be specified The MBF file is processed before the data file is read in and so the mapping to coded levels has not been defined in ASReml when the MBF file is processed although the user can must anticipate what it will be Comment If this MBF process is to be used repeatedly for example to process a large set of marker variables in conjunction with CYCLE processing will be much faster if the markers variables are in separate files ASReml will read 10 files containing a single field much faster than reading a single file containing 400 fields ten times to extract 10 different markers When missing values occur in the design ASReml will report this fact and abort the job unless MVINCLUDE is specified see Section 6 9 then missing values are treated as zeros Use the DV transformation to drop the records with the missing values instructs ASReml to discard records which have missing values in the design matrix see Section 6 9 suppresses the graphic display of the variogram and residuals which is otherwise produced for spatial analyses in the PC and M
362. lyses can be conducted in ASReml For these analyses it is convenient to arrange the data in a multivariate form with 7 fields representing the plant number treatment identification and the 5 heights The 282 16 5 Balanced repeated measures Height ASReml input file up to the specification of the R structure is This is plant data multivariate tmt IA Diseased Healthy plant 14 yl y3 y5 y7 y10 grass asd skip 1 ASUV The focus is modelling of the error variance for the data Specifically we fit the multivariate regression model given by Y DT E 16 1 where Y is the matrix of heights DU is the design matrix T2 is the matrix of fixed effects and E is the matrix of errors The heights taken on the same plants will be correlated and so we assume that var vec E I14 6 X 16 2 where N is a symmetric positive definite matrix The variance models used for 2 are given in Table 16 4 These represent some commonly used models for the analysis of repeated measures data see Wolfinger 1986 The variance models are fitted by changing the last four lines of the input file The sequence of commands for the first model fitted is y1 y3 y5 y7 y10 Trait tmt Tr tmt r units 1 20 14 Trait Table 16 4 Summary of variance models fitted to the plant data number of REML model parameters log likelihood BIC Uniform 2 196 88 401 95 Power 2 182 98 374 15 Heterogeneous Power 6 171 50 367 57 Antedependenc
363. m defined as the combined residual unless the data records were sorted within ASReml in which case the units and the correlated residuals are in different orders data file order and field order respectively the residuals are printed in the yht file but the statistics in the res file are calculated from the combined residual the Covariance Variance Correlation C V C matrix calculated directly from the residuals it contains the covariance below the diagonals the variances on the diagonal and the correlations above the diagonal The fitted matrix is the same as is reported in the asr file and if the Logl has converged is the one you would report The BLUPs matrix is calculated from the BLUPs and is provided so it can be used as starting values when a simple initial model has been used and you are wanting to attempt to fit a full unstructured matrix For computational reasons it pertains to the parameters and so may differ from the parameter values generated by the last iteration The BLUPs matrix may look quite different from the fitted matrix because BLUPs are shrunken phenotypes The BLUPs matrix retains much of the character of the phenotypes the rescaled has the variance from the fitted and the covariance from the BLUPs and might be more suitable as an initial matrix if the variances have been estimated The BLUPs and rescaled matrices should not be reported relevant portions of the estimated variance matrix for each term for w
364. m the linear mixed model are to be used when predicting the cells in the multiway hyper table in order to obtain either conditional or marginal predictions That is you may choose to ignore some random terms in addition to those ignored because they involve variables in the ignored set All terms involving associated factors are by default included d Choose the weights to be used when averaging cells in the hyper table to produce the multiway table to be reported The multiway table may require partial and or sequential averaging over associated factors Operationally ASReml does the averaging in the pre diction design matrix rather than actually predicting the cells of the hyper table and then averaging them The main difference in this prediction process compared to that described by Lane and Nelder 1982 is the choice of whether to include or exclude model terms when forming predictions In linear models since all terms are fixed factors not in the classify set must be in the averaging set and all terms must contribute to the predictions 10 3 2 Predict syntax The first step is to specify the classify set of NIN Alliance trial 1989 variety A explanatory variables after the predict direc tive The predict statement s may appear Column 11 immediately after the model line before or ning9 asd skip 1 after any tabulate statements or after the yield mu variety r repl R and G structure lines The syntax is predict
365. mation 51 syntax 53 typographic conventions 4 unbalanced data 279 nested design 276 UNIX 195 Unix crashes 200 Unix debugging 231 unreplicated trial 295 variance components 356 INDEX functions of 214 variance header line 118 119 variance model combining 12 138 description 123 forming from correlation models 128 qualifiers 137 specification 109 specifying 110 variance parameters 12 constraining 118 141 within a model 141 relationships 144 variance structure parameters simple relationships 142 variance structures 32 117 multivariate 155 VCM 70 Wald F statistics 20 weight 100 weights 41 Working Folder 62 workspace options 202 XFA extension 134 357
366. ml border pin will perform the pinfile calculations defined in border pin on the results in files border asr and border vvp ASReml Pborderwwt border pin will perform the pinfile calculations defined in border pin on the results in files borderwwt asr and borderwwt vvp 11 2 3 Forming a job template from a data file The facility to generate a template as file has been moved to the command line and extended Normally the name of a as command file is specified on the command line If a as file does not exist and a file with file extension asd csv dat gsh txt or xls is specified ASReml assumes the data file has field labels in the first row and generates a as file template First it seeks to convert the gsh Genstat or x1s Excel see page 42 196 11 3 Command line options file to csv format In generating the as template ASReml takes the first line of the csv or other file as providing column headings and generates field definition lines from them If some labels have appended these are defined as factors otherwise ASReml attempts to identify factors from the field contents The template needs further editing before it is ready to run but does have the field names copied across 11 3 Command line options Command line options and arguments may be specified on the command line or on the top job control line This is an optional first line of the as file which sets command line options and argumen
367. mm into days Jmmd converts a date in the form ccyym mdd yymmdd or mmdd into days Jyyd converts a date in the form ccyyddd or yyddd into days These calculate the number of days since December 31 1900 and are valid for dates from January 1 1900 to De cember 31 2099 note that if cc is omitted it is taken as 19 if yy gt 32 and 20 if yy lt 33 the date must be entirely numeric charac ters such as may not be present but see DATE IMu converts data values of v to missing if IM is used after A or I v should refer to the encoded fac tor level rather than the value in the data file see also Section 4 2 the maximum minimum and mod ulus of the field values and the value v assigns Haldane map positions s to marker variables and imputes miss ing values to the markers see be low replaces any missing values in the variate with the value v If v is an other field its value is copied replaces the variate with normal random variables having variance v replaces data values o with n in the current variable I e IF DataValue EQ o DataValue n rescales the column s in the current variable G group of variables us ing Y Y 0 xs sets the seed for the random number generator 56 yield M 9 yield M lt 0 M gt 100 yield MAX 9 ChrAadd IG 10 IMM 1 Rate NA O WT Wt2 INA Wt1 Ndat 0 Normal 4 5 is equivalent to Ndat Normal 4 5 Rate REPLACE 9 0 Rate RESCALE
368. model This enables it to analyse large and complex data sets quite efficiently One of the strengths of ASReml is the wide range of variance models for the random effects in the linear mixed model that are available There is a potential cost for this wide choice Users should be aware of the dangers of either overfitting or attempting to fit inappropriate variance models to small or highly unbalanced data sets We stress the importance of using data driven diagnostics and encourage the user to read the examples chapter in which we have attempted to not only present the syntax of ASReml in the context of real analyses but also to indicate some of the modelling approaches we have found useful There are several interfaces to the core functionality of ASReml The program name ASReml relates to the primary program ASReml W refers to the user interface program developed by VSN and distributed with ASReml ASReml R refers to the S language interface to a DLL of the core ASReml routines GenStat uses the same core routines for its REML directive Both of these have good data manipulation and graphical facilities The focus in developing ASReml has been on the core engine and it is freely acknowledged that its user interface is not to the level of these other packages Nevertheless as the developer s interface it is functional it gives access to everything that the core can do and is especially suited to batch processing and running of large models wi
369. month PRWTS YMprwts txt where YMprwts txt contains 11 2 21 0 11 2 10 6 11 4 12 08 4 0 0 0 0 0 0 0 0 0 00 7 2 0 0 0 0 10 6 46 4 8 10 8 10 88 68 7 0 0 0 0 0 14 0 0 4 2 3 4 0 0 0 0 0 0 14 0 0 0 0 10 6 0 0 10 6 11 2 4 4 18 4 3 8 8 8 0 o T 2 0 0 9 8 0 4 4 0 10 6 14 4 4 0 10 2 3 2 10 2 0 0 We have presented both sets of predict statements to show how the weights were derived and presented Notice that the order in PRESENT year month implies that the weight coefficients are presented in standard order with the levels for months cycling within levels for years There is a check which reports if non zero weights are associated with cells that have no data The weights are reported in the pvs file PRESENT counts are reported in 192 10 3 Prediction the res file 10 3 6 Examples Examples are as follows yield mu variety r repl predict variety is used to predict variety means in the NIN field trial analysis Random repl is ignored in the prediction yield mu x variety r repl predict variety predicts variety means at the average of x ignoring random repl yield mu x variety repl predict variety x 2 forms the hyper table based on variety and repl at the covariate value of 2 and then averages across repl to produce variety predictions GFW Fdiam Trait Trait Year r Trait Team predict Trait Team forms the hyper table for each trait based on Year and Team with each linear combination in each cell of the hype
370. mplicated example from a rotation experiment conducted over several years One analysis was of the daily live weight gain per hectare of the sheep grazing the plots There were periods when no sheep grazed Different flocks grazed in the different years Daily liveweight gain was assessed between 5 and 8 times in the various years To obtain a measure of total productivity in terms of sheep liveweight we need to weight the daily gain by the number of sheep grazing days per month The production for each year is given by predict year 1 crop 1 pasture lime AVE month 56 55 56 53 57 63 6 0 predict year 2 crop 1 pasture lime AVE month 36 0 0 53 23 24 54 54 43 35 0 0 predict year 3 crop 1 pasture lime AVE month 70 0 21 17000 70 00 53 0 predict year 4 crop 1 pasture lime AVE month 53 56 22 92 19 44 0 0 36 0 0 49 predict year 5 crop 1 pasture lime AVE month 0 22 0 53 70 22 0 51 16 5100 but to average over years as well we need one of the following predict statements predict crop 1 pasture lime PRES year month PRWTS 1 56 55 56 53 87 63 0 0 0 0 0 0 36 0 053 23 24 54 54 43 35 0 0 TO O 2117 0 0 070 0 053 0 53 56 22 92 1944 0 036 0 0 49 0 220 537022 051 16 51 0 0 5 predict crop 1 pasture lime PRES month year IPRWTS 56 36 70 53 O 55 0 0 56 22 56 02122 0 53 53 17 92 53 57 23 0 1 70 63 24 0 44 22 054 0 0 0 0 54 70 0 51 0 43 0 36 16 G35 0 51 0 053 0 0 O O 0 49 0 5 predict crop 1 pasture lime PRES year
371. multinomial distribution fori lt j lt t Typically the response variable is a single variable containing the ordinal score 1 k or a set of k variables containing counts r in the k categories The response d NEk may also be a series of t binary variables or a series of t variables containing counts yiln yi pi If counts are supplied the total including the kth category must be given in where another variable indicated by the TOTAL qualifier Y Thay ui E Y and Pi Hi Hi 1 The multinomial threshold model is fitted as a cumulative probability model The proportions y r n in the ordered categories are summed to form the cumu lative proportions Y which are modelled with logit LOGIT probit PROBIT or Complementary LogLog CLOG link functions The implicit residual variance on the underlying scale is 77 3 3 3 underlying logistic distribution for the logit link 1 for the probit link The distribution underlying the Complementary LogLog link is the Gumbel distribution with implicit residual variance on the underlying scale of 72 6 1 65 For example Lodging MULTINOMIAL 4 CUMULATIVE Trait Variety r block predict Variety where Lodging is a factor with 4 ordered categories Predicted values are reported for the cumulative proportions IPOISSON LOGARITHM IDENTITY SQRT v p Natural logarithms are the default link function d 2 yln y p ASReml assumes the Poisson variable is not neg
372. n column 1 If the problem is not resolved after these checks you may need to email Customer Support at support asreml co uk Please send the as file a sample of the data the asr file and the as1 file produced by the debug options d1 asreml dl basename as In this chapter we show some of the common NIN Alliance Trial 1989 coding problems The code box on the right variety 56 4 shows our familiar job modified to generate id pid raw repl 4 8 coding problems Errors arising from at e yield Lar Long B z row 22 column 11 tempts to fit an inappropriate model are often ine sed lip eS harder to resolve In this chapter we use this PART 4 example to discuss code debugging in detail yield mu variety 6 lr repl 001 Repl 1 2 0 IDV 0 1 Ipart 2 yield mu variety 9 Ls 11 row ARI 1 22 col ARI 1 part predict voriety 8 Following is the output from running this job ASReml 3 01d 01 Apr 2008 nin alliance trial Build f 11 Apr 2008 32 bit 11 Apr 2008 16 19 29 031 32 Mbyte Windows ninerri memory info Licensed to NSW Primary Industries permanent FEAR k k k 3k ak 3k k K K K k k k k k 3k A A ACI I I I IKK 21 21 21 21 K KKK K A K CK 2K 2K ak Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au EEEE E oo e k kk ARG Folder C data ex manex working folder Warning FIELD DEFINITION lines should be INDENTED There is no file called nine asd I
373. n defined by L The log residual likelihood ignoring constants can be written as 1 le 5 log det C log det R log det G y Py 2 12 We can also write P R R WC W R with W X Z Letting k er 0 the REML estimates of are found by calculating the score 1 U x lr ki zt PH y PH Py 2 13 and equating to zero Note that H 0H 04 The elements of the observed information matrix are lr 1 1 tr PH tr PH PH 1 y PH PH Py zy PHP 2 14 where H 0 H 0 04 The elements of the expected information matrix are R EN es PH PH 2 15 OK OK 2 i al l Given an initial estimate an update of K using the Fisher scoring FS algorithm is KY RO 4 KO KOU 6 2 16 where U is the score vector 2 13 and I K is the expected information matrix 2 15 of k evaluated at 6 For large models or large data sets the evaluation of the trace terms in either 2 14 or 2 15 is either not feasible or is very computer intensive To overcome this problem ASReml uses the Al algorithm Gilmour Thompson and Cullis 1995 The matrix denoted by Za is obtained by averaging 2 14 and 2 15 and approximating y PH Py by its expectation tr PH in those cases when H 4 0 For variance components models that is those linear with respect to variances in H the terms in Z4 are exact averages of those in 2 14 and 2 15 The basic
374. n in terms of the variance components g It was often easier to specify initial values in terms of these ratios rather than the variance components which is why this approach was adopted Where R o can be written as a scaled correlation matrix that is R o 0 R 7 this suggests the alternative specification of 2 2 ejoa lop ele 2001 en where y and y represent the variance structure parameters associated with scaled by 0 variance matrices In this case var y 02 ZG y Z R 7 2 8 which we will refer to as the gamma parameterization and the individual variance structure parameters in y and y will be referred to as gammas ASReml switches between the sigma and gamma parameterizations for estimation This is discussed in Section 2 1 14 2 1 7 Parameter types Each sigma in o and and each gamma in y and y has a parameter type for ex ample variance components variance component ratios autocorrelation parameters factor loadings Furthermore the parameters in o Or Yg and y can span multiple types For example the spatial analysis of a simple column trial would involve variance components sigma parameterization or variance component ratios gamma parameterization and spa tial autocorrelation parameters 2 1 8 Variance structures for the random model terms The random model terms u in u define the random effects and associated design matrices Zi Z but additional information is requ
375. n the field definitions Otherwise a list of levels may be specified at a b creates a series of model terms representing b nested within a for any model term b A model term is created for each level of a each has the size of b For example if site and geno are factors with 3 and 10 levels respectively then for at site geno AS Reml constructs 3 model terms at site 1 geno at site 2 geno at site 3 geno each with 10 levels this is similar to forming an interaction except that a separate model term is created for each level of the first factor this is useful for random terms when each component can have a different variance The same effect is achieved by using an interaction e g site geno and associating a DIAG variance structure with the first component see Section 7 5 any at term to be expanded MUST be the FIRST component of the interaction geno at site will not work at site 1 at year geno will not work but at year at site 1 geno is OK the at factor must be declared with the correct number of levels because the model line is expanded BEFORE the data is read Thus if site is declared as site or site A in the data definitions at site geno will expand to at site 01 geno at site 02 geno regardless of the actual number of sites 6 5 4 Associated Factors Sometimes there is a hierarchical structure to factors which should be recognised as it aids formulation of prediction tables see ASSOCIATE
376. n using ASReml is e Prepare the data typically using a spreadsheet or data base program e Export that data as an ASCII file for example export it as a csv comma separated values file from Excel e Prepare a job file with filename extension as e Run the job file with ASReml e Review the various output files e revise the job and re run it or e extract pertinent results for your report You need an ASCII editor to prepare input files and review and print output files Two commonly used editors are 1 3 1 ASReml W The ASReml W interface is a graphical tool allowing the user to edit programs run and then view the output before saving results It is available on the following platforms e Windows 32 bit and 64 bit e Linux 32 bit and 64 bit various incantations ASReml W has a built in help system explaining its use 1 3 2 ConTEXT ConTEXT is a third party freeware text editor with programming extensions which make it a suitable environment for running ASReml under Windows The ConTEXT directory on 1 5 Getting assistance and the ASReml forum the CD ROM includes installation files and instructions for configuring it for use in ASReml Full details of ConTEXT are available from http www contexteditor org 1 4 How to use this guide The guide consists of 16 chapters Chapter 1 introduces ASReml and describes the conven tions used in the guide Chapter 2 outlines some basic theory which you may need to come
377. n variety trial Wheat To further illustrate the approaches presented in the previous section we consider an un replicated field experiment conducted at Tullibigeal situated in south western NSW The trial was an S1 early stage wheat variety evaluation trial and consisted of 525 test lines which were randomly assigned to plots in a 67 by 10 array There was a check plot variety every 6 plots within each column That is the check variety was sown on rows 1 7 13 67 of each column This variety was numbered 526 A further 6 replicated commercially available varieties numbered 527 to 532 were also randomly assigned to plots with between 3 to 5 plots of each The aim of these trials is to identify and retain the top say 20 of lines for further testing Cullis et al 1989 considered the analysis of early generation variety trials and presented a one dimensional spatial analysis which was an extension of the approach developed by Gleeson and Cullis 1987 The test line effects are assumed random while the check variety effects are considered fixed This may not be sensible or justifiable for most trials and can lead to inconsistent comparisons between check varieties and test lines Given the large amount of replication afforded to check varieties there will be very little shrinkage irrespective of the realised heritability We consider an initial analysis with spatial correlation in one direction and fitting the variety 295 16 7 Unreplica
378. name as is the name of the command file Typically a system PATH is defined which includes ASRemlPath bin so that just the program name ASReml is required at the command prompt For example the command to run nin89 as from the command prompt when attached to the appropriate folder is ASReml nin89 as However if the path to ASReml is not specified in your system s PATH environment variable the path must also be given and the path is required when configuring ASReml W or Context In this guide we assume the command file has a filename extension as ASReml also recognises the filename extension asc as an ASReml command file When these are used the extension as or asc may be omitted from basename as in the command line if there is no file in the working directory with the name basename The options and arguments that can be supplied on the command line to modify a job at run time are described in Chapter LL 33 3 6 Description of output files 3 5 1 Generating a template Notice that the data files nin89 asd and nin89aug asd commenced with a line of column headings Since these headings do not contain embedded blanks we can use ASReml to make a template for the as file by running ASReml with the datafile as the command argument see Chapter 11 For example running the command asreml nin89aug asd writes a file nin89aug as if it does not already exist which looks like Title nin89aug variety id pid raw rep nloc yi
379. nce matrix 2 5 4 Approximate stratum variances ASReml reports approximate stratum variances and degrees of freedom for simple variance components models For the linear mixed effects model with variance components setting o 1 where G 04_17 0 it is often possible to consider a natural ordering of the variance component parameters including o Based on an idea due to Thompson 1980 ASReml computes approximate stratum degrees of freedom and stratum variances by a mod ified Cholesky diagonalisation of the average information matrix That is if F is the average information matrix for let U be an upper triangular matrix such that F U U We 23 2 5 Inference Fixed effects define U D U where D is a diagonal matrix whose elements are given by the inverse elements of the last column of U ie deai 1 uir i 1 r The matrix U is therefore upper triangular with the elements in the last column equal to one If the vector is ordered in the natural way with 0 being the last element then we can define the vector of so called pseudo stratum variance components by U o Thence ad D The diagonal elements can be manipulated to produce effective stratum degrees of freedom Thompson 1980 viz Vi oe deii In this way the closeness to an orthogonal block structure can be assessed 24 3 A guided tour 3 1 Introduction This chapter presents a guided tour of ASReml from data file preparation and
380. nce model 7 9 2 Simple relationships among variance structure parameters 7 9 3 Equating variance structures ee ee eee ee ee ee A eS 7 9 4 Fitting linear relationships among variance structure parameters TAS Writing out a design matrix occiso criar RR RR RR 7 10 Ways to present initial values to ASReml 2 008 7 10 1 New R4 Using templates to set parametric information associated with variance structures using tsv and msvfiles 7 10 2 Using estimates from simpler models 2 0 7 11 Convergence issues Ss risa ce eee we ee ae ees Command file Multivariate analysis 8 1 RO eh 8 ee ee a Se oe ba ne Se oe Pe he Bee 8 1 1 Repeated measures on rats v v v vs ee ee 2 8 12 Wether trial data eae vs ee A A 8 2 Model specification ooo sic RE ERS EE eM See eR ees 8 3 AICS SUCES ck airi GC ee EA ERE REESE A 8 3 1 Specifying multivariate variance structures in ASReml 8 4 The output for a multivariate analysis ee ee ee ee is Command file Genetic analysis 9 1 Mira e MAINE 9 2 Thecommand DE A A AA 9 3 The pedigree THE ceo eo ges redes ares ee eS 9 4 Reading in the pedigree file 0 o 9 5 e groups AI 9 6 Reading a user defined inverse relationship matrix viii 9 6 1 New model names 00 00 a ee ee 168 9 62 Genetic groups in GIV matrices 6 v v v ee ee ee eS 168 9
381. nd dropping the DF qualifier Rot bin TOTAL Total mu SEX GRP SEX GRP r SIRE 16783 The pertinant results are Distribution and link Binomial Logit Mu P 1 1 exp XB V Mu 1 Mu N Warning The LogL value is unsuitable for comparing GLM models Notice 4 singularities detected in design matrix 1 LogL 28 1544 S2 1 0000 48 df Dev DF 0 9060 2 LogL 28 7417 S2 1 0000 48 df Dev DF 0 8897 3 LogL 28 7186 S2 1 0000 48 df Dev DF 0 8805 4 LogL 28 6705 S2 1 0000 48 df Dev DF 0 8551 5 LogL 28 6494 gas 1 0000 48 df Dev DF 0 8238 6 LogL 28 6687 S2 1 0000 48 df Dev DF 0 7959 7 LogL 28 6774 S2 1 0000 48 df Dev DF 0 7915 8 LogL 28 6784 S2 1 0000 48 df Dev DF 0 7909 9 LogL 28 6785 S2 1 0000 48 df Dev DF 0 7908 Final parameter values 0 26321 1 0000 Deviance from GLM fit 48 37 96 Variance heterogeneity factor Deviance DF 0 79 Results from analysis of Rot Notice While convergence of the LogL value indicates that the model has stabilized its value CANNOT be used to formally test differences between Generalized Linear Mixed Models Approximate stratum variance decomposition Stratum Degrees Freedom Variance Component Coefficients SIRE 3 10 0 263207 1 0 Model_Term Sigma Sigma Sigma SE C SIRE 34 34 0 263207 0 263207 1 25 0P Variance 56 48 1 00000 1 00000 0 00 OF Wald F statistics Source of Variation NumDF DenDF F_inc Prob 11 mu il 20 2 418 38 lt 001 3 SEX 1 48 0 0 02 0 881 2 GRP 3 21 5 1 99 0
382. nd line options Bb Gg Hg Rr Ss Yu CONTINUE FINAL LOGFILE NOGRAPHS WORKSPACE w IARGS a ASK BRIEF b DEBUG IDEBUG 2 IGRAPHICS y HARDCOPY y INTERACTIVE ONERUN QUTFOLDER NA QUIET IRENAME NA IYVAR v NA XML job control job control screen output graphics workspace job control job control output control debug debug graphics graphics graphics job control output control post processing graphics job control workspace job control license output control continue iterations using previous estimates as initial values continue for one more iteration using previous esti mates as initial values copy screen output to basename asl suppress interactive graphics set workspace size to w Mbyte to set arguments a in job rather than on command line prompt for options and arguments reduce output to asr file invoke debug mode invoke extended debug mode set interactive graphics device set interactive graphics device graphics screens not displayed display graphics screen override rerunning requested by RENAME changes output folder calculation of functions of variance components suppress screen output repeat run for each argument renaming output file names set workspace size over ride y variate specified in the command file with variate number v reports current license details requests that the main output from
383. nd line options G H I N Q 200 11 3 5 Job control command line options C F O R 201 11 3 6 Workspace command line options S W 202 EF AA III 203 11 4 Advanced processing arguments o e 203 11 4 1 Standard use of arguments ooc oo e 0 203 1142 Prompting for Input sa CRE SE REE AEE SAR we S 204 TAS PASADO Loopa eot s a HHS Ree YR ee eee 204 TL44 Order of OO lt lt s s iss ee ES ORE KOE ES 209 11 5 Performance issues ae ee ke ee EES ee ee e ee 209 11 5 1 Multiple processors lt oe c kee eR ERG Se gn RC EMR ASG ADS ie 209 11 5 2 Slow processes ok ee ea 209 ILS TIMNE Processes o coso ee ee Sal AR Oe ee Pee ee Pee es 210 12 Command file Merging data files 211 e o 2 2 ay oe e ewe 64 5 ea Bow ee dee Wok Sg oh we ES 211 122 Merge Symtak oea re moa be ARA RA N 212 PARE 213 13 Functions of variance components 214 131 INNOCENTI See eS EY 214 o AAA 214 13 2 1 Functions of components is c oessa cese estent uaa oa 215 13 2 2 Convert CORUH and XFA to US v v v ee cm 217 132 3 LOS e de a A SR eee ee dees 217 13 2 4 A more detailed example o 218 133 VPREDICT PIN file processing eo hs ocres carr Gg 219 14 Description of output files 221 EA ARS 221 e example scene ie ig PES SAV ESHER EOWA gi Sir Me Se sise dB 222 14 3 Keyo tp t files lt a Shwe ek we hw eS AC TA ee ee eee BRS 223 431 Th as
384. nd the diagonal elements of the hat matrix This final column can be used in tests involving the residuals see Section 2 4 under Diagnostics Record Yhat Residual Hat 1 30 442 1 192 13 01 2 27 955 3 595 13 01 B 32 380 2 670 13 01 4 23 092 7 008 13 01 5 31 317 1 733 13 01 6 29 267 0 9829 13 01 7 26 155 9 045 13 01 8 24 567 di LOL 13 01 9 23530 0 8204 12 041 222 16 673 9 877 12301 223 24 548 1 052 13 01 224 23 786 3 114 T301 3 7 Tabulation predicted values and functions of the vari ance components It may take several runs of ASReml to determine an appropriate model for the data that is the fixed and random effects that are important During this process you may wish to explore the data by simple tabulation Having identified an appropriate model you may then wish to form predicted values or functions of the variance components The facilities in ASReml to form predicted values and functions of the variance components are described in Chapters 10 and 13 respectively Our example only includes tabulation and prediction The statement tabulate yield variety 37 3 7 Tabulation predicted values and functions of the variance components in nin89 as results in nin89 tab as follows NIN alliance trial 1989 11 Jul 2005 13 55 21 Simple tabulation of yield variety LANCER 28 56 BRULE 26 07 REDLAND 30 50 CODY 21 21 ARAPAHOE 29 44 NE83404 27 39 NE83406 24 28 NE83407 22 69 CENTURA 21 65 SCOUT66 21 52 COLT 27
385. ndard EM plus 10 local EM steps Options 3 and 4 cause all US structures to be updated by PX EM if any particular one requires EM updates 17 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action EQORDER o EXTRA n FOWN The test of whether the AI updated matrix is positive definitite is based on absorbing the matrix to check all pivots are positive Repeated EM updates may bring the matrix closer to being singular This is assessed by dividing the pivot of the first element with the first diagonal element of the matrix If it is less than 1077 this value is consistent with the multiple partial correlation of the first variable with the rest being greater than 0 9999999 ASReml fixes the matrix at that point and estimates any other parameters conditional on these values To preceed with further iterations without fixing the matrix values would ultimately make the matrix such that it would be judged singular resulting the analysis being aborted modifies the algorithm used for choosing the order for solving the mixed model equations A new algorithm devised for release 2 is now the default and is formally selected by EQORDER 3 The algorithm used for release 1 is essentially that selected by EQORDER 1 The new order is generally superior EQORDER 1 instructs ASReml to process the equations in the order they are specified in the model Generally this will make a j
386. ndom effects in the model Note that residuals are not included in the output forced by this qualifier This option is primarily intended to help debugging a job that is not converging properly When forming a design matrix for the sp1 model term ASReml uses a standardized scale independent of the actual scale of the variable The qualifier SCALE 1 forces ASReml to use the scale of the variable The default standardised scale is appropriate in most circumstances requests ASReml write the SCORE vector and the Average Information matrix to files basename SCO and basename AIM The values written are from the last iteration reduces the update step sizes of the variance parameters more persistently than the STEP r qualifier If specified ASReml looks at the potential size of the updates and if any are large it reduces the size of r If n is greater than 10 ASReml also modifies the Information matrix by multiplying the diagonal elements by n This has the effect of further reducing the updates In the iteration subroutine if the calculated LogL is more than 1 0 less than the LogL for the previous iteration and SLOW is set and NIT gt 1 ASReml immediately moves the variance parameters back towards the previous values and restarts the iteration modifies the ability of ASReml to detect singularities in the mixed model equations This is intended for use on the rare occasions when ASReml detects singularities after the first iteration they ar
387. near dependence in the design matrix means there is no information left to estimate the effect ASReml handles singularities by using a generalized inverse in which the singular row column is zero and the associated fixed effect is zero Which equations are singular depends on the order the equations are processed This is controlled by ASReml for the sparse terms but by the user for the dense terms They should be specified with main effects before interactions so that the table of Wald F statistics has correct marginalization Since ASReml processes the dense terms from the bottom up the first level the last level processed is often singular The number of singularities is reported in the asr file immediately prior to the REML log likelihood LogL line for that iteration see Section 14 3 The effects and associated standard or prediction error which correspond to these singularities are zero in the sln file 106 6 11 Wald F Statistics Singularities in the sparse_fized terms of the model may change with changes in the random terms included in the model If this happens it will mean that changes in the REML log likelihood are not valid for testing the changes made to the random model This situation is not easily detected as the only evidence will be in the s1n file where different fixed effects are singular A likelihood ratio test is not valid if the fixed model has changed 6 10 4 Examples of aliassing The sequence of models
388. ng value for the first record and otherwise to the values from the preceding record after transformation Thus A B LagA V4 V4 A reads two fields A and B and constructs LagA as the value of A from the previous record by extracting a value for LagA from working variable V4 before loading V4 with the current value of A 5 5 1 Transformation syntax Transformation qualifiers have one of seven forms namely operator to perform an operation on the current field for example absY ABS to take absolute values operator value to perform an operation involving an argument on the cur rent field for example logY Y 0 copies Y and then takes logs operator V field to perform an operation on the current field using the data in another field for example V2 to subtract field 2 from the current field IV target to reset the focus for subsequent transformations to field number target TARGET target to reset the focus for subsequent transformations to the pre viously named field target V target value to set the target field to a particular value IV target V field to overwrite the data in a target field by the data values of another field a special case is when field is 0 instructing ASReml to put the record number into the target field e operator is one of the symbols defined in Table 5 1 e value is the argument a real number required by the transformation e Vis the literal character and is followed by
389. ng value where v is not 0 Le v raises the data which must be pos yield itive to the power v SQRyld yield 170 5 i 0 takes natural logarithms of the data yield which must be positive LNyield yield LU ia 1 takes reciprocal of data data must yield be positive INVyield yield eg Sl ley v logical operators forming 1 if true 0 yield los lt if false high yield gt 10 gt ABS takes absolute values no argument yield required ABSyield yield ABS ARCSIN v forms an ArcSin transformation us Germ Total ing the sample size specified in ASG Germ ARCSIN Total the argument a number or another field In the side example for two existing fields Germ and Total con taining counts we form the ArcSin for their ratio ASG by copying the Germ field and applying the ArcSin transformation using the Total field as sample size 54 5 5 Transforming the data Table 5 1 List of transformation qualifiers and their actions with examples qualifier argument action examples COS SIN s takes cosine and sine of the data Day variable with period s having default CosDay Day C0S 27 omit s if data is in radians set 365 s to 360 if data is in degrees ID D lt gt v D o v discards records which have yield D lt 0 ID D lt v v or missing value in the field sub yield D lt 1 D gt 100 ID gt D gt v ject to the logical operator o IDV v DV o v discards records subject to yield DV lt
390. ngs are inserted into the command file at run time When the input routine finds a n in the command file it substitutes the nth argument string n may take the values 1 9 to indicate up to 9 strings after the command file name If the argument has 1 character a trailing blank is attached to the character and inserted into the command file If no argu ment exists a zero is inserted For example asreml rat as alpha beta tells ASReml to process the job in rat as as if it read alpha wherever 1 appears in the command file beta wherever 2 appears and 0 wherever 3 appears Table 11 2 The use of arguments in ASReml in command file on command line becomes in ASReml run abc ldef no argument abcO def abc ldef with argument X abcX def 203 11 4 Advanced processing arguments The use of arguments in ASReml in command file on command line becomes in ASReml run abc 1def with argument XY abcXYdef abc 1def with argument XYZ abcXYZdef abc 1 def with argument XX abcXX def abc 1 def with argument XXX abcXXX def abc 1 def with argument XXX abcXXX def multiple spaces 11 4 2 Prompting for input Another way to gain some interactive control of a job in the PC environment is to insert text in the as file where you want to specify the rest of the line at run time ASReml prompts with text and waits for a response which is used to compete the line The qualifier may be used anywhere in the job and the line is modif
391. ngth 49 MDY 49 PRUNE 50 SORT 50 SORTALL 50 TIME 49 factors 41 file GIV 165 pedigree 160 Fisher scoring algorithm 14 fixed effects 5 Fixed format files 63 fixed terms 85 91 multivariate 154 primary 91 sparse 92 For FOR 207 Forming a job template 34 forum 3 free format 41 functions of variance components 37 214 Convert CORUH and XFA to US 217 correlation 217 linear combinations 215 syntax 214 G structure 109 definition lines 118 121 header 121 more than one term 139 Gamma distribution 101 GBLUP 171 Generalized Mixed Linear Models 100 genetic data 1 350 INDEX groups 164 links 159 models 159 qualifiers 159 relationships 160 genetic markers 71 GIV 165 GLM distribution Binomial 101 Gamma 101 Negative Binomial 102 Normal 101 Ordinal data 101 Poisson 101 GLMM 104 graphics options 200 half sib analysis 328 help via email 3 heritability 243 identifiable 12 IID 10 inbreeding coefficients 163 226 Incremental F Statistics 20 Information Criteria 17 information matrix 14 expected 14 observed 14 initial values 121 input file extension BIN 43 DBL 43 bin 41 43 csv 41 dbl 41 43 pin 220 interactions 93 Introduction 19 job control options 201 qualifiers 65 key output files 223 likelihood comparison 223 convergence 68 log residual 14 offset 223 residual 13 longitudinal data 1 balance
392. nstraints are applied Following is an example of Helmert and sum to zero covariables for a factor with 5 levels Hl H2 H3 H4 C1 C2 C3 C4 Fl 1 1 1 1 1 0 0 0 F2 1 1 1 1 0 1 0 0 F3 0 2 1 1 0 0 1 0 F4 0 0 3 1 0 0 0 1 F5 0 0 0 4 1 1 1 1 is used to take a copy of a pedigree factor f and fit it without the genetic relationship covariance This facilitates fitting a second animal effect Thus to form a direct maternal genetic and maternal environment model the maternal environment is defined as a second animal effect coded the same as dams viz r animal dam ide dam forms the reciprocal of v r This may also be used to transform the response variable forms n 1 Legendre polynomials of order 0 intercept 1 linear n from the values in v the intercept polynomial is omitted if n is preceded by the negative sign The actual values of the coefficients are written to the res file This is similar to the pol 0 function described below takes the coding of factor f as a covariate The function is defined for f being a simple factor Trait and units The lin f function does not centre or scale the variable Motivation Sometimes you may wish to fit a covariate as a random factor as well If the coding is say 1 n then you should define the field as a factor in the field definition and use the 1in function to include it as a covariate in the model Do not centre the field in this case If the covariate values are irreg
393. nvalid label for data field nine asd contains a reserved character or may get confused with a previous label or reserved word NB File names must not be indented Fault Error parsing nine asd SLIP 1 248 15 3 Things to check in the asr file Last line read was nine asd SLIP 1 Currently defined structures COLS and LEVELS 1 variety 1 56 id pid raw repl nloc yield lat long o ON 0 nu PrP rere BP PP h e aD N N row Eb p nn column ORRRRBPRPR BR BP in O Oo OOOO oO CC g Coco GO O O OS SO O O O O 2 O YO O Oo 0 oO amp Oo 00 0 filename o 12 nine asd ninerri C data ex manex 12 factors defined max 500 O variance parameters max1500 2 special structures Last line read was nine asd SLIP 1 last line read Finished 11 Apr 2008 16 19 29 093 Error parsing nine asd SLIP 1 fault message ASReml happily reads down to the nine asd line This line is not indented so nine asd is expected to be a file name but there is no such file in the folder C data ex manex 15 3 Things to check in the asr file The information that ASReml dumps in the asr file when an error is encountered is intended to give you some idea of the particular error e if there is no data summary ASReml has failed before or while reading the model line e if ASReml has completed one iteration the problem is probably associated with starting values of the variance parameters or the logic of the model rathe
394. nverged to the best estimate a common reason is that some constraints have restricted the gammas Add the GU qualifier to any factor definition whose gamma value is approaching zero or the correlation is ap proaching 1 Alternatively more singularities may have been detected You should identify where the singularities are ex pected and modify the data so that they are omitted or consis tently detected One possibility is to centre and scale covariates involved in interactions so that their standard deviation is close to 1 264 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy PRINT Cannot open output file AINV GIV matrix undefined or wrong size ASReml command file is EMPTY ASReml failed in Continue from rsv file Convergence failed Correlation structure is not positive definite Define structure for Error The indicated number of input fields exceeds the limit Error in CONTRAST label factor values Error in SUBGROUP label factor values Error in R structure model checks Error opening file Error reading something Check filename Check the size of the factor associated with the AINV GIV structure The job file should be in ASCII format Try running the job with increased workspace or us ing a simpler model Otherwise send the job to VSN mailto
395. ny files and the sln and yht files in particular are often quite large and could fill up your disk space You should therefore regularly tidy your working directories maybe just keeping the as asr and pvs files 14 2 An example In this chapter the ASReml output files are qin Alliance Trial 1989 discussed with reference to a two dimensional variety A separable autoregressive spatial analysis of id the NIN field trial data see model 3b on page 7 114 of Chapter 7 for details The ASReml E command file for this analysis is presented to yield the right Recall that this model specifies a Jst separable autoregressive correlation structure long for residual or plot errors that is the direct row 22 product of an autoregressive correlation ma column 11 trix of order 22 for rows and an autoregressive E E ee S lsti tr ford 11 f 1 yield mu variety f mv correlation matrix of order or columns predict variety 120 222 row row ARi 0 5 column column AR1 0 5 14 3 Key output files In this case 0 5 is the starting correlation for both columns and rows 14 3 Key output files The key ASReml output files are the asr sln and yht files 14 3 1 The asr file This file contains e a general announcements box outlined in asterisks containing current messages e asummary of the data to for the user to confirm the data file has been interpreted correctly and to review the basic structure of the da
396. ob much slower if it can run at all It is useful if the model has a suitable order as in the IBD model Y mu r giv id id giv id invokes a dense inverse of an IBD matrix and id has a sparse structured inverse of an additive relationship matrix While EQORDER 3 generates a more sparse solution EQORDER 1 runs faster forces another mod n 10 rounds of iteration after apparent convergence The default for n is 1 This qualifier has lower priority than MAXIT and ABORTASR NOW see MAXIT for details Convergence is judged by changes in the REML log likelihood value and variance parameters However sometimes the variance parameter con vergence criteria has not been satisfied allows the user to specify the test reported in the F con column of the Wald F Statistics table It has the form FOWN terms to test background terms placed on a separate line immediately after the model line Multiple FOWN statements should appear together It generates a Wald F statistic for each model term in terms to test which tests its contribution after all other terms in terms to test and background terms conditional on all terms that appear in the SPARSE equations It should only specify terms which will appear in the table of Wald F statistics 78 5 8 Job control qualifiers Table 5 5 List of rarely used job control qualifiers qualifier action GDENSE GLMM n HPGL 2 For example IFOWN ABC mu FOWN A B B C
397. ociation with the V0 transformation forms a set of orthogonal polynomials of order n based on the unique values in variate or factor v and any additional interpolated points see PPOINTS and PVAL in Table 5 4 It includes the intercept if n is positive omits it if n is negative For example pol time 2 forms a design matrix with three columns of the orthogonal polynomial of degree 2 from the variable time Alternatively pol time 2 is a term with two columns having centred and scaled linear coefficients in the first column and centred and scaled quadratic coefficients in the second column The actual values Robson 1959 Steep and Torrie 1960 of the coefficients are written to the res file This factor could be interacted with a design factor to fit random regression models The leg function differs from the pol function in the way the quadratic and higher polynomials are calculated defines the covariable x o for use in the model where x is a variable in the data p is a power and o is an offset pow x 0 5 0 1 is equivalent to sqr x 0 pow x 0 0 is equivalent to log 0 pow x 1 01 is equiva lent to inv x 01 97 6 6 Alphabetic list of model functions Table 6 2 Alphabetic list of model functions and descriptions model function action qtl f r sin v 7r spl v k s u k sqrt v r Trait units uni f 0 n11 uni f k n calculates an expected marker state
398. of arguments in ASReml aaa a 203 High level qualifiers eke PAS ER eka a 205 bret OF MERGE gualilers as est eae eo eRe BE ORR BER EES 212 xii 14 1 14 2 15 1 15 2 15 3 16 1 16 2 16 3 16 4 16 5 16 6 16 7 16 8 16 9 16 10 16 11 16 12 16 13 16 14 16 15 16 16 Summary of ASReml output files gt 22 sossa asieran era 221 ASReml output objects and where to find them 243 Some information messages and comments 0004 261 List of warning messages and likely meaning s 262 Alphabetical list of error messages and probable cause s remedies 265 A split plot field trial of oat varieties and nitrogen application 273 Rat data AOV decomposition ee a 277 REML log likelihood ratio for the variance components in the voltage data 282 Summary of variance models fitted to the plant data 283 Summary of Wald F statistics for fixed effects for variance models fitted to the plaut data EA 289 Field layout of Slate Hall Farm experiment 290 Summary of models for the Slate Hall data 294 Estimated variance components from univariate analyses of bloodworm data a Model with homogeneous variance for all terms and b Model with het erogeneous variance for interactions involving tmt 304 Equivalence of random effects in bivariate and univariate analyses 306 Estimated varian
399. ol column 1 1 18 5 4 84 0 040 The increase in REML log likelihood is significant The predicted means for the varieties can be produced and printed in the pvs file as Warning mv_estimates is ignored for prediction Warning units is ignored for prediction A T ee es column evaluated at 5 5000 weed is evaluated at average value of 0 4597 Predicted values of yield 299 16 8 Paired Case Control study Rice variety Predicted_Value Standard_Error Ecode 1 0000 2917 1792 179 2881 E 2 0000 2957 7405 178 7688 E 3 0000 2872 7615 176 9880 E 4 0000 2986 4725 178 7424 E 522 0000 2784 7683 179 1541 E 523 0000 2904 9421 179 5383 E 524 0000 2740 0330 178 8465 E 525 0000 2669 9565 179 2444 E 526 0000 2385 9806 44 2159 E 527 0000 2697 0670 133 4406 E 528 0000 2727 0324 112 2650 E 529 0000 2699 8243 103 9062 E 530 0000 3010 3907 112 3080 E 531 0000 3020 0720 112 2553 E 532 0000 3067 4479 112 6645 E SED Overall Standard Error of Difference 245 8 Note that the replicated check lines have lower SE than the unreplicated test lines There will also be large diffeneces in SEDs Rather than obtaining the large table of all SEDs you could do the prediction in parts predict var 1 525 column 5 5 predict var 526 532 column 5 5 SED to examine the matrix o
400. olves two steps Regulators are taken from the production line to a setting station and adjusted to operate within a specified voltage range From the setting station the regulator is then passed to a testing station where it is tested and returned if outside the required range The voltage of 64 regulators was set at 10 setting stations setstat between 4 and 8 regulators were set at each station The regulators were each tested at four testing stations 279 16 4 Source of variability in unbalanced data Volts teststat The ASReml input file is presented below Voltage data teststat 4 4 testing stations tested each regulator setstat A 10 setting stations each set 4 8 regulators regulatr 8 regulators numbered within setting stations voltage voltage asd skip 1 voltage mu r setstat setstat regulatr teststat setstat teststat 000 The factor regulatr numbers the regulators within each setting station Thus the term setstat regulatr allows for differential effects of each regulator while the other terms ex amine the effects of the setting and testing stations and possible interaction The abbreviated output is given below LogL 188 604 S2 0 67074E 01 255 df LogL 199 530 S2 0 59303E 01 255 df LogL 203 007 S2 0 52814E 01 255 df LogL 203 240 S2 0 51278E 01 255 df LogL 203 242 S2 0 51141E 01 255 df LogL 203 242 S2 0 51140E 01 255 df Model_Term Gamma Sigma Sigma SE C setstat 10 10 0 233418 0 1193 18 01 1 35 0
401. omer Sup port for debugging See the discussion on AISINGULARITIES the field order coding in the spatial error model does not gen erate a complete grid with one observation in each cell missing values may be deleted they should be fitted Also may be due to incorrect specification of number of rows or columns 270 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy STOP SCRATCH FILE DATA STORAGE ERROR Structure Factor mismatch Too many alphanumeric factor level labels Too many factors with A or II max 100 Too many max 20 dependent variables Unable to invert R or G US matrix Unable to invert R or G CORR matrix Variance structure is not positive definite XFA model not permitted in R structures XFA may not be used as an R structure ASReml attempts to hold the data on a scratch file Check that the disk partition where the scratch files might be written is not too full use the NOSCRATCH qualifier to avoid these scratch files the declared size of a variance structure does not match the size of the model term that it is associated with if the factor level labels are actually all integers use the I option instead Otherwise you will have to convert a factor with alphanumeric labels to numeric sequential codes external to ASReml so that an A option can be avo
402. on 2 1 15 under Combining variance models variance structures are some times formed as a direct product of variance models For example the variance structure for a a two factor interaction is typically formed as the direct product of two variance models one for each of the two factors in the interaction Some of the rules for combining vari ance models in direct products differ for R structures and G structures because R structures usually have an implicit scaling parameter while G structures never do 138 7 8 G structures involving more than one random term A summary of the rules is as follows WIN Alliance Trial 1989 variety A when combining variance models in both R ia and G structures the resulting direct prod uct structure must match the ordered ef row 22 fects with the outer factor first for exam column 11 ple the G structure in the example opposite nin89 asd skip 1 is for column row which tells ASReml that Yield mu variety r repl the direct product structure matches the ef ed fects ordered rows within columns The column row 2 variance model can be written as g f column 0 AR1 0 4 Xc 6 AUR This is why the G structure row 0 ARV1 0 3 0 1 definition line for column is specified first ASReml automatically includes and estimates an error variance parameter for each section of an R structure The variance structures defined by the user should therefore normally be correlation matrices
403. on 7 10 1 fitting a simpler model and using parameter values derived from the simpler model through the rsv file Section 7 10 2 7 10 1 New R4 Using templates to set parametric information associ ated with variance structures using tsv and msv files ASReml 3 needed initial values for most variance structure parameters and allowed specifi cation of parametric constraints and relationships equality and scale between parameters to be defined This parametric information was interspersed within the structure definition Release 4 allows an alternative way of specifying this parametric information essentially con structing a table in a tsv file with the rows labelled by the specific parameters columns for initial values and parametric constraints and two columns that allow specification of relationships This tsv file is written by ASReml after the input file has been parsed using to represent initial values and setting MAXITER O gives an easy construction Once the tsv file has been edited it can be read by inserting TSV on the data file line As an example Wolfinger Rat data treat A wt0 wti wt2 wt3 wt4 subject V0 wolfrat dat skip 1 ASUV MAXITER 0 wt0 wti wt2 wt3 wt4 Trait treat Trait treat 1 2 9 27 O ID error variance Trait 0 US indicates generates initial values generates a tsv file This tsv file is a mechanism for resetting initial parameter values by changing the values here and rerunning
404. on of denominator degrees of freedom see DDF e calculation of outlier statistics see OUTLIER 209 11 5 Performance issues If a job is being run a large number of times significant gains in processing time can some times be made by reorganising the data so reading of irrelevant data is avoided using binary data files use of CONTINUE to reduce the number of iterations and avoiding unnecessary output see SLNFORM YHTFORM and NOGRAPHICS 11 5 3 Timing processes The elapsed time for the whole job can be calculated approximately by comparing the start time with the finish time Timings of particular processes can be obtained by using the IDEBUG LOGFILE qualifiers on the first line of the job This requests the asl file be created and hold some intermediate results especially from data setup and the first iteration Included in that information is timing information on each phase of the job 210 12 Command file Merging data files 12 1 Introduction The MERGE directive described in this chapter is designed to combine information from two files into a third file with a range of qualifiers to accomodate various scenarios It was developed with assistance from Chandrapal Kailasanathan to replace the MERGE qualifier see page 64 which had very limited functionality The MERGE directive is placed BEFORE the data filename lines It is an independent part of the ASReml job in the sense that none of the files are nece
405. on splines play a role in modelling the conditional curves for each tree and variance modelling The intercept and 312 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges Trunk circumference mm a po a o o o po D L O D 2 o 3 oo oa o oe o 0 Ss o o 7 3 B E 0O oO o i no a o co o E E o D o S 9 D 2 fa a aa ars o E A o o Figure 16 13 Fitted cubic smoothing spline for tree 1 Table 16 11 Orange data AOV decomposition stratum decomposition type df or ne constant 1 F 1 age age F 1 spl age 7 R 5 fac age R 7 tree tree RC 5 age tree x tree RC 5 spl age 7 tree R 25 error R slope for each tree are included as random coefficients denoted by RC in Table 16 11 Thus if U is the matrix of intercepts column 1 and slopes column 2 for each tree then we assume that var vec U X 8 I where gt is a 2 x 2 symmetric positive definite matrix Non smooth variation can be mod 313 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges elled at the overall mean across trees level and this is achieved in ASReml by inclusion of fac age as a random term 314 16 9 Balanced longitudinal data Random coefficients and cubic smoothing splines Oranges Table 16 12 Sequence of models fitted to the Orange data model term 1 2
406. on the line immediately preceding the data file line in the command file e use identity 0 or for unknown parents harvey ped harvey dat 160 9 3 The pedigree file 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 SIRE_1 SIRE_1 SIRE_1 SIRE_1 SIRE 1 SIRE_1 SIRE_1 SIRE_1 SIRE_2 SIRE_2 SIRE_2 STRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_3 SIRE_3 SIRE_3 SIRE_3 So Oo Oo OC CO CO CO So CG Oo eo 0 10 0 000 3 101 102 103 104 105 106 107 108 109 110 a 112 113 114 115 116 117 118 119 120 SIRE_1 SIRE_1 SIRE_1 SIRE_1 SIRE_1 SIRE 1 SIRE_1 SIRE_1 SIRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_2 SIRE_3 SIRE_3 SIRE_3 SIRE_3 oc OOO Oo Oo Ce oo Oo oO oO Oo SO PRPRPRPRPRPRP PRP PRP RP PRP PRP RPP RB mm mm ud 03 anaa an artr hr 010100442 W 02 192 154 185 183 186 177 177 163 188 178 198 193 186 175 174 168 154 184 174 170 390 403 432 457 483 469 428 439 439 407 498 459 459 375 382 417 389 414 483 430 2241 2651 2411 2251 2581 2671 2711 2471 2292 2262 1972 2142 2442 2522 1722 2752 2383 2463 2293 2303 161 9 4 Reading in the pedigree file 9 4 Reading in the pedigree file The syntax for specifying a pedigree file in the ASReml command file is pedigree_file qualifiers e the qualifiers are listed in Table 9 1 the identities individual male_parent
407. onjunction with the first PRESENT v list to specify the weights that ASReml will use for averaging that PRESENT table More details are given below Controlling inclusion of model terms EXCEPT t causes the prediction to include all fitted model terms not in t 184 10 3 Prediction Table 10 1 List of prediction qualifiers qualifier action IGNORE ONLYUSE t USE t Printing IDEC n PLOT z PRINTALL SED TDIFF ITURNINGPOINTS n causes ASReml to set up a prediction model based on the default rules and then removes the terms in t This might be used to omit the spline Lack of fit term IGNORE fac x from predictions as in yield mu x variety r spl x fac x predict x IGNORE fac x which would predict points on the spline curve averaging over variety causes the prediction to include only model terms in t It can be used for example to form a table of slopes as in HI mu X variety X variety predict variety X 1 onlyuse X X variety causes ASReml to set up a prediction model based on the default rules and then adds the terms listed in t gives the user control of the number of decimal places reported in the table of predicted values where n is 0 9 The default is 4 G15 9 format is used if n exceeds 9 When VVP or SED are used the values are displayed with 6 significant digits unless n is specified and even then the values are displayed with 9 significant digits
408. ons and now di rectly supports Arthur Gilmour and Sue Welham for further computational developments and research on the analysis of mixed models Release 4 of ASReml was first distributed in 2014 A major enhancement in this release is the introduction of an alternative functional specification of linear mixed models For the convenience of users three documents have been prepared i this document which is a guide to Release 4 using the original still supported structural model specification ti a guide using the new functional model specification and iii a document ASReml Update What s new in Release 4 which highlights the changes from Release 3 Linear mixed effects models provide a rich and flexible tool for the analysis of many data sets commonly arising in the agricultural biological medical and environmental sciences Typical applications include the analysis of un balanced longitudinal data repeated measures anal ysis the analysis of un balanced designed experiments the analysis of multi environment trials the analysis of both univariate and multivariate animal breeding and genetics data and the analysis of regular or irregular spatial data ASReml provides a stable platform for delivering well established procedures while also deliv ering current research in the application of linear mixed models The strength of ASReml is the use of the Average Information Al algorithm and sparse matrix methods for fitting the linear mixed
409. op fmt IPART 2 pcoop fmt CONTINUE pcoopsi rsv MAXI 40 IPART 3 pcoop fmt CONTINUE pcoops2 rsv MAXI 40 IPART 4 pcoop fmt CONTINUE pcoops2 rsv MAXI 40 IPART 5 pcoop fmt CONTINUE pcoops4 rsv MAXI 40 IPART O USING SUBSET TO ALLOW EASY TRAIT ASSOCIATION WITH FACTORS IN MODEL ISUBSET TrDami2 Trait 12000 SUBSET TrLit1234 Trait 123 40 ISUBSET TrAG1245 Trait 1245 ISUBSET TrSG123 Trait 12300 ISUBSET TrDai23 Trait 12300 USING ASSIGN TO MAKE SPECIFICATION CLEARER ASSIGN TDIAGI 2 3759 6 2256 0 60075E 01 0 63086 0 13069 GP ASSIGN DDIAGI 2 1584 2 3048 GP ASSIGN LDIAGI 3 55265 2 55777 0 191238E 01 0 897272 1GP ASSIGN RUSI I lt IGP 13 390 9 0747 17 798 0 31961 0 87272 0 13452 339 16 11 Multivariate animal genetics data Sheep 0 71374 1 4028 0 23141 4 0677 0 72812 2 0831 0 75977E 01 0 25782 1 5337 I gt ASSIGN VARS TrAG1245 age grp TrSG123 sex grp PATH 1 USING DIAG FOR TAG DAM AND LIT US FOR RESIDUAL wwt ywt gfw fdm fat Trait Trait age Trait brr Trait sex Trait age sex r VARS Trait tag TrDami2 dam TrLit1234 1it lf Trait grp 125 1 R STRUCTURE WITH 2 COMPONENTS AND 5 G STRUCTURES O O O INDEPENDENT ACROSS ANIMALS Trait 0 US RUSI UNSTRUCTURED TRAIT MATRIX INITIAL VALUES FROM UNIVARIATE ANALYSES TrAG1245 age grp 2 TrAG1245 0 DIAG 0 0024 0 0019 0 0020 0 00026 age grp O ID TrSG123 sex grp 2 TrSG123 0 DIAG 0 93 16 0 0 28 sex grp 0 ID Trait tag 2 Trait 0 DIAG TDIAGI tag 0 AINV TrDam12 d
410. ormations that apply to the whole set are DOM MM and RESCALE ASReml code action yield MO yield 70 score 5 score ISET 0 5 1 5 2 5 score SUB 0 5 1 5 2 5 block 8 variety 20 yield plot variety SEQ Var 3 Nit 4 VxN 12 Var 1 4 4Nit YA V98 YA NA O YB V99 YB NA O V98 DO changes the zero entries in yield to missing values takes natural logarithms of the yield data subtracts 5 from all values in score replaces data values of 1 2 and 3 with 0 5 1 5 and 2 5 respectively replaces data values of 0 5 1 5 and 2 5 with 1 2 and 3 respectively a data value of 1 51 would be replaced by 0 since it is not in the list or very close to a number in the list in the case where there are multiple units per plot contiguous plots have different treatments and the records are sorted units within plots within blocks this code generates a plot factor assuming a new plot whenever the code in V2 variety changes whether this creates a variable or overwrites an input variable depends on whether any subsequent variables are input variables assuming Var is coded 1 3 and Nit is coded 1 4 this syntax could be used to create a new factor VxN with the 12 levels of the com posite Var by Nit factor will discard records where both YA and YB have missing values assuming neither have zero as valid data The first line sets the focus to variable 98 copies YA into V98 and changes any missing
411. ors may contribute to predictions in several ways They may be evaluated at levels specified by the user they may be averaged over or they may be ignored omitting all model terms that involve the factor from the prediction Averaging over the set of random effects gives a prediction specific to the random effects observed We call this a conditional prediction Omitting the term from the prediction model produces a prediction at the population average often zero that is substituting the assumed population mean for an predicted random effect We call this a marginal prediction Note that in any prediction some random factors for example Genotype may be evaluated as conditional and others for example Blocks at marginal values depending on the aim of prediction For fixed factors there is no pre defined population average so there is no natural interpre tation for a prediction derived by omitting a fixed term from the fitted values Therefore any prediction will be either for specific levels of the fixed factor or averaging in some way over the levels of the fixed factor The prediction will therefore involve all fixed model terms Covariates must be predicted at specified values If interest lies in the relationship of the response variable to the covariate predict a suitable grid of covariate values to reveal the relationship Otherwise predict at an average or typical value of the covariate Omission of a covariate from the
412. ot required and the word ASReml will suffice for example ASReml nin89 as will run the NIN analysis assuming it is in the current working folder if asreml exe ASRem1 is not in the search path then path is required for example if asreml exe is in the usual place then C Program Files ASRem13 bin Asreml nin89 as 195 11 2 The command line will run nin89 as e ASRem1 invokes the ASReml program e basename is the name of the as c command file The basic command line can be extended with options and arguments to path ASRem1 options basenamel as c arguments e options is a string preceded by a minus sign Its components control several operations batch graphic workspace at run time for example the command line ASReml w128 rat as tells ASReml to run the job rat as with workspace allocation of 128mb e arguments provide a mechanism mostly for advanced users to modify a job at run time for example the command line ASReml rat as alpha beta tells ASReml to process the job in rat as as if it read alpha wherever 1 appears in the file rat as beta wherever 2 appears and 0 wherever 3 appears see below 11 2 2 Processing a pin file If the filename argument is a pin file see Chapter 13 then ASReml processes it If the pinfile basename differs from the basename of the output files it is processing then the basename of the output files must be specified with the P option letter Thus ASRe
413. oundary GP Warning Dropped records were not evenly distributed across Warning Eigen analysis check of US matrix skipped WARNING Extra lines on the end of the input file Warning Failed to find header blocks to skip This is to reduce the number of knot points used in fitting a spline data values should be positive usually means the variance model is overparameterized Look up AISING the structures are probably at the boundary of the parameter space either use MVINCLUDE or delete the records it is better to avoid negative weights unless you can check AS Reml is doing the correct thing with them check the data summary has the correct number of records and all variables have valid data values If ASReml does not find sufficient values on a data line it continues reading from the next line You have probably mis specified the number of levels in the factor or omitted the I qualifier see Section 5 4 on data field definition syntax ASReml corrects the number of levels the term did not appear in the model the term did not appear in the model terms like units and mv cannot be included in prediction RECODE may be needed when using a pedigree and reading data from a binary file that was not prepared with ASReml suggest drop the term and refit the model MVREMOVE has been used to delete records which have a missing value in design variables This has resulted in multivariate data no longer h
414. ous when the data grr file is large and there are many cycles to execute where the model changes but the data grr file doesn t The CYCLE mechanism now acts as an inner loop when used with RENAME ARG Previously both could not be used together As an example the IRENAME ARG arguments might list a set of traits and the CYCLE argu ments sequentially test a set of markers A cycle string may consist of up to 4 substrings separated by a semicolon and referenced as I J K and L respectively For example ICYCLE YV1 X1 YO x2 I mu J When cycling is active an extra line is written to the asr file containing some details of the cycle in a form which can be extracted to form an analysis summary by searching for LogL A heading for this extra line is written in the first cycle For example LogL LogL Residual NEDF NIT Cycle Text LogL 208 97 0 703148 587 6 1466 LogL Converged The LogL line with the highest LogL value is repeated at the end of the asr file The qualifiers DOPART and PART have been extended in release 2 0 and DOPATH and PATH are thought to be more appropriate names Both spellings can be used interchangably DOPATH allows several analyses to be coded and run sequentially without having to edit the as file between runs Which particular lines in the as file are honoured is controlled by the argument n of the DOPATH qualifier in conjunction with PATH or PART statements The argument n
415. ow wise binary file and dgiv is a double precision lower triangle row wise binary file PRECISION n changes the value used to declare a singularity when inverting a GRM file from 1D 7 to 1D n The giv file can be associated with a factor in two ways e the first is to declare a G structure for the model term and to refer to the giv file with the corresponding identifier GIV1 GIV2 GIV3 for example animal 1 for a one dimensional structure put the scale pa animal 0 GIV1 0 12 rameter 0 12 in this case after the GIVg iden tifier site variety 2 for a two dimensional structure site O CORUH 0 5 8 1 5 variety 0 GIV1 the second is for one dimensional structures in this case the giv structure can be directly associated with the term using the giv f 7 model function which associates the 7th giv file with factor f for example giv animal 1 0 12 is equivalent to the first of the preceding examples It is imperative that the GIV GRM matrix be defined with the correct row column order the order that matches the order of the levels in the factor it is associated with The easiest way to check this is to compare the order used in the GIV GRM file with the order reported in the sln file when the model is fitted Another example of L Section 5 4 1 is in analysis on data with 2 relationship matrices based on two separate pedigrees ASReml only allows one pedigree file to be specified but can create an inverse relations
416. p dependent variable to each trait in turn IF 1 2 ASSIGN YV ywt IF 1 3 ASSIGN YV gfw IF 1 4 ASSIGN YV fdm IF 1 5 ASSIGN YV fat tag sire 92 lI dam 3561 I grp 49 sex brr 4 litter 4871 age wwt IMO MO identifies missing values ywt MO gfw IMO fdm IMO fat MO coop fmt IPART 1235 328 16 11 Multivariate animal genetics data Sheep YV mu age brr sex age sex r sire dam lit age grp sex grp f grp traits are substituted for YV PART 4 leaves out sex grp for fdm YV mu age brr sex age sex r sire dam lit age grp f grp fdm is substituted for YV Table 16 14 REML estimates of a subset of the variance parameters for each trait for the genetic example expressed as a ratio to their asymptotic s e term wwt ywt gfw fdm fat sire 3 68 3 57 3 95 1 92 1 92 dam 6 25 4 93 2 78 0 37 0 05 litter 8 79 0 99 2 23 1 91 0 00 age grp 2 29 1 39 0 31 1 15 1 74 sex grp 2 90 3 43 3 70 1 83 Tables 16 14 and 16 15 present the summary of these analyses Fibre diameter was measured on only 2 female lambs and so interactions with sex were not fitted The dam variance component was quite small for both fibre diameter and fat The REML estimate of the variance component associated with litters was effectively zero for fat Thus in the multivariate analysis we consider fitting the following models to the sire dam and litter effects var us Ys 6 go var ua Ya I3561 Var uy
417. phenvar appended to the list For example the F func tion appends component k c v and forms cov c v v and var c v where v is the vector of existing variance components c is the vector of coefficients for the linear function and k is an optional offset which is usually omitted but would be 1 to represent the residual variance in a probit analysis and 3 289 to represent the residual variance in a logit analysis The 215 13 2 Syntax general form of the directive is F label a bxC c d mxk where a b c and dare the numbers or names of existing components Ug Up Ue and vg and cp is a multiplier for vp mis a number greater than the current length of v to flag the special case of adding the offset k When using the component numbers the form a b can be used to reference blocks of components as in F label a b k c d Assuming that the instructions in the ASReml code box corresponds to a simple sire model mu r Sire so that variance component 1 is the Sire variance and variance component 2 is the Residual variance then F phenvar 1 2 or F phenvar Sire Residual creates a third component called phenvar which is the sum of the variance components that is the phenotypic variance F genvar 1 4 or F genvar Sire 4 creates a fourth component called genvar which is the sire variance component multiplied by 4 that is the genotypic variance Ratios or in particular cases heritabilities are VPREDICT DEFINE
418. qualifier on page 189 Common examples are Genotypes grouped into Families and Locations grouped by Region We call these associated factors The key characteristic of associated factors is that they are coded such that the levels of one are uniquely nested in the levels of another If one is unknown coded as missing all associated factors must be unknown for that data record It is typically unnecessary to interact associated factors except when required to adequately define the variance structure 94 6 6 Alphabetic list of model functions 6 6 Alphabetic list of model functions Table 6 2 presents detailed descriptions of the model functions discussed above Note that some three letter function names may be abbreviated to the first letter Table 6 2 Alphabetic list of model functions and descriptions model function action and t r overlays adds r times the design matrix for model term t to the existing design a t r matrix Specifically if the model up to this point has p effects and t has a effects the a columns of the design matrix for t are multiplied by the scalar r default value 1 0 and added to the last a of the p columns already defined The overlaid term must agree in size with the term it overlays This can be used to force a correlation of 1 between two terms as in a diallel analysis male and female assuming the ith male is the same individual as the ith female Note that if the overlaid term is complex it ma
419. r predictions are erroneous Warning This US structure is not positive definite Warning Unrecognised qualifier at character Warning US matrix was not positive definite MODIFIED Warning User specified spline points Warning Variance parameters were modified by BENDing Warning Likelihood decreased Check gammas and singularities revise the qualifier arguments The issue is to match the declared R structure to the physical data Dropping observations which are missing will often usu ally destroy the pattern Estimating missing values allows the pattern to be retained Do not accept the estimates printed The FOWN test requested is not calculated because it results in different numbers of degrees of freedom to that obtained for the incremental tests for the terms in the model as fitted the FOWN calculations are based on the reduced design matrix formed for the incremental model ASReml performs the stan dard conditional test instead The user must reorder swap the terms in the model specification and rerun the job to per form the requested FOWN test the labels for predicted terms are probably out of kilter Try a simpler predict statement If the problem persists send for help check the initial values the qualifier either is misspelt or is in the wrong place the initial values were modified by a bending process the points have been rescaled to suit the data values ASReml may not have co
420. r AINV and the use of nrm f on the model line Furthermore GRMn and grmn f can be used as synonyms for GIVn and giv f n respectively where fis the model term variable to which the structure is applied and n is the ordinal number of the GIV GRM matrix being associated with f 9 6 2 Genetic groups in GIV matrices If a user creates a GIV file outside ASReml which has fixed degrees of freedom associated with it a GROUPSDF n qualifier is provided to specify the number of fixed degrees of freedom n incorporated into the GIV matrix The GROUPSDF qualifier is written into the first line of the giv matrix produced by the GIV qualifier of the pedigree line if the pedigree includes genetic groups and will be honoured from there when reusing a GIV matrix formed from a pedigree with genetic groups in ASReml When groups are constrained then it will be the number of groups less number of constraints For example if the pedigree file qualified by GROUPS 7 begins A00 Q um O ABC is not present in the subsequent pedigree lines Hur lus O iC a Oo amp 6 DE 0 0 DE is not present in the subsequent pedigree lines there are actually only 5 genetic groups and two constraints so that the fixed effects for A 168 9 7 The reduced animal model RAM B and C sum to zero and for D and E sum to zero leaving only 3 fixed degrees of freedom fitted Therefore if the A inverse for this pedigree was saved it will contain GROUPSDF 3 in
421. r file ce eag a ek piara ee ee ee ee 223 143 2 The eT ascii arica 226 14 3 3 The ybt file na u esc ia A 227 144 Other ASReml output files oaa a 228 14 4 1 The aov file ira a a eR RS ERR SS 228 1442 The asl file ew ces pa des rodri we a oS 231 MAS The do fE s bh ek ae gn ae dhe AE a Ae se 231 MAA The pE se se og a ee se ES Ag agh Be eee ee 232 1445 The pys file ars hs os Awe EES ewe 233 14 4 6 The res file Soe Cee Se CEE SS CRE ee ERE SRE 233 1447 The LERMA cc SORES EEG RSE ac ar CL EE AR SS 238 TAS The ab THE rece sos eor Be pe ee eee ewe eS 240 MAS The Ie ck ee wee PRE REPRE ESE REE RS RES AES 240 SAAT ee vyp file o iio serende k ES eR ee ee ees 241 14 5 ASReml output objects and where to find them 243 15 Error messages 246 151 INEGI co ee ea es de rs oe eee Bee ee a 246 15 2 Common PED ccce cu bomp ee b OE Re oe we ERE Sew ed 247 15 3 Things to check in the asr file 249 A A 252 15 5 Information Warning and Error messages o e 261 16 Examples 272 TO II NN 272 Pa plot design e Oats lt saa eR eee arder ee we a 272 16 3 Unbalanced nested design Rats 2 0 0 ee ee ee 276 16 4 Source of variability in unbalanced data Volts 279 16 5 Balanced repeated measures Height o 282 16 6 Spatial analysis of a field experiment Barley 289 16 7 Unreplicated early
422. r table for each trait using Team and Year effects Team predictions are produced by averaging over years yield variety r site variety predict variety will ignore the site variety term in forming the predictions while predict variety AVERAGE site forms the hyper table based on site and variety with each linear combination in each cell using variety and site variety effects and then forms averages across sites to produce variety predictions yield site variety r site variety at site block predict variety puts variety in the classify set site in the averaging set and block in the ignore set Consequently it forms the sitex variety hyper table from model terms site variety and site variety but ignoring all terms in at site block and then forms averages across sites to produce variety predictions 10 3 7 New R4 Prediction using two way interaction effects In some cases we wish to calculate from two way interaction effects bc say effects for one of the factors B say that are a weighted sum averaged over the c levels of C ie C bi J j 1 DCigt 193 10 3 Prediction TPREDICT C AVE B weights ONLYUSE B C allows this to be produced more computationally efficiently than it would be using PREDICT For example TPREDICT Animal AVE Trait 2 1 1 2 7 4 ONLYUSE Trait Animal Part of the motivation for this is the calculation of selection indices The index coefficients are typically derived as w a Go Ga
423. r than the syntax per se Part of the file nin89 asr presented in Chapter 14 is displayed below to indicate the lines of the asr file that should be checked You should check that e sufficient workspace has been obtained e the records read lines read records used are correct e mean min max information is correct for each variable e the Loglikelihood has converged and the variance parameters are stable e the fixed effects have the expected degrees of freedom 249 15 3 Things to check in the asr file ASReml 3 01d 01 Apr 2008 NIN alliance trial 1989 Build f 11 Apr 2008 32 bit 11 Apr 2008 15 58 39 484 32 Mbyte Windows nin89a workspace Licensed to NSW Primary Industries permanent FEA k ak k k k ak k ak ak ak I I 3k K K ak ak ak 2k 2k 2K 3K a a A A A K K AC I I kk 1 21 1 1 3K K K ACC CR ak 2k ak Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au EEEE E E o o e k k kkk ARG Folder C data asr3 ug3 manex working directory variety A QUALIFIERS SKIP 1 IDISPLAY 15 QUALIFIER DOPART 1 is active Reading nin89aug asd FREE FORMAT skipping 1 Lines Univariate analysis of yield Summary of 242 records retained of 242 read records read Model term Size miss zero MinNon0 Mean MaxNon0 StndDevn 1 variety 56 0 0 1 26 454556 2 id 0 o 1 000 26 45 56 00 17 18 data 3 pid 18 O 1101 2628 4156 1121 summary 4 raw 16 o 21 00 510 5 840 0 149 0 5 repl 4 0 0 1 2 4132 4 6 nloc 0 O 4 000 4
424. r variety UnStruct 2 1 96173 1 96173 2 69 OU Tr run UnStruct 1 1 f0788 1 70788 2 62 OU TE yun UnStruct 1 0 319145 0 319145 0 89 OU Te run UnStruct 2 2 54326 2 54326 3 20 OU 306 16 8 Paired Case Control study Rice Covariance Variance Correlation Matrix UnStructured 2 144 0 4402 0 9874 2 348 Covariance Variance Correlation Matrix UnStructured 3 840 0 8504 2 334 1 962 Covariance Variance Correlation Matrix UnStructured 1 708 0 1631 0 3191 2 543 The resultant REML log likelihood is identical to that of the heterogeneous univariate analysis column b of table 16 8 The estimated variance parameters are given in Table 16 10 The predicted variety means in the pvs file are used in the following section on interpretation of results A portion of the file is presented below There is a wide range in SED reflecting the imbalance of the variety concurrence within runs Assuming Power transformation was Y 0 000 0 500 run is ignored in the prediction except where specifically included Trait variety Power value Stand_Error Ecode Retransformed approx_SE sqrt yc A1iCombo 14 9532 0 9181 E 223 5982 27 4571 sqrt ye AliCombo 7 9941 0 7993 E 63 9054 12 790 sqrt yc Bluebelle 13 1033 0 9310 E 171 6969 24 3980 sqrt ye Bluebelle 6 6299 0 8062 E 43 9559 10 6901 sqrt yc C22 16 6679 0 9161 E 214 8192 30 6057 sqrt ye C22 8 9543 0 7993 E 80 1798 14 3140 sqrt yc YRK1 15 1859 0 9549 E 230 6103 29 0012 sqrt ye YRK1 8 3356 0 81
425. ray of r rows by c columns we could arrange the residuals as a matrix and might consider that they were autocorrelated within rows and columns Writing the residuals as a vector in field order that is by sorting the residuals rows within columns plots within blocks the variance of the residuals might then be g Delp D Er pr where 2 p and 2 p are correlation matrices for the row model order r autocorrelation parameter p and column model order c autocorrelation parameter pe respectively More specifically a two dimensional separable autoregressive spatial structure AR1 amp AR1 is sometimes assumed for the common errors in a field trial analysis see Gogel 1997 and Cullis et al 1998 for examples In this case 1 1 Pr 1 Pe 1 Sole e l and D Pe Pe 1 gt Pe PEPE ae 1 Alternatively the residuals might relate to a multivariate analysis with n traits and n units and be ordered traits within units In this case an appropriate variance structure might be T 6 52 where E un ig a general or unstructured variance matrix See Chapter 7 for details on specifying separable R structures in ASReml 2 1 12 Direct products in G structures Likewise the random model terms in u may have a direct product variance structure For example for a field trial with s sites g varieties and the effects ordered varieties within sites 10 2 1 The general linear mixed model the random model term site variety may have
426. rder Had sorting not been requested ASReml would not have been able to detect that the lines of the data file were not sorted into the appropriate field order and spatial analysis would be wrong 10 row 22 0 0 1 11 5000 22 11 column 11 0 0 1 6 0000 11 12 mu 1 13 mv_estimates 18 11 AR AutoReg 0 1000 22 AR AutoReg 0 1000 Warning Spatial mapping information for side 1 of order 11 ranges from 1 0 te 22 0 Warning Spatial mapping information for side 2 of order 22 ranges from 1 0 to 11 0 Error Failed to sort data records Sortkeys range 11 22 2 2 1 failed at record 2 1 1 1 1 2 2 1 1 3 3 i 23 4 4 1 23 22 22 1 221 Fault Sorting data into field order Last line read was 22 column AR1 0 100000 ninerri0 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 mv_estimates 18 SECTIONS 242 4 i STRUCT 11 1 1 5 1 1 10 22 1 1 6 1 1 11 13 factors defined max 500 6 variance parameters max1500 2 special structures Final parameter values 3 6 0 0000 10000E 360 10000 0 10000 Last line read was 22 column AR1 0 100000 Finished 11 Apr 2008 20 41 46 421 Sorting data into field order 260 15 5 Information Warning and Error messages 15 5 Information Warning and Error messages ASReml prints information warning and error messages in the asr file The major in formation messages are in Table 15 1 A list of warning messages together with the likely meaning s is presented in Ta
427. reated and labelled are also available for subsequent use in the analysis and those created or read but not labelled intermediate calculations not required for subsequent analysis When listing variables in the field definitions list those read from the data file first After them list and define the labelled variables that are to be created The number of variables read can be explicitly set using the READ qualifier described in Table 5 5 Otherwise if the first transformation on a field overwrites its contents for instance using ASReml recognises that the field does not need to be read in unless a subsequent field does need to be read For example A B C A B reads two fields A and B and constructs C as A B All three are available for analysis However A B C A B D E D B reads four fields A B C and D because the fourth field is not obviously created and must therefore be read even though the third field C is overwritten The fifth field is not read but just created E Variables that have an explicit label may be referenced by their explicit label or their internal label Therefore to avoid confusion do not use explicit labels of the form Vz where 7 is a number for variables to be referred to in a transformation Vi always refers to field variable 1 in a transformation statement 52 5 5 Transforming the data Variables that are not initialized from the data file are initialized to missi
428. records retained of 242 read data summary Model term Size miss zero MinNon0 Mean MaxNonO StndDevn 1 variety 56 0 0 il 26 4545 56 2 id 0 O 1 000 26 45 56 00 17 18 3 pid 18 1101 2628 4156 1121 4 raw 18 o 21 00 510 5 840 0 149 0 5 repl 4 0 0 1 2 4132 4 6 nloc 0 O 4 000 4 000 4 000 0 000 7 yield Variate 18 O 1 050 25 53 42 00 7 450 8 lat 0 O 4 300 25 80 47 30 13 63 9 long 0 o 1 200 13 80 26 40 7 629 10 row ae 0 0 1 11 5000 22 11 column 41 0 0 1 6 0000 11 12 mu 1 13 mv estimates 18 22 AR AutoReg 5 5 0 5000 11 AR AutoReg 6 6 0 5000 Forming 75 equations 57 dense Initial updates will be shrunk by factor 0 316 Notice 1 singularities detected in design matrix 1 LogL 401 827 S2 42 467 168 df 1 000 0 5000 0 5000 iterations 2 LogL 400 780 S2 43 301 168 df 1 000 0 5388 0 4876 3 LogL 399 807 S2 45 066 168 df 1 000 0 5895 0 4698 4 LogL 399 353 S2 47 745 168 df 1 000 0 6395 0 4489 5 LogL 399 326 S2 48 466 168 df 1 000 0 6514 0 4409 6 LogL 399 324 S2 48 649 168 df 1 000 0 6544 0 4384 7 LogL 399 324 S2 48 696 168 df 1 000 0 6552 0 4377 224 14 3 Key output files 8 LogL 399 324 s2 48 708 168 df 1 000 0 6554 0 4375 Final parameter values 1 0000 0 65550 0 43748 Results from analysis of yield Model_Term Sigma Sigma Sigma SE C Variance 242 168 1 00000 48 7085 6 81 OP parameter Residual AR AutoR 22 0 655505 0 655505 11 63 OU estimates Residual AR AutoR 11 0 437483 0 437483 5 43 0U Wald F sta
429. ree sections we present an exhaustive analysis of these data using equivalent 300 16 8 Paired Case Control study Rice univariate and multivariate techniques It is convenient to use two data files one for each approach The univariate data file consists of factors pair run variety tmt unit and variate rootwt The factor unit labels the individual trays pair labels pairs of trays to which varieties are allocated and tmt is the two level bloodworm treatment factor control treated The multivariate data file consists of factors variety and run and variates for root weight of both the control and exposed treatments labelled yc and ye respectively Preliminary analyses indicated variance heterogeneity so that subsequent analyses were con ducted on the square root scale Figure 16 8 presents a plot of the treated and the control root area on the square root scale for each variety There is a strong dependence between the treated and control root area which is not surprising The aim of the experiment was to determine the tolerance of varieties to bloodworms and thence identify the most tolerant varieties The definition of tolerance should allow for the fact that varieties differ in their inherent seedling vigour Figure 16 8 The original approach of the scientist was to regress the treated root area against the control root area and define the index of vigour as the residual from this regression This approach is clearly inefficient s
430. riance model being fitted Try increasing the memory simplifying the model and changing starting values for the gammas If this fails send the problem to the VSN mailto support asreml co uk for investigation Check the argument POWER structures are the spatial variance models which re quire a list of distances Distances should be in increasing order If the distances are not obtained from variables the SORT field is zero and the distances are presented after all the R and G structures are defined 269 15 5 Information Warning and Error messages Table 15 3 Alphabetical list of error messages and probable cause s remedies error message probable cause remedy Reading factor names reading Overdispersion factor READING OWN structures Reading the data Reading Update step size Residual Variance is Zero R header SECTIONS DIMNS GSTRUCT R structure header SITE DIM GSTRUCT Variance header SEC DIM GSTRUCT R structure error ORDER SORTCOL MODEL GAMMAS R structures are larger than number of records REQUIRE ASUV qualifier for this R structure REQUIRE 1 x E R structure Scratch Segmentation fault Singularity appeared in Al matrix Singularity in Average Information Matrix Sorting data by Section Row Sorting the data into field order something is wrong in the terms definitions It could also be that the data file is misnamed Check the argument There is
431. riptive of the appropriate test nor is the algorithm for determining the MCM foolproof The Wald statistics are collectively presented in a summary table in the asr file The basic table includes the numerator degrees of freedom 1 and the incremental Wald F statistic for each term To this is added the conditional Wald F statistic and the M code if FCON 22 2 5 Inference Fixed effects is specified A conditional Wald F statistic is not reported for mu in the asr but is in the aov file adjusted for covariates The FOWN qualifier page 78 allows the user to replace any all of the conditional Wald F statistics with tests of the same terms but adjusted for other model terms as specified by the user the FOWN test is not performed if it implies a change in degrees of freedom from that obtained by the incremental model 2 5 3 Kenward and Roger adjustments In moderately sized analyses ASReml will also include the denominator degrees of freedom DenDF denoted by v2 Kenward and Roger 1997 and a probablity value if these can be computed They will be for the conditional Wald F statistic if it is reported The DDF 2 see page 67 qualifier can be used to suppress the DenDF calculation DDF 1 or request a particular algorithmic method DDF 1 for numerical derivatives DDF 2 for algebraic derivatives The value in the probability column either P_inc or P_con is computed from an Fava reference distribution An approximation i
432. rlying principles Our approach to prediction is a generalization of that of Lane and Nelder 1982 who consider fixed effects models They form fitted values for all combinations of the explanatory variables in the model then take marginal means across the explanatory variables not relevent to the current prediction Our case is more general in that we also consider the case of associated factors see page 94 and options for random effects that appear in our mixed models A formal description can be found in Gilmour et al 2004 and Welham et al 2004 Associated factors have a particular one to many association such that the levels of one factor say Region define groups of the levels of another factor say Location In prediction it is necessary to correctly associate the levels of associated factors Terms in the model may be fitted as fixed or random and are formed from explanatory 178 10 3 Prediction variables which are either factors or covariates For this exposition we define a fixed factor as an explanatory variable which is a factor and appears in the model in terms that are fixed it may also appear in random terms a random factor as an explanatory variable which is a factor and appears in the model only in terms that are fitted as random effects Covariates generally appear in fixed terms but may appear in random terms as well random regression In special cases they may appear only in random terms Random fact
433. rmally ap pear in the model For default averaging in prediction the weights for the levels of the grouped factor Year will be in this example 0 3 0 2 0 3 0 2 derived from the weights for the base factor YearLoc Use AVE YearLoc 2 2 2 3 3 2 2 2 3 3 24 to produce equal weighting of Year effects If G sets of variables are included in the classify set only the first variable is reported in labelling the predict values except that for G MM sets the marker position is reported Having identified the explanatory variables in the classify set the second step is to check the averaging set The default averaging set is those explanatory variables involved in fixed effect model terms that are not in the classify set By default variables that are not in any ASSOCIATE list and that only define random model terms are ignored Use the AVERAGE ASSOCIATE or PRESENT qualifiers to force variables into the averaging set The third step is to check the linear model terms to use in prediction The default is that all model terms based entirely on variables in the classifying and averaging sets are used Two qualifiers allow this default to be modified by adding USE or removing IGNORE model terms The qualifier ONLYUSE explicitly specifies the model terms to use ignoring all others The qualifier EXCEPT explicitly specifies the model terms not to use including all 181 10 3 Prediction others These qualifiers will not overri
434. rms and qualifiers Model terms include variety factor and variate labels Section 5 4 functions of la bels special terms and interactions of these The model column 11 is specified immediately after the datafile and any job nin89 asd skip 1 control qualifier and or tabulate lines The syntax for Yield mu variety r on repl specifying the model is eas 12 11 column AR1 3 22 row AR1 3 response qualifiers fixed r random f sparse fixed e response is the label for the response variable s to be analysed multivariate analysis is discussed in Chapter 8 e qualifiers allow for weighted analysis Section 6 7 and Generalized Linear Models Section 6 8 e separates response from the list of fixed and random terms e fixed represents the list of primary fixed explanatory terms that is variates factors interactions and special terms for which Wald F statistics are required See Table 6 1 for a brief definition of reserved model terms operators and commonly used functions The 85 6 2 Specifying model formulae in ASReml full definition is in Section 6 6 e random represents the list of explanatory terms to be fitted as random effects see Table 6 1 e sparse_fixed are additional fixed terms not included in the table of Wald F statistics 6 2 1 General rules The following general rules apply in specifying the linear mixed model e all elements in the model must be space separated e
435. rning This qualifier is ignored when reading binary data IDATAFILE f specifies the datafile name replacing the one obtained from the datafile line It is required when different PATHS see DOPATH in Table 11 3 of a job must read different files The SKIP qualifier if specified will be applied when reading the file FILTER v SELECT New R4 enables a subset of the data to be analysed v is the number or n EXCLUDE n name of a data field When reading data the value in field v is checked after any transformations are performed If SELECT and EXCLUDE are omitted records with zero in field v are omitted from the analysis If SELECT n is specified records with n in field v are retained and all other records are omitted Conversely if EXCLUDE n is specified records with n in field v are ignored FOLDER s specifies an alternative folder for ASReml to find input files This qualifier is usually placed on a separate line BEFORE the data filename line and any pedigree giv grm filename lines For example FOLDER Data data asd SKIP 1 is equivalent to Data data asd SKIP 1 62 5 7 Data file qualifiers Table 5 2 Qualifiers relating to data input and output qualifier action FORMAT S supplies a Fortran like FORMAT statement for reading fixed format files A simple example is FORMAT 314 5F6 2 which reads 3 integer fields and 5 floating point fields from the first 42 characters of each data line
436. rranged in lots of n records where n is the num ber of traits It may be necessary to expand the data file to achieve this structure inserting a missing value NA on the additional records This option is sometimes relevant for some forms of repeated measures analysis There will need to be a factor in the data to code for trait as the intrinsic Trait factor is undefined when the data is presented in a univariate manner allows you to have an error variance other than J amp X where gt is the unstructured US see Table 7 3 variance structure if the data is pre sented in a multivariate form If there are missing values in the data include f mv on the end of the linear model It is often also necessary to specify the S2 1 qualifier on the R structure lines The intrinsic factor Trait is defined and may be used in the model See Chapter 8 for more information This option is used for repeated measures analysis when the variance structure required is not the standard multivariate unstructured matrix is used with SECTION and ROWFACTOR to instruct ASReml to set up R structures for analysing a multi environment trial with a separable first order autoregressive model for each site environment and to insert extra data records to complete the grid of plots defined by the RowFactor and the ColumnFactor for each Section so that a two dimensional error structure can be defined v is the name of a factor or variate containing column numbers 1
437. rvey dat harvey dat All individuals appearing in the data file must adailygain mu lines r animal 0 25 appear in the pedigree file When all the pedi gree information individual male_parent female_parent appears as the first three fields of the data file the data file can double as the pedigree file In this example the line harvey ped 159 9 3 The pedigree file ALPHA could be replaced with harvey dat ALPHA Typically additional individuals pro viding additional genetic links are present in the pedigree file 9 3 The pedigree file The pedigree file is used to define the genetic relationships for fitting a genetic animal model and is required if the P qualifier is associated with a data field The pedigree file has three fields the identities of an individual its sire and its dam or maternal grand sire if the MGS qualifier Table 9 1 is specified in that order an optional fourth field may supply inbreeding selfing information used if the FGEN qual ifier Table 9 1 is specified a fourth field specifying the SEX of the individual is required if the XLINK qualifier Table 9 1 is specified is sorted so that the line giving the pedigree of an individual appears before any line where that individual appears as a parent is read free format it may be the same file as the data file if the data file is free format and has the necessary identities in the first three fields see below is specified
438. s where a tdci Pee se repl it is coded 1 If mv 12 11 column ARi 424 22 row AR1 904 The action when mv is omitted from the model depends on whether a univariate or mul tivariate analysis is being performed For a univariate analysis ASReml discards records which have a missing response In multivariate analyses all records are retained and the R matrix is modified to reflect the missing value pattern 6 9 2 Missing values in the explanatory variables ASRem will abort the analysis if it finds missing values in the design matrix unless MVINCLUDE or MVREMOVE is specified see Section 5 8 MVINCLUDE causes the missing value to be treated as a zero MVREMOVE causes ASReml to discard the whole record Records with missing val ues in particular fields can be explicitly dropped using the DV transformation Table Sl Covariates Treating missing values as zero in covariates is usually only sensible if the covariate is centred has mean of zero Design factors Where the factor level is zero or missing and the MVINCLUDE qualifier is specified no level is assigned to the factor for that record These effectively defines an extra level class in the factor which becomes a reference level 105 6 10 Some technical details about model fitting in ASReml 6 10 Some technical details about model fitting in ASReml 6 10 1 Sparse versus dense ASReml partitions the terms in the linear model into two parts a dense se
439. s computation of the approximate denominator degrees of freedom according to Kenward and Roger 1997 for the testing of fixed effects terms in the dense part of the linear mixed model There are three options for i i 1 suppresses computation i 1 and i 2 compute the denominator d f using numerical and algebraic methods respectively If i is omitted then i 2 is assumed If DDF is omitted i 1 is assumed except for small jobs lt 10 parameters lt 500 fixed effects lt 10 000 equations and lt 100 Mbyte workspace when i 2 Calculation of the denominator degrees of freedom is computationally ex pensive Numerical derivatives require an extra evaluation of the mixed model equations for every variance parameter Algebraic derivatives re quire a large dense matrix potentially of order number of equations plus number of records and is not available when MAXIT is 1 or for multivariate analysis adds a conditional Wald F statistic column to the Wald F Statistics table It enables inference for fixed effects in the dense part of the lin ear mixed model to be conducted so as to respect both structural and intrinsic marginality see Section 2 5 The detail of exactly which terms are conditioned on is reported in the aov file The marginality principle used in determining this conditional test is that a term cannot be ad justed for another term which encompasses it explicitly e g term A C cannot be adjusted for A
440. s essentially because the unit vector defining X can be found by summing the columns of the Z matrix This linear dependence of the matrices translates to dependence of the BLUPs and hence constraints This aspect occurs whenever the column space of X is contained in the column space of Z The dependence is slightly more complex with correlated random effects 2 4 Inference Random effects 2 4 1 Tests of hypotheses variance parameters Inference concerning variance parameters of a linear mixed effects model usually relies on approximate distributions for the RE ML estimates derived from asymptotic results It can be shown that the approximate variance matrix for the REML estimates is given by the inverse of the expected information matrix Cox and Hinkley 1974 section 4 8 Since this matrix is not available in ASReml we replace the expected information matrix by the Al matrix Furthermore the REML estimates are consistent and asymptotically normal though in small samples this approximation appears to be unreliable see later A general method for comparing the fit of nested models fitted by REML is the REML likelihood ratio test or REMLRT The REMLRT is only valid if the fixed effects are the same 16 2 4 Inference Random effects for both models In ASReml this requires not only the same fixed effects model but also the same parameterisation If pa is the REML log likelihood of the more general model and ni is the REML log lik
441. s for consistency with other analyses conducted by Cox and Snell 1981 and in the GENSTAT manual 280 16 4 Source of variability in unbalanced data Volts ltage example 5 3 6 from the GENSTAT REML manual Residuals vs Fitted valu Residuals Y 1 08 1 45 Fitted values X 15 56 16 81 o o o o a o o Po i o e y o o 00 9o o o 9 os o oo 9o o om Co 0o o o o _ 2o ie 00 2 o o o g Sa 5 COS e o o 00 o o o ao 9 90 o o Do Si Po 5 o o o o o a o a o o o a Figure 16 2 Residual plot for the voltage data The REML log likelihood from the model without the setstat teststat term was 203 242 the same as the REML log likelihood for the previous model Table 16 3 presents a summary of the REML log likelihood ratio for the remaining terms in the model The summary of the ASReml output for the current model is given below The column labelled Sigma SE is printed by ASReml to give a guide as to the significance of the variance component for each term in the model The statistic is simply the REML estimate of the variance component divided by the square root of the diagonal element for each component of the inverse of the average information matrix The diagonal elements of the expected not the average information matrix are the asymptotic variances of the REML estimates of the variance parameters These Sigma SE statistics cannot be used to test the null hypothesis that the variance component is zero If we had used t
442. s in the grr file are not needed and if present should be skipped using CSKIP Values are typically TAB COMMA or SPACE separated but may be packed no separator when all values are integers 0 1 2 Missing values in the regression variables may be repre sented by NA Invalid data is also treated as missing Missing values are replaced by the mean of the respective regressor Alternative missing data methods that involve imputation from neighbouring markers have not been implemented Some general qualifiers are 172 9 8 Factor effects with large Random Regression models ISAVEGIV instructs ASReml to write the G matrix in dgiv format PSD s declares that the derived variance matrix may have up to s singularities PEV requests calculation of Prediction Error Variance of marker effects which are reported in the mef file Calculation of Prediction error variances is computationally very expensive CENTRE c requests ASReml to centre the regressors at c if c is specified else at the individual regressor means otherwise the G matrix is formed from uncentered regressors Note that centring introduces a singularity in the G matrix and PSV s will need to be set Other qualifiers relate specifically to whether the regressors are markers Markers are typi cally coded 0 1 2 being counts of the minor allele However if they are imputed they will take real values between 0 and 2 Since marker files may be huge SMODE b sets the storag
443. s is facilitated by using the my basis function mbf function associating the regressor variables to the levels of the factor essentially fitting ZMv where Z is the design matrix linking observations to the levels of the factor But if m is much bigger than f it is more computational efficient 171 9 8 Factor effects with large Random Regression models to fit an equivalent model Zu with a variance structure for u based on MM ASReml can read the matrix M associated with a factor and group of regressor variables from a grr file construct a GRM matrix G MM s fit the equivalent model and report both factor and regressor predictions One common case of this model is when u represents genotype effects the regressors represent SNP marker counts typically 0 1 2 and v are marker effects The grr file is specified after any pedigree file and before the data file with any other GRM files There may only be one grr file It is assumed to contain a row for each level of the factor each row containing m regressor values Optionally the factor level name associated with the i th row can be included before the relevant regressor values Also a heading row might include a name for each field regressor variable Superfluous fields before the factor or regressor fields can be skipped and superfluous rows before the regressor information can be skipped The syntax for specifying and reading the grr file is M grr CSKIP c Factor f
444. s it recognises as being for the same terms from the rsv file Fur thermore ASRem1 will use estimates in the rsv file for certain models to provide starting values for certain more general models inserting rea sonable defaults where necessary The transitions recognised are listed and discussed in Section 7 10 2 66 5 8 Job control qualifiers Table 5 3 List of commonly used job control qualifiers qualifier action ICONTRAST s t p IDDF i FCON provides a convenient way to define contrasts among treatment levels CONTRAST lines occur as separate lines between the datafile line and the model line s is the name of the model term being defined t is the name of an existing factor p is the list of contrast coefficients For example ICONTRAST LinN Nitrogen 3 1 1 3 defines LinN as a contrast based on the 4 implied by the length of the list levels of factor Nitrogen Missing values in the factor become missing values in the contrast Zero values in the factor no level assigned become zeros in the contrast The user should check that the levels of the factor are in the order assumed by contrast check the ass or sln or tab files It may also be used on the implicit factor Trait in a multivariate analysis provided it implicitly identifies the number of levels of Trait the number of traits is implied by the length of the list Thus if the analysis involves 5 traits ICONTRAST Time Trait 1 3 5 10 20 request
445. s plotted against Row and Column position 1 Range 45 11 34 86 8 al O o a oe cee o 8 8 o O O O o o 6 B Bog 8 Pe oinpe Bg a O E pA O Noy O Y Q O 8 O Figure 16 4 Residual plots for the EXP variance model for the plant data The residual plot from this analysis is presented in Figure 16 4 This suggests increasing variance over time This can be modelled by using the EXPH model which models by ya Dc po where D is a diagonal matrix of variances and C is a correlation matrix with elements given by ci 4l The coding for this is y1 y3 y5 y7 y10 Trait tmt Tr tmt 120 285 16 5 Balanced repeated measures Height 14 52 Tr 0 EXPH 5 100 200 300 300 300 135 7 10 Note that it is necessary to fix the scale parameter to 1 S2 1 to ensure that the elements of D are identifiable Abbreviated output from this analysis is 1 LogL 195 598 s2 1 0000 60 df i 1 components constrained 2 LogL 179 036 S2 1 0000 60 df 3 LogL 175 483 S2 1 0000 60 df 4 LogL 173 128 s2 1 0000 60 df 5 LogL 171 980 s2 1 0000 60 df 6 LogL 171 615 s2 1 0000 60 df 7 LogL 171 527 s2 1 0000 60 df 8 LogL 171 504 s2 1 0000 60 df 9 LogL 171 498 s2 1 0000 60 df 10 LogL 171 496 S2 1 0000 60 df Model_Term Sigma Sigma Sigma SE C Residual POW EXP 5 0 906917 0 906917 21 89 OU Residual POW EXP 5 60 9599 60 9599 2 12 OU Residual POW EXP 5 72 9904 72 9904 1 99 OU Residual POW EXP 5 309 259 309 259 2 22 OU Residual POW EXP
446. s used for computational convenience when calculating the DenDF for Conditional F statistics using numerical derivatives The DenDF reported then relates to a maximal conditional incremental model MCIM which depending on the model order may not always coincide with the maximal conditional model MCM under which the conditional F statistic is calculated The MCIM model omits terms fitted after any terms ignored for the conditional test I after in marginality pattern In the example above MCIM ignores variety sow when calculating DenDF for the test of water and ignores water sow when calculating DenDF for the test of variety When DenDF is not available it is often possible though anti conservative to use the residual degrees of freedom for the denominator Kenward and Roger 1997 pursued the concept of construction of Wald type test statistics through an adjusted variance matrix of 7 They argued that it is useful to consider an improved estimator of the variance matrix of 7 which has less bias and accounts for the variability in estimation of the variance parameters There are two reasons for this Firstly the small sample distribution of Wald F statistics is simplified when the adjusted variance matrix is used Secondly if measures of precision are required for 7 or effects therein those obtained from the adjusted variance matrix will generally be preferred Unfortunately the Wald statistics are currently computed using an unadjusted varia
447. s4 rsv Notice LogL values are reported relative to a base of 20000 000 Note XFA model lower loadings initially held fixed Notice 29764 singularities detected in design matrix 1 LogL 1558 44 S2 1 00000 18085 df i 1 components restrained lreported in the asr file 342 16 11 Multivariate animal genetics data Sheep 2 LogL 1541 76 S2 1 00000 18085 df 3 LogL 1538 26 s2 1 00000 18085 df 4 LogL 1534 52 s2 1 00000 18085 df 5 LogL 1832 82 s2 1 00000 18085 df 6 LogL 1531 89 s2 1 00000 18085 df Note XFA model fitted with rotation 7 LogL 1531 67 s2 1 00000 18085 df 8 LogL 1531 64 S2 1 00000 18085 df 9 LogL 1531 64 S2 1 00000 18085 df 10 LogL 1531 64 s2 1 00000 18085 df 11 LogL 1531 64 s2 1 00000 18085 df Akaike Information Criterion Results from Be PF components components components components analysis of wwt ywt gfw fdm fat Bayesian Information Criterion 43494 60 Model_Term Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual Residual TrAG1245 TrAG1245 TrAG1245 TrAG1245 TrSG123 sex grp age age age age TrSG123 sex grp TrSG123 sex grp xfa Trait 3 xfa Trait 3 xfa Trait 3 xfalTrait 3 xfalTralt 3 xfa Trait 3 xtallrait 3 xfa Trait 3 xiallrait 3 yfa Trait 3 xfa Trait 3 xfa Trait 3 xfa Trait 3 xfa Trait 3 3520 US_V 1 US_C 2 US_V 2 US_C 3 U
448. scaling parameter for G 7 V V nonidentifiable 2 scaling parameters for G 8 V C V y nonidentifiable scale for R and overall scale 9 V V nonidentifiable 2 scaling parameters for R indicates the entry is not relevant in this case Note that G and G are interchangeable in this table as are R and R where H ZG o Z R o REML does not use 2 10 for estimation of variance parameters but rather uses a distribution free of 7 essentially based on error contrasts or residuals The derivation given below is presented in Verbyla 1990 We transform y using a non singular matrix L L L such that LX l LX 0 If Yj T L y J 1 2 Y N 7 LHL LHL Y 0 E HL LHL The full distribution of L y can be partitioned into a conditional distribution namely y Yo for estimation of T and a marginal distribution based on y for estimation of cr and o the latter is the basis of the residual likelihood The estimate of 7 is found by equating y to its conditional expectation and after some algebra we find 7 X H X X H y Estimation of k oj 01 is based on the log residual likelihood 1 ln 5 log det L H Lo y L H Lo y 1 5 log det X H X log det H y Py 2 11 where P H H X XH X ix Hg 13 2 2 Estimation Note that y Py y X 7 TH y X7 The log likelihood 2 11 depends on X and not on the particular non unique transformatio
449. sers may complain Having started with an initial allocation if ASReml realises more space is required as it is running it will attempt to restart the job with increased workspace If the system has already allocated all available memory the job will stop 202 11 4 Advanced processing arguments 11 3 7 Examples ASReml code action asreml LW64 rat as increase workspace to 64 Mbyte send screen output to rat asl and sup press interactive graphics asreml IL rat as send screen output to rat asl but display interactive graphics asreml N rat as allow screen output but suppress interactive graphics asreml ILW512 increase workspace to 512 Mbyte send screen output to rat asl but display rat as interactive graphics asreml rs3 coop wwt runs coop as twice writing results to coopwwt as and coopywt as using ywt 64Mb workspace and substituting wwt and ywt for 1 in the two runs 11 4 Advanced processing arguments 11 4 1 Standard use of arguments Command line arguments are intended to facilitate the running of a sequence of jobs that require small changes to the command file between runs The output file name is modified by the use of this feature if the R option is specified This use is demonstrated in the Coopworth example of Section 16 11 Command line arguments are strings listed on the command line after basename the com mand file name or specified on the top job control line after the ARGS qualifier These stri
450. sidual Residual a amp 2 2 48313 0 128460 13 Residual Residual C 5 3 0 786089E 01 0 111660E 01 14 Residual Residual C 5 4 0 115894 0 990547E 01 15 Residual Residual Vo 6 5 1 63176 0 495973E 01 16 TrAG1245 age grp V 1 0 132755E 02 0 660473E 03 17 TrAG1245 age grp V 2 0 976533E 03 0 807052E 03 18 TrAG1245 age grp V 3 0 176684E 02 0 156358E 02 19 TrAG1245 age grp V 4 0 208076E 03 0 128442E 03 20 TrSG123 sex grp V 1 1 01106 0 340424 21 TrSG123 sex grp V 2 16 0229 4 56493 22 TrSG123 sex grp V 3 0 280259 0 755415E 01 23 Trait sire y 1 4 0 593942 0 161397 24 Trait sire Gc 2 0 677334 0 212998 25 Trait sire v a 2 1 55632 0 399056 26 Trait sire C gt 0 280482E 01 U 183322E 01 27 Trait sire G 2 0 287861E 02 0 287861E 01 28 Trait sire 3 B 0 150192E 01 0 374544E 02 29 Trait sire C 4 1 0 596227E 01 0 110412 30 Trait sire C 4 2 0 657014E 01 0 410000 31 Trait sire C 4 3 0 477561E 02 0 191024E 01 32 Trait sire V 4 4 0 157854 0 857902E 01 33 Trait sire Ga amp 4 0 407282E 01 0 411396E 01 34 Trait sire Cc 6 2 0 133338 0 673424E 01 336 16 11 Multivariate animal genetics data Sheep 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 T2 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 Trait sire Trait sire Trait sire xfa TrDam123 1 xfa TrDam123 1 xfa TrDam123 1 xfa TrDam123 1 xfa TrDami23 1 xfa TrDam123 1
451. sis of multi environment early generation trials Biometrics 54 1 18 Dempster A P Selwyn M R Patel C M and Roth A J 1984 Statistical and computational aspects of mixed model analysis Applied Statistics 33 203 214 Draper N R and Smith H 1998 Applied Regression Analysis John Wiley and Sons New York 3rd Edition Fernando R and Grossman M 1990 Genetic evaluation with autosomal and x chromosomal inheritance Theoretical and Applied Genetics 80 75 80 Gilmour A R 2007 Mixed model regression mapping for qtl detection in experimental crosses Computational Statistics and Data Analysis 51 3749 3764 345 BIBLIOGRAPHY Gilmour A R Cullis B R and Verbyla A P 1997 Accounting for natural and ex traneous variation in the analysis of field experiments Journal of Agricultural Biological and Environmental Statistics 2 269 273 Gilmour A R Cullis B R Welham S J Gogel B J and Thompson R 2004 An efficient computing strategy for prediction in mixed linear models Computational Statistics and Data Analysis 44 571 586 Gilmour A R Thompson R and Cullis B R 1995 AI an efficient algorithm for REML estimation in linear mixed models Biometrics 51 1440 1450 Gleeson A C and Cullis B R 1987 Residual maximum likelihood REML estimation of a neighbour model for field experiments Biometrics 43 277 288 Gogel B J 1997 Spatial analysis of multi
452. ssarily involved in the subsequent analyses performed by the job and there may be multiple MERGE directives Indeed the job may just consist of a title line and MERGE directives The MERGE qualifier on the other hand combines information from two files into the internal data set which ASReml uses for analysis and does not save it to file It has very limited in functionality The files to be merged must conform to the following basic structure e the data fields must be TAB COMMA or SPACE separated e there will be one heading line that names the columns in the file e the names may not have embedded spaces e the number of fields is determined from the number of names e missing values are implied by adjacent commas in comma delimited files Otherwise they are indicated by NA or as in normal ASReml files e the merged file will be TAB separated if a txt file COMMA separated if a csv file and SPACE separated otherwise 211 12 2 Merge Syntax 12 2 Merge Syntax The basic merge command is MERGE filel WITH file2 TO newfie Typically files to be merged will have common key fields In the basic merge KEY not specified any fields having the same names are taken as the key fields and if the files have no fields in common they are assumed to match on row number Fields are referenced by name case sensitive The full command is MERGE filel KEY keyfields KEEP SKIP fields WITH file2 KEY keyfiel
453. ssing values Multiple tabulate statements are permitted either immediately before or after the linear model If a linear mixed model is not supplied tabulation is based on all records The tabulate statement has the form tabulate response_variables WT weight COUNT DECIMALS d SD RANGE STATS FILTER filter SELECT value factors 177 10 3 Prediction e tabulate is the directive name and must begin in column 1 e response_variables is a list of variates for which means are required e IWT weight nominates a variable containing weights e COUNT requests counts as well as means to be reported e DECIMALS d 1 lt d lt 7 requests means be reported with d decimal places If omitted ASReml reports 5 significant digits if specified without an argument 2 decimal places are reported e RANGE requests the minimum and maximum of each cell be reported e SD requests the standard deviation within each cell be reported e STATS is shorthand for COUNT SD RANGE e FILTER filter nominates a factor for selecting a portion of the data e SELECT value indicates that only records with value in the filter column are to be in cluded e factors identifies the factors to be used for classifying the data Only factors not covariates may be nominated and no more than six may be nominated ASReml prints the multiway table of means omitting empty cells to a file with extension tab 10 3 Prediction 10 3 1 Unde
454. st be linked together with the and qualifiers Table 6 1 While ASReml will check the overall size it does not check that the order of effects matches the structure definition so the user must be careful to get this right Check that the terms are conformable by considering the order of the fitted effects and ensuring the first term of the direct product corresponds to the outer factor in the nesting of the effects Two examples are random regressions where we want a covariance between intercept and slope Ir animal animal time 139 7 8 G structures involving more than one random term animal 2 2 0 US a b 2 animal is equivalent though not identical because of the scaling differences to lr pol time 1 animal pol time 1 animal 2 pol time 1 0 US 1 1 2 animal maternal direct genetic covariance lambid P sireid P damid P wwt ywt Trait Trait sex r Trait lambid at Trait 2 damid Trait lambid 2 3 0 US 1 3 Var wwt_D 102 2 Cov wwt_D ywt_D Var ywt_D 1 0 8 Cov wwt_D wwt_M Cov ywt_D wwt_M Var wwt_M lambid O AINV AINV explicitly requests to use A inverse Table 7 5 Examples of constraining variance parameters in ASReml ASReml code action ABACBAOCBA constrain all parameters corresponding to A to be equal similarly for B and C The 7th parameter would be left unconstrained This sequence applied to an unstructured 4 x 4 matrix would make it banded that is
455. stics are numerically the same as the ANOVA Wald F statistics and ASReml has calculated the appropriate denominator df for testing fixed effects This is a simple problem for balanced designs such as the split plot design but it is not straightforward to determine the relevant denominator df in unbalanced designs such as the rat data set described in the next section Tables of predicted means are presented for the nitrogen variety and variety by nitrogen tables in the pvs file The qualifier SED has been used on the third predict statement and so the matrix of SEDs for the variety by nitrogen table is printed For the first two predictions the average SED is calculated from the average variance of differences Note also that the order of the predictions e g 0 6 cwt 0 4 cwt 0 2 cwt 0_cwt for nitrogen is simply the order those treatment labels were discovered in the data file 274 16 2 Split plot design Oats Split plot analysis oat Variety Nitrogen 14 Apr 2008 16 15 49 oats Ecode is E for Estimable for Not Estimable The predictions are obtained by averaging across the hypertable calculated from model terms constructed solely from factors in the averaging and classify sets Use AVERAGE to move ignored factors into the averaging set me a 1 Predicted values of yield The averaging set variety
456. structure definition lines In this case r Repl the replicate term in the first G structure def 0 0 1 inition line has been spelt incorrectly To cor Repl 1 rect this error replace Repl with repl a AEA G a Folder C data ex manex variety A QUALIFIERS SKIP 1 QUALIFIER DOPART 1 is active Reading nin asd FREE FORMAT skipping 1 lines Univariate analysis of yield Summary of 224 records retained of 242 read Model term Size miss zero MinNon0 Mean MaxNon0 1 variety 56 0 0 i 28 5000 56 11 column 11 0 0 1 6 3304 11 12 mu 1 Fault G structure header Term not found Last line read was Repl 10000 ninerr6 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 repl 4 0 100 3 SECTIONS 224 4 1 TYPE 0 0 0 STRUCT 224 0 0 0 0 0 0 12 factors defined max 500 4 variance parameters max1500 2 special structures Final parameter values 0 10000 1 0000 Last line read was Repl 10000 Finished 11 Apr 2008 15 41 53 668 G structure header Term not found Fixing the header line we then get the error message Structure Factor mismatch This arose because repl1 has 4 levels but we have only declared 2 in the G structure model 257 15 4 An example line The G structure should read repl 1 4 0 IDV 0 1 The last lines of the output with this error are displayed below 11 column 11 0 0 1 6 3304 11 12 mu 2 identity 0 1000 Structure for repl has 2 levels defined Fault Struct
457. structure is known except for the scale Note that in many cases the variance or scaling parameter will actually be a variance ratio see page 117 This depends on how the R structure is defined It is important to recognise whether it is a variance or a variance ratio when setting initial values Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance Correlation models One dimensional equally spaced ID identity C 1 C 0 149 0 1 w AR 1 1 order Ca 1 Cai Q 1 2 l w autoregressive C 4 C 1 gt j 1 Ig lt 1 AR2 2 order C 1 2 3 2 w autoregressive Ci 04 1 60 C CORONE aa C i gt 1 ld lt 1 si 9 10 lt 1 AR3 3 order C 1 28 1 4 3 4 3 w autoregressive Cu 0 9 0 is o sir Q 1 Q Co E PU O 4 DO g 95 i gt jt 2 PA lt 1 lt 1 lt 1 SAR symmetric C L 1 2 l w autoregressive Cas 1 92 4 C AC p 4 cad 1 gt 3 1 lp lt 1 123 7 5 Variance model description Table 7 3 Details of the variance models available in ASReml base description algebraic number of parameters identifier form corr homo s hetero s variance variance SAR2 constrained as for AR3 using 2 3 2 w autoregressive 2 3 used for 0 mai Yes competition
458. supplied These qualifiers do not modify the matrix they just instruct ASReml to proceed regard less If the matrix has positive and negative eigenvalues ND instructs ASReml to ignore the condition and proceed anyway If the matrix is positive semi definite positive and zero eigenvalues PSD allows ASReml to introduce Lagrangian multipliers to accommodate linear dependencies and rows with zero elements and allows ASReml to proceed Linear depen dencies occur for example when the list of individuals includes clones Rows with zero elements occur when the GRM represents a dominance matrix and the list of individuals includes fully inbred individuals which by definition have zero dominance variance If the 166 9 6 Reading a user defined inverse relationship matrix matrix has positive zero and negative eigenvalues NSD may be used to allow ASReml to continue The zero eigenvalues are handled as for PSD Sometimes with negative eigen values the iteration sequence may fail as some parameter values will result in a negative residual sum of squares If the specified giv file does not exist but there is a grm file of the same name ASReml will read and invert the grm file and write the inverse to the giv file if SAVEGIV f is specified It is written in DENSE format unless f 1 SAVEGIV 3 writes the GIV matrix as an sgiv file SAVEGIV 4 writes the GIV matrix as a dgiv file where sgiv is a single precision lower triangle r
459. support asreml co uk for investigation Try running without the CONTINUE qualifier the program did not proceed to convergence because the REML log likelihood was fluctuating wildly One possible reason is that some singular terms in the model are not being detected consistently Otherwise the updated G structures are not pos itive definite There are some things to try define US structures as positive definite by using GP supply better starting values fix parameters that you are confident of while getting better estimates for others that is fix variances when estimating covariances fit a simpler model reorganise the model to reduce covariance terms for exam ple use CORUH instead of US It is best to start with a positive definite correlation structure Maybe use a structured correlation matrix A variance structure should be specified for this term The reported limit is hardcoded The number of variables to be read must be reduced The error could be in the variable factor name or in the num ber of values or the list of values The error could be in the variable factor name or in the num ber of values or the list of values the error model is not correctly specified the file did not exist or was of the wrong file type binary unformatted sequential There are several messages of this form where something is what ASReml is attempting to read Either there is an error telling ASReml
460. t v xfa f k forms a factor with a level for each record where factor f has level n is used in a multivariate analysis on a multivariate set of covariates v to pair them with the variates is formally a copy of factor f with k extra levels This is used when fitting extended factor analytic models XFA Table 7 3 of order k 90 v 6 3 Fixed terms in the model 6 2 2 Examples ASReml code action yield mu variety yield mu variety r block yield mu time variety time variety livewt mu breed sex breed sex r sire fits a model with a constant and fixed variety effects fits a model with a constant term fixed variety effects and random block effects fits a saturated model with fixed time and variety main effects and time by va riety interaction effects fits a model with fixed breed sex and breed by sex interaction effects and ran dom sire effects 6 3 Fixed terms in the model 6 3 1 Primary fixed terms The fixed list in the model formula NIN Alliance Trial 1989 variety e describes the fixed covariates factors and interactions including special functions to be included in the table row 22 of Wald F statistics column 11 e generally begins with the reserved word mu which fits nin89 asd skip 1 a constant term mean or intercept see Table 6 1 mvinclude yield mu variety r repl f mv 12 11 column ARi 3 22 row AR1 3 91 6 4 Random terms in t
461. t and a sparse set The partition is at the r point unless explicitly set with the DENSE data line qualifier or mv is included before r see Table 5 5 The special term mv is always included in sparse Thus random and sparse terms are estimated using sparse matrix methods which result in faster processing The inverse coefficient matrix is fully formed for the terms in the dense set The inverse coefficient matrix is only partially formed for terms in the sparse set Typically the sparse set is large and sparse storage results in savings in memory and computing A consequence is that the variance matrix for estimates is only available for equations in the dense portion 6 10 2 Ordering of terms in ASReml The order in which estimates for the fixed and random effects in linear mixed model are reported will usually differ from the order the model terms are specified Solutions to the mixed model equations are obtained using the methods outlined Gilmour et al 1995 AS Reml orders the equations in the sparse part to maintain as much sparsity as it can during the solution After absorbing them it absorbs the model terms associated with the dense equations in the order specified 6 10 3 Aliassing and singularities A singularity is reported in ASReml when the diagonal element of the mixed model equations is effectively zero see the TOLERANCE qualifier during absorption It indicates there is either e no data for that fixed effect or e a li
462. t showing these components is FORMAT D 314 8X A6 3 2x F5 2 4x BZ 2011 and is suitable for reading 27 fields from 2 data records such as 111122223333xxxxxxxxALPHAFxx 4 12xx 5 32xx 6 32 xxxx123 567 901 345 7890 63 5 7 Data file qualifiers Table 5 2 Qualifiers relating to data input and output qualifier action IMERGE c f SKIP n IMATCH a b READ n RECODE IRREC n may be specified on a line following the datafile line The purpose is to combine data fields from the primary data file with data fields from a secondary file f This MERGE qualifier has been superseded by the much more powerful MERGE statement see Chapter 12 The effect is to open the named file skip n lines and then insert the columns from the new file into field positions starting at position c If IMATCH a b is specified ASReml checks that the field a 0 lt a lt c has the same value as field b If not it is assumed that the merged file has some missing records and missing values are inserted into the data record and the line from the MERGE file is kept for comparison with the next record It is assumed that the lines in the MERGE file are in the same order as the corresponding lines occur in the primary data file and that there are no extraneous lines in the MERGE file A much more powerful merging facility is provided by the MERGE directive described in Chapter 12 For example assuming the field definitions define 10
463. ta and validate the specification of the model e the iteration sequence of REML loglikelihood values to check convergence e asummary of the variance parameters The Gamma Sigma column reports the actual parameter fitted the Sigma column reports the gamma converted to a variance scale if appropriate Sigma SE is the ratio of the component relative to the square root of the diagonal element of the inverse of the average information matrix Warning Sigma SE should not be used for formal testing The shows the percentage change in the parameter at the last iteration use the pin file described Chapter 13 to calculate meaningful functions of the variance components e an table of Wald F statistics for testing fixed effects Section 6 11 The table contains the numerator degrees of freedom for the terms and incremental F statistics for approximate testing of effects It may also contain denominator degrees of freedon a conditional Wald F statistic and a significance probability e estimated effects their standard errors and t values for equations in the DENSE portion of the SSP matrix are reported if BRIEF 1 is invoked the T prev column tests difference between successive coefficients in the same factor The reported log likelihood value may be positive or negative and typically excludes some constants from its calculation It is sometimes reported relative to an offset when its magnitude exceeds 10000 any
464. ta to allow for a nugget effect 4 Two dimensional separable autoregressive spatial model with random replicate effects This is essentially a combination of 2b and 3c to demonstrate specifying an R structure and a G structure in the same model The vari ance header line 1 2 1 indicates that there is one R structure 1 that involves two vari ance models 2 and is therefore the direct product of two matrices and there is one G structure 1 The R structures are defined first so the next two lines are the R struc ture definition lines for e as in 3b The last two lines are the G structure definition lines for repl as in 2b In this case V ga PL Sel Oe Ll 115 NIN Alliance Trial 1989 variety A id row 22 column 11 nin89aug asd skip 1 yield mu variety r repl If mv t id 11 column AR1 0 3 22 row AR1 0 3 repl 1 repl 0 IDV 0 1 7 3 A sequence of structures for the NIN data Table 7 1 Sequence of variance structures for the NIN field trial data ASReml syntax extra random terms residual error term term G structure term R structure models models 1 2 1 2 2a 2b 3a 3b 3c yield mu variety repl error ID yield mu variety repl IDV error ID Ir repl yield mu variety repl IDV error ID z lr repl 001 repl 1 4 0 IDV 0 1 yield mu variety column row ID AR1 If mv 120 11 column 1D 22 row AR1 0 3 yield mu variety column row A
465. ted 6 possible outliers in section 1 see res file Finished 11 Apr 2008 15 58 45 843 LogL Converged 251 outliers parameter estimates testing fixed effects 15 4 An example 15 4 An example This is the command file for a simple RCB analysis of the NIN variety trial data in the first part However this file contains eight common mistakes in coding ASReml We also show two common mistakes associated with spatial analyses in the second part The er rors are highlighted and the numbers indicate the order in which they are detected Each er ror is discussed with reference to the output written to the asr file Briefly the errors are 1 there is no file nine asd in the working folder 2 unrecognised qualifier should be SKIP 3 incorrectly defined factor A required be cause factor is alphanumeric 4 comma missing from first line of model in dicating model is incomplete 5 misspelt variable label in linear model Repl should be rep1 nin alliance trial variety 56 3 id pid raw repl 4 nloc yield lat long row 22 column 11 nine asd slip 1 dopart 1 1 amp 2 Ipart 1 yield mu variety 4 Ir Repl 5 001 Repl 1 6 2 0 IDV 0 1 7 Ipart 2 yield mu variety 9 1 2 11 row AR1 1 10 22 col ARI 1 part predict voriety 8 6 misspelt variable label in G structure header line Repl should be rep1 7 wrong levels declared in G str
466. ted early generation variety trial Wheat effects check replicated and unreplicated lines as random We present three further spatial models for comparison The ASReml input file is Tullibigeal trial linenum yield weed column 10 row 67 variety 532 testlines 1 525 check lines 526 532 wheat asd skip 1 DOPATH 1 PATH 1 ARI x I y mu weed mv r variety 12 67 row AR1 0 1 10 column I 0 IPATH 2 AR1 x AR1 y mu weed mv r variety 12 67 row AR1 0 1 10 column AR1 0 1 PATH 3 AR1 x AR1 column trend y mu weed pol column 1 mv r variety a 67 row AR1 0 1 10 column AR1 0 1 PATH 4 AR1 x AR1 Nugget column trend y mu weed pol column 1 mv r variety units 12 67 row AR1 0 1 10 column AR1 0 1 predict var The data fields represent the factors variety row and column a covariate weed and the plot yield yield There are three paths in the ASReml file We begin with the one dimensional spatial model which assumes the variance model for the plot effects within columns is described by a first order autoregressive process The abbreviated output file is 1 LogL 4280 75 S2 0 12850E 06 666 df 0 1000 1 000 0 1000 2 LogL 4268 57 S2 0 12138E 06 666 df 0 1516 1 000 0 1798 3 LogL 4255 89 S2 0 10968E 06 666 df 0 2977 1 000 0 2980 4 LogL 4243 76 S2 88033 666 df 0 7398 1 000 0 4939 5 LogL 4240 59 S2 84420 666 df 0 9125 1 000 0 6016 6 LogL 4240 01 S2 85617 666 df 0 9344 1 000 0 6428 7 LogL
467. ted with u and the variance component g associated with e Mapping this equation back to 2 3 we have O 0 G o 02I 0 g and R o 07In 2 1 2 Partitioning the fixed and random model terms Typically 7 and u are composed of several model terms that is 7 can be partitioned as T r TI and u can be partitioned as u u u with X and Z partitioned conformably as X X X and Z Z Zal 1 2 1 3 G structure for the random model terms T For u partitioned as u u u we impose a direct sum structure on the matrix G written G 0 0 0 0 G 0 0 Gseeeis En 0 0 Gya 0 0 Oo 0 Gy where 6 is the direct sum operator each G is of size q and q J qi The default assumption is that each random model term generates one component of this direct sum then b b and var u G for i 1 b This means that the random effects from any two distinct model terms are uncorrelated However in some models one component of G may apply across several model terms for example in random coefficient regression where the random intercepts and slopes for subjects are correlated To accommo date these cases one component of G may apply across several model terms then b lt b Example 2 2 Variance components mixed models Building example 2 1 to a linear mixed model with more than one b gt 1 random effect typically known as a variance components mixed model the random effects w in
468. ter the first letter is sufficient to identify the term e interactions can involve model functions 6 5 2 Expansions e is ignored e makes sure the following term is defined but does not include it in the model e indicates factorial expansion up to 5 way a b is expanded to a b a b a b c d is expanded to abcda ba ca db c b d c d a b c a b d a c d b c d a b c d indicates nested expansion a b is expanded to a a b a b c d e is expanded to a b a c a d e This syntax is detected by the string and the closing parenthesis must occur on the same line and before any comma indicating continuation Any number of terms may be enclosed Each may have prepended to suppress it from the model Each enclosed term may have initial values and qualifiers following For example yield site site lin row r variety at site 1 row 3 col 2 expands to yield site site lin row r site variety at site 1 row 3 at site 1 col 2 93 6 5 Interactions and conditional factors 6 5 3 Conditional factors A conditional factor is a factor that is present only when another factor has a particular level e individual components are specified using the at f n function see Table 6 2 for exam ple at site 1 row will fit row as a factor only for site 1 e acomplete set of conditional terms are specified by omitting the level specification in the at f function provided the correct number of levels of fis specified i
469. the GIV file 9 6 3 The example continued Below is an extension of harvey as to use harvey giv which is partly shown to the right This G inverse matrix is an identity matrix of order 74 scaled by 0 5 that is 0 51 This model is simply an example which is easy to verify Note that harvey giv is specified on the line immediately preceding harvey dat command file giv file GIV file example 01 01 5 animal P 02 02 5 sire P 03 03 5 dam 04 04 5 lines 2 05 05 5 damage adailygain harvey ped ALPHA harvey giv giv structure file TA T2 ae harvey dat Ta 73 5 adailygain mu line r giv sire 1 25 74 74 5 Model term specification associating the harvey giv structure to the coding of sire takes precedence over the relationship matrix structure implied by the P qualifier for sire In this case the P is being used to amalgamate animals and sires into a single list and the giv matrix must agree with the list order 9 7 The reduced animal model RAM The reduced animal model was devised to reduce the computation involved in fitting a large animal model When there is at most one record per individual a large proportion of the individuals are non parents and have no progeny and there is interest in predictions for parents alone This can happen in large forestry trials The reduced animal model expresses the non parent genetic effect in terms of parent effects and a Mendelian sampling term that is combined wit
470. the prediction is required can be specified separately for X and Y using two PVAL statements Normally predict points will be defined for all combinations of X and Y values This qualifier is required with optional argument 1 to specify the lists are to be taken in parallel The lists must be the same length if to be taken in parallel Be aware that adding two dimensional prediction points is likely to sub stantially slow iterations because the variance structure is dense and becomes larger For this reason ASReml will ignore the extra PVAL points unless either FINAL or GKRIGE are set to save processing time The GROUPFACTOR qualifier like SUBSET must appear on a line by itself after the data line and before the model line Its purpose is to define a factor t by merging levels of an existing factor v The syntax is GROUPFACTOR lt Group_factor gt lt Exist_factor gt lt new codes gt for example IGROUPFACTOR Year YearLoc 1112233344 forms a new factor Year with 4 levels from the existing factor YearLoc with 10 levels Alternatively Year could be formed by data transformation Year YearLoc set 111223334 4 L 2001 2002 2003 2004 70 5 8 Job control qualifiers Table 5 4 List of occasionally used job control qualifiers qualifier action IDLIMIT v JOIN IMBF mbf v n f FACTOR FIELD s IKEY k NOKEY IRENAME t RFIELD r ISKIP k I SPARSE is used with SECTION ROWFAC COLFAC
471. the yield data for the missing plots have all been made NA one of the missing value indicators in ASReml and variety has been arbitrarily coded LANCER for all of the missing plots any of the variety names could have been used f mv is now included in the model specification This tells ASReml to estimate themissing values The f before mv indicates that the missing values are fixed effects in the sparse set of terms 113 7 3 A sequence of structures for the NIN data e unlike the case with G structures ASReml automatically includes and estimates a scale parameter for R structures 0 for V o I X p in this case This is why the variance models specified for row AR1 and column ID are correlation models The user could specify a non correlation model diagonal elements 4 1 in the R structure definition for example ID could be replaced by IDV to represent V 0 0 1 6 X p However IDV would then need to be followed by S2 1 to fix o at 1 and prevent ASReml trying unsuccessfully to estimate both parameters as they are confounded the scale parameter associated with IDV and the implicit error variance parameter see Section 2 1 under Combining variance models Specifically the code 11 column IDV 48 S2 would be required in this case where 48 is the starting value for the variances This complexity allows for heterogeneous error variance 3b Two dimensional separable autoregressive spatial model This
472. these two processes have been linked as an addi tional meaning for the ATLOADING n qualifier When fitting k factors with N gt k the first k 1 loadings are held fixed no rotation for the first k iterations Then for iterations k 1 to n loadings vectors are updated in pairs and rotated If AILOADING is not set by the user and the model is an upgrade from a lower order XFA AILOADING is set to 4 It is not unusual for users to have trouble comprehending and fitting extended factor analytic models especially with more than two factors Two examples are developed in a separate document available on request 7 5 6 Notes on OWN models The OWN variance structure is a facility whereby users may specify their own variance struc ture This facility requires the user to supply a program MYOWNGDG that reads the current set of parameters forms the G matrix and a full set of derivative matrices and writes these to disk Before each iteration ASReml writes the OWN parameters to a file runs MYOWNGDG which it presumes forms the G and derivative matrix and then reads the matrices back in An example of MYOWNGDG 90 is distributed with ASReml It duplicates the AR1 and AR2 134 7 5 Variance model description structures The following job fits an AR2 structure using this program Example of using the OWN structure rep blcol blrow variety 25 yield barley asd skip 1 OWN MYOWN EXE y variety 1 2 10 0 AR1 al 15 0 OWN2
473. thout the overheads of other systems This guide has 16 chapters Chapter 1 introduces ASReml and describes the conventions used in this guide Chapter 2 outlines some basic theory while Chapter 3 presents an overview of the syntax of ASReml through a simple example Data file preparation is described in Chapter 4 and Chapter 5 describes how to input data into ASReml Chapters 6 and 7 are key chapters which present the syntax for specifying the linear model and the variance models for the random effects in the linear mixed model Chapters 8 and 9 describe special commands for multivariate and genetic analyses respectively Chapter 10 deals with prediction of linear functions of fixed and random effects in the linear mixed model Chapter 11 demonstrates running an ASReml job Chapter 12 describes the merging of data files and Chapter 13 presents the syntax for forming functions of variance components Chapter 14 gives a detailed explanation of the output files Chapter 15 gives an overview of the error messages generated in ASReml and some guidance as to their probable cause The guide concludes with the most extensive chapter which presents the analysis of a range of data examples In brief the improvements in Release 4 include developments associated with input include generating initial values generating a template to allow an alternative way of presenting parametric information associated with variance structures new facilities for reading in data
474. tion Criterion 65517 84 Model_Term Gamma Sigma Sigma SE C rep iblk IDV_V 640 0 307856 2370 52 13 00 OP grm1 Clone GRM_V 923 0 275656 2122 58 5 82 OP Clone IDV_V 926 0 152554 1174 68 6 08 OP Residual SCA_V 6399 1 000000 7700 10 49 64 OP Wald F statistics Source of Variation NumDF F inc 20 mu 1 0 11E 06 12 culture 1 2615 96 21 culture rep 6 30 44 23 rep iblk 640 effects fitted 22 grm1i Clone 923 effects fitted 4 Clone 926 effects fitted 66 are zero 78 possible outliers see res file Notes e of 926 clones identified 860 have data and 923 have genomic data e The res file contains additional details about the analysis including a listing of the 175 9 8 Factor effects with large Random Regression models larger marker effects All marker effects are reported in the mef file e Particular columns of the grr data can be included in the model using the grr Factor i model term where and i specifies which number regressor variable to include Listing of the larger marker effects 368 0 12761 01 121 1 40736 0 00000 617 0 14383 01 111 1 26081 0 00000 777 0 15417 01 138 1 25597 0 00000 1246 0 18644 02 210 1 22522 0 00000 1903 0 6963 01 202 1 24800 0 00000 2102 0 8683 02 432 1 15496 0 00000 2445 2 1563 02 244 1 35181 0 00000 2497 2 2167 01 413 1 21339 0 00000 3180 2 8668 03 42 1 21629 0 00000 3521 CL1577Contig1 03 1 15833 0 00000 3802 CL2573Contig1 03 1 17005 0 00000 4195 CL595Contigi O1 1 19330 0 0000
475. tions In each run ASReml writes the initial values of the variance parameters to a file with extension tsv template start values with information to identify individual variance parameters After each iteration ASReml writes the current values of the variance parameters to files with extension rsv re start values and msv the msv version has information to clearly identify each vari ance parameter If f is not set then ASReml looks for a rsv file with the same name used for the output files ie the as name possibly appended by arguments ASReml then scans this file for parameter values related to the current model replacing the values obtained from the as file be fore iteration resumes If CONTINUE 2 or TSV is used then the tsv file is used instead of the rsv file Similarly if CONTINUE 3 or MSV are used then the msv file is used instead of the rsv file If f filename with no extension is used with CONTINUE TSV or MSV ASReml will use the file f rsv f tsv or f msv If f filename xsv with x r t or m is used with CONTINUE TSV or MSV ASReml will use the file f xsv If the specified file is not present ASReml reverts to reading the previous rsv file Some users may prefer rather than specifying initial values in the model formulation to generate a default tsv file using MAXIT O and then edit the tsv file with more appropriate values If the model has changed and CONTINUE is used ASReml will pick up the value
476. tions with the appropriate combination of random effects and e n x 1 is the vector of residual errors 2 1 1 Sigma parameterization of the linear mixed model Model 2 1 is called a linear mixed model or linear mixed effects model It is assumed lo a asal where the matrices G and R are variance matrices for u and e and are functions of pa rameters og and o This requires that the random effects u and residual errors e are uncorrelated The variance matrix for y is then of the form var y ZG o Z R 0 2 3 which we will refer to as the sigma parameterization of the G and R variance structures and the individual variance structure parameters in cr and will be referred to as sigmas The variance models given by G and R are referred to as G structures and R structures respectively We illustrate these concepts using the simplest linear mixed model that is the one way classification Example 2 1 A simple example Consider a one way classification comprising a single ran dom effect u and a residual error term e The two random components of this model 5 2 1 The general linear mixed model namely u and e are each assumed to be independent and identically distributed IID and to follow a normal distribution such that u N 0 02I and e N 0 02J Hence the variance of y has the form var y ZZ I 2 4 This model has two variance structure parameters or sigmas the variance component g associa
477. tionship matrix for the dam dimension since dam is defined with P In this case it makes no difference since there is no pedigree information on dams It is preferable to be explicit specify dam 0 AINV when the relationship matrix is required and otherwise use ide dam in the model specification and ide dam O ID in the G structure definition In this case PATHS 1 2 and 3 were run in turn but in PATH 3 ASReml had trouble converging because in each iteration the unstructured us tag matrix is not positive definite and so ASReml uses a slower EM algorithm that keeps the estimates in the parameter space but the convergence is very slow Here is the convergence log for PATH 3 Warning US matrix is not positive definite Modified Notice US matrix updates modified 1 time s to keep them positive definite Notice 15358 singularities detected in design matrix 1 LogL 1543 55 52 1 00000 18085 df 15 components restrained Notice US matrix updates modified 1 time s to keep them positive definite 2 LogL 1540 93 S2 1 00000 18085 df 15 components restra 38 LogL 1538 34 52 1 00000 18085 df 15 components restrained 39 LogL 1538 33 52 1 00000 18085 df 14 components restrained 40 LogL 1538 32 S2 1 00000 18085 df 15 components restrain To avoid this problem in PATH 4 and PATH 5 we use xfa2 and xfa3 structures These converge much faster Here is the convergence log and resulting estimates for PATH 5 Notice ReStartValues taken from pcoop
478. tistics testing fixed effects Source of Variation NumDF DenDF F ine Prob 12 mu 1 25 0 331 85 lt 001 1 variety 55 110 8 2 22 lt 001 Notice The DenDF values are calculated ignoring fixed boundary singular variance parameters using algebraic derivatives 13 mv_estimates 18 effects fitted 6 possible outliers in section 1 see res file Finished 10 Apr 2008 16 47 47 765 LogL Converged Following is a table of Wald F statistics augmented with a portion of Regression Screen output The qualifier was SCREEN 3 SMX 3 Mode1 Term Sigma Sigma Sigma SE C idsize 92 92 0 581102 0 136683 3 31 OP expt idsize 828 828 0 121231 0 285153E 01 1 12 OP Variance 504 438 1 00000 0 235214 12 70 OP Wald F statistics Source of Variation NumDF DenDF_con F_inc F_con M P_con 113 mu pl 72 4 65452 25 56223 68 lt 001 2 expt 6 3 5 6 27 0 64 A 0 695 4 type 4 63 8 22 95 3 01 A 0 024 114 expt type 10 PRES 1 31 0 93 B 0 508 23 x20 i 55 41 4 33 2 37 B 0 130 24 x21 il 63 3 1 91 0 87 B 0 355 25 x23 il 68 3 293 93 0 11 B 0 745 26 x39 il Su 1 85 0 35 B 0 556 27 x48 ak 69 9 1 58 2 08 B 0 154 28 x59 i 49 7 1 41 0 08 B 0 779 29 x60 i 59 6 1 46 0 42 B 0 518 30 x61 I 64 0 1 11 0 04 B 0 838 ai x62 1 61 8 2 18 0 09 B 0 770 32 x64 1 55 6 31 48 4 50 B 0 038 33 X65 1 57 8 4 72 6 12 B 0 016 34 x66 1 58 5 isis 0 03 B 0 872 35 X70 il 59 3 Lord 1 40 B 0 242 36 XT1 il 64 4 0 08 0 01 B 0 929 37 X73 1 59 0 Lye 3 01 B 0 088 38 x75 1 59 9 0 04 0 26 B 0 613 39 x91 1 63
479. tivariate analysis T YED 0 0 60 30 0 EL 88 60 4 379 8 FDIAM Variate 0 O 15 90 22 29 30 60 2 190 9 Trait 2 10 Trait YEAR 6 9 Trait 2 5 YEAR 7 3 11 Trait TEAM TO 9 Trait f 2 4 TEAM 35 12 Trait TAG 1042 9 Trait i 2 1 TAG 2 521 1485 identity 2 UnStructure 9 11 0 2000 0 2000 0 4000 2970 records assumed pre sorted 2 within 1485 Trait TEAM variance structure is 2 UnStructure 12 14 0 4000 0 3000 1 3000 35 identity Structure for Trait TEAM has 70 levels defined Trait TAG variance structure is 2 UnStructure 15 17 0 2000 0 2000 2 0000 521 identity Structure for Trait TAG has 1042 levels defined Forming 1120 equations 8 dense Initial updates will be shrunk by factor 0 316 Notice Algebraic Denominator DF calculation is not available Numerical derivatives will be used Notice 2 singularities detected in design matrix 1 LogL 886 521 s2 1 0000 2964 df 2 LogL 818 508 s2 1 0000 2964 df 3 LogL 755 911 s2 1 0000 2964 df 4 LogL 725 374 s2 1 0000 2964 df 5 LogL 723 475 s2 1 0000 2964 df 6 LogL 723 462 s2 1 0000 2964 df 7 LogL 723 462 s2 1 0000 2964 df 8 LogL 723 462 s2 1 0000 2964 df Results from analysis of GFW FDIAM Model_Term Sigma Sigma Sigma SE C Residual UnStructured 1 1 0 198351 0 198351 21 94 OU Residual UnStructured 2 1 0 128890 0 128890 12 40 OU Residual UnStructured 2 2 0 440601 0 440601 21 93 OU Trait TEAM UnStructured 1 1 0 374493 0 374493 3 89 0U Trait TEAM UnStructure
480. tivariate analysis are ASUV and ASMV t see Table 5 4 for detail to use an error structure other than US for the residual stratum you must also specify ASUV see Table 5 4 and include mv in the model if there are missing values to perform a multivariate analysis when the data have already been expanded use ASMV t see Table 5 4 tis the number of traits that ASReml should expect the data file must have t records for each multivariate record although some may be coded missing 8 4 The output for a multivariate analysis Below is the output returned in the asr file for this analysis ASReml 3 01d 01 Apr 2008 Orange Wether Trial 1984 88 Build e 01 Apr 2008 32 bit 08 Apr 2008 11 46 33 968 32 Mbyte Windows wether Licensed to NSW Primary Industries permanent FEA III A ICICI I I I IKK k k 21 21 21 kkk kk kk kK K K K Contact support asreml co uk for licensing and support arthur gilmour dpi nsw gov au FECA AAO KKK ARG Folder C data asr3 ug3 manex TAG II BloodLine I QUALIFIERS SKIP 1 Reading wether dat FREE FORMAT skipping 1 lines Bivariate analysis of GFW and FDIAM Summary of 1485 records retained of 1485 read Model term Size miss zero MinNonO Mean MaxNonO StndDevn 1 TAG 21 0 0 1 261 0956 521 2 TRIAL 0 O 3 000 3 000 3 000 0 000 3 BloodLine 27 0 0 1 13 4323 27 4 TEAM 35 0 0 pl 18 0067 35 5 YEAR 3 0 0 1 2 0391 3 6 GFW Variate 0 O 4 100 7 478 11 20 1 050 156 8 4 The output for a mul
481. tor k n an integer number 86 6 2 Specifying model formulae in ASReml r areal number t a model term label includes data variables v y the label of a data variable Parsing of model terms in ASReml is not very sophisticated Where a model term takes an other model term as an argument the argument may need to be be predefined If necessary include the argument in the model line with a leading which will cause the term to be defined but not fitted For example Trait male Trait female and Trait female 87 6 2 Specifying model formulae in ASReml Table 6 1 Summary of reserved words operators and functions model brief description common usage term fixed random reserved mu the constant term or intercept J terms mv a term to estimate missing values lt Trait multivariate counterpart to mu J units forms a factor with a level for each experimental J unit operators Or placed between labels to specify an interaction J J forms nested expansion Section 6 5 y y forms factorial expansion Section 6 5 y J placed before model terms to exclude them from y J the model A placed at the end of a line to indicate that the model specification continues on the next line treated as a space J J I placed around some model terms when it is impor J 1 tant the terms not be reordered Section 6 4 commonly at f n condition on level n of factor f J J used n may be a l
482. treated as a normal variate no syntax is provided for specifying GLM attributes for it The ASUV qualifier is required in this situation for the GLM weights to be utilized 103 6 8 Generalized Linear Mixed Models 6 8 1 Generalized Linear Mixed Models This section was written by Damian Collins A Generalized Linear Mixed Model GLMM is an extension of a GLM to include random terms in the linear predictor Inference concerning GLMMs is impeded by the lack of a closed form expression for the likelihood ASReml currently uses an approximate likelihood technique called penalized quasi likelihood or PQL Breslow and Clayton 1993 which is based on a first order Taylor series approximation This technique is also known as Schalls technique Schall 1991 pseudo likelihood Wolfinger and OConnell 1993 and joint maximisation Harville and Mee 1984 Gilmour et al 1985 Implementations of PQL are found in many statistical packages for instance in the GLMM Welham 2005 and the IRREML procedures of Genstat Keen 1994 the MLwiN package Goldstein et al 1998 the GLMMIX macro in SAS Wolfinger 1994 and in the GLMMPQL function in R The PQL technique is well known to suffer from estimation biases for some types of GLMMs For grouped binary data with small group sizes estimation biases can be over 50 e g Bres low and Lin 1995 Goldstein and Rasbash 1996 Rodriguez and Goldman 2001 Wadding ton et al 1994 For other GL
483. trols form of the tab file TABFORM 1 is TAB separated tab becomes _tab txt TABFORM 2 is COMMA separated tab becomes _tab csv TABFORM 3 is Ampersand separated tab becomes _tab tex See TXTFORM for more detail sets the default argument for PVSFORM SLNFORM TABFORM and YHTFORM if these are not explicitly set TXTFORM or TXTFORM 1 re places multiple spaces with TAB and changes the file extension to say sln txt This makes it easier to load the solutions into Excel TXTFORM 2 replaces multiple spaces with COMMA and changes the file extension to say _sln csv However since factor labels sometimes con tain COMMAS this form is not so convenient TXTFORM 3 replaces multiple spaces with Ampersand appends a double backslash to each line and changes the file extension to say _sln tex Latex style Additional significant digits are reported with these formats Omitting the qualifier means the standard fixed field format is used For yht and sln files setting n to 1 means the file is not formed modifies the appearance of the variogram calculated from the residuals obtained when the sampling coordinates of the spatial process are defined on a lattice The default form is based on absolute distance in each direction This form distinguishes same sign and different sign distances and plots the variances separately as two layers in the same figure specifies that n constraints are to be applied to the variance par
484. ts from within the job If the first line of the as file contains a qualifier other than DOPATH it is interpreted as setting command line options and the Title is taken as the next line The option string actually used by ASReml is the combination of what is on the command line and what is on the job control line with options set in both places taking arguments from the command line Arguments on the top job control line are ignored if there are arguments on the command line This section defines the options Arguments are discussed in detail in a following section Command line options are not case sensitive and are combined in a single string preceded by a minus sign for example LNW128 The options can be set on the command line or on the first line of the job either as a concatenated string in the same format as for the command line or as a list of qualifiers For example the command line ASReml h22r jobname 1 2 3 could be replaced with ASReml jobname if the first line of jobname as was either l h2Z2r 1 2 3 or IHARDCOPY EPS RENAME ARGS 1 2 3 Table 11 1 presents the command line options available in ASReml with brief descriptions It also specifies the equivalent qualifier name used on the top job control line Detailed descriptions follow 197 11 3 Command line options Table 11 1 Command line options option qualifier type action Frequently used command line options C N Ww Other comma
485. ts under the same model The value of y is appended to the basename so that output files are not overwritten when the next trait is analysed 11 3 6 Workspace command line options S W The workspace requirements depend on problem size and may be quite large An initial workspace allocation may be requested on the command line with the S or W options if neither is specified 32Mbyte 4 million double precision words is allocated Wm WORKSPACE m sets the initial size of the workspace in Mbytes For example W1600 requests 1600 Mbytes of workspace the maximum typically available under Windows W2000 is the maximum available on 32bit Unix Linux systems On 64bit systems the argument if less than 32 is taken as Gbyte Alternatively Ss can be used to set the initial workspace allocation s is a digit The workspace allocated is 2 x 8 Mbyte S3 is 64Mb S4 is 128Mb S5 is 256Mb S6 is 512Mb S7 is 1024Mb S8 is 2048Mb S9 is 4096Mb This option was in Release 1 0 the more flexible option Wm has been introduced in Release 2 0 The W option is ignored if the S option is also specified Otherwise additional workspace may be requested with the Ss or Wm options or the WORKSPACE m qualifier on the top job control line if not specified on the command line If your system cannot provide the requested workspace the request will be diminished until it can be satis fied On multi user systems do not unnecessarily request the maximum or other u
486. tter in the structure are treated as the same parameter e 1 9 are different from a z which are different from A Z so that 61 equalities can be specified 0 and mean unconstrained A colon generates a sequence viz a e is the same as abcde e Putting as the first character in s makes the interpretation of codes absolute so that they apply across structures e Putting as the first character in s indicates that numbers are repeat counts A Z are equality codes only represents unconstrained and a z is not distinquised from A Z giving only 26 equalities Thus 3A2 is equivalent to OAAA00 or 0aaa00 This syntax is limited in that it cannot apply constraints to simple variance components random terms which do not have an explicit variance structure or to residual variance parameters The VCC syntax is required for these cases Examples are presented in Table 7 5 141 7 9 Constraining variance parameters 7 9 2 Simple relationships among variance structure parameters It is possible to define simple equality relationships between variance structure parameters using the s qualifier see Section 7 9 4 and Table 7 4 More general relationships between variance structure parameters can be defined by placing the VCC c qualifier on the data file definition line Unlike the case of parameter equality all parameters can be accessed and the linear relationship is not limited to equality However identification of the param
487. ty r repl the variance header line may be omitted if the default IID R structure is required no G structures are being explicitly defined 1f my and there are no parameter constraints see 1 2 1 VCC and examples 1 and 2a 22 row AR1 0 3 11 column AR1 0 3 repl i sis used to code the number of independent epl 0 IDV 0 1 sections in the error term if s 0 the default IID R structure is assumed and no R structure definition lines are required as in examples 2b and 5 if s gt 0 s R structure definitions are required one for each of the s sections as in examples 3a 3b 3c and 4 for the analysis of multi section data s can be replaced by the name of a factor with the appropriate number of levels one for each section c is the number of component variance models involved in the variance structure for the error term for each section for example 3a 3b and 3c have column row as the error term and the variance structure for column row involves 2 variance models the first for column and the second for row Chas a default value of 2 when sis not specified as zero e gis the number of variance structures G structures that will be explicitly specified for the random terms in the model R and G structures are now discussed with reference to s c and g As already noted each variance structure may involve several variance models which relate to the individual terms involved in the random effect or
488. ucture model line Rep1 has 4 levels 8 misspelt variable label in predict statement voriety should be variety 9 mv omitted from spatial model 10 wrong levels declared in R structure model lines 252 15 4 An example 1 Data file not found Running this job produces the asr file in qin alliance trial Section 15 1 The first problem is that AS Reml cannot find the data file nine asd in nine asd Islip 1 the current working folder as indicated in the yield mu variety error message above the Fault line ASReml reports the last line read before the job was terminated an error message Error parsing nine asd SLIP 1 and other information obtained to that point In this case the program only made it to the data file definition line in the command file Since nine asd commences in column 1 AS Reml checks for a file of this name in the working directory since no path is supplied Since ASReml did not find the data file it tried to interpret the line as a variable definition but is not permitted in a variable label The problem is either that the filename is misspelt or a pathname is required In this case the data file was given as nine asd rather than nin asd 2 An unrecognised qualifier and 3 An incorrectly defined factor After supplying the correct pathname and re running the job ASReml produces the warning message WARNING Unrecognised qualifier at character 9 slip 1 followed by the fau
489. ular you would leave the field as a covariate and use the fac function to derive a factor version forms the natural log of v r This may also be used to transform the response variable creates a first differenced by rows design matrix which when defining a random effect is equivalent to fitting a moving average variance structure in one dimension In the mat form the first difference operator is coded across all data points assuming they are in time space order Otherwise the coding is based on the codes in the field indicated is a term that is predefined by using the MBF qualifier see page 71 96 6 6 Alphabetic list of model functions Table 6 2 Alphabetic list of model functions and descriptions model function action mu mv out n out n t pol v n p v n pow x p o1 is used to fit the intercept constant term It is normally present and listed first in the model It should be present in the model if there are no other fixed factors or if all fixed terms are covariates or contrasts except in the special case of regression through the origin is used to estimate missing values in the response variable Formally this creates a model term with a column for each missing value Each column contains zeros except for a solitary 1 in the record containing the corresponding missing value This is used in spatial analyses so that computing advantages arising from a balanced spatial layout can be e
490. uld be aware of as it may affect the interpretation of results They are not in themselves errors in that the syntax is valid but they may reflect errors in the sense that the user may have intended something different Messages beginning with the word Warning highlight information that the user should check Again it may reflect an error if the user has intended something different Messages beginning with the word Error indicate that something is inconsistent as far as ASReml is concerned It may be a coding error that the user can fix easily or a processing error which will generally be harder to diagnose Often the error reported is a symptom of something else being wrong 261 15 5 Information Warning and Error messages Table 15 2 List of warning messages and likely meaning s warning message likely meaning Notice ASReml has merged design points closer than Warning e missing values generated by transformation Warning i singularities in AT matrix Warning m variance structures were modified Warning n missing values were detected in the design Warning n negative weights Warning r records were read from multiple lines WARNING term has more levels than expected Warning term in the predict IGNORE list Warning term in the predict IUSE list Warning term is ignored for prediction Warning Check if you need the RECODE qualifier Warning Code B fixed at a b
491. ure Factor mismatch Last line read was 20 IDV0 100000 ninerr7 variety id pid raw rep nloc yield lat Model specification TERM LEVELS GAMMAS variety 56 mu 1 repl 4 0 100 3 SECTIONS 224 4 i TYPE 0 0 1002 STRUCT 224 0 0 0 0 0 0 2 1 0 5 0 1 0 12 factors defined max 500 5 variance parameters max1500 2 special structures Final parameter values 0 10000 1 0000 0 10000 Last line read was 20 IDV 0 100000 Finished 11 Apr 2008 16 21 52 609 Structure Factor mismatch 8 A misspelt factor name in the predict statement The final error in the job is that a factor name is misspelt in the predict statement This is a non fatal error The asr file contains the messages Notice Invalid argument unrecognised qualifier or vector space exhausted at voriety i Warning Extra lines on the end of the input file are ignored from predict voriety The faulty statement is otherwise ignored by ASReml and no pvs file is produced To rectify this statement correct voriety to variety 9 Forgetting mv in a spatial analysis The first error message from running part 2 of the job is 258 15 4 An example R structures imply 0 242 records only 224 exist Checking the seventh line of the output below we see that there were 242 records read but only 224 were retained for analysis There are three reasons records are dropped 1 the FILTER qualifier has been specified 2 the D transformation qualifier has been specified and 3
492. values for variate j j c for control and j t for treated T corresponds to a constant term and u and u correspond to random variety and run effects The design matrices are the same for both traits The random effects and error are assumed to be independent Gaussian variables with zero means and variance structures var u op 1 4a Var u o 1 66 and var e 071132 The bivariate model can be written as a direct extension of 16 9 namely y 1 X 7T 4 Ie Z uy I 6 Z u e 16 10 where y Y yf Uy ul ul ur ul ul and e el ef There is an equivalence between the effects in this bivariate model and the univariate model of 16 7 The variety effects for each trait u in the bivariate model are partitioned in 16 7 into variety main effects and tmt variety interactions so that u 12 Q uy u2 There is a similar partitioning for the run effects and the errors see table 16 9 In addition to the assumptions in the models for individual traits 16 9 the bivariate analysis involves the assumptions cov Uy Ul 0 144 COV Ur UL FreL6e and cov e e Oct1 132 Thus random effects and errors are correlated between traits So for example the variance matrix for the variety effects for each trait is given by 2 a var Uy te Ce eo T Over Ou 305 16 8 Paired Case Control study Rice Table 16 9 Equivalence of random effects in bivariate and univari
493. values in V98 to zero The second line sets the focus to variable 99 copies YB into V99 and changes any missing values in V99 to zero It then adds V98 and discards the whole record if the result is zero i e both YA and YB have missing values for that record Variables 98 and 99 are not labelled and so are not retained for subsequent use in analysis 60 5 6 Datafile line 5 5 4 Special note on covariates Covariates are variates that appear as independent variables in the model It is recommended that covariates be centred and scaled to have a mean near zero and a variance of about one to avoid failure to detect singularities This can be achieved either e externally to ASReml in data file preparation e using RESCALE mean scale where mean and scale are user supplied values for example age rescale 140 142857 in weeks 5 6 Datafile line The purpose of the datafile line is to NIN Alliance Trial 1989 variety A e nominate the data file e specify qualifiers to modify row 22 the reading of the data column 11 the output produced nin89aug asd skip 1 the operation of ASReml yield mu variety 5 6 1 Data line syntax The datafile line appears in the ASReml command file in the form datafile qualifiers e datafile is the path name of the file that contains the variates factors covariates traits response variates and weight variables represented as data fields see Chapter 4 enclose the
494. vel will generate a singularity but in the first coefficient rather than in the coefficient corresponding to the missing treatment In this case the coefficients will not be readily interpretable When interacting constrained factors all cells in the cross tabulation should have data fac u fac v forms a factor with a level for each value of x and any additional points fac u y inserted as discussed with the qualifiers PPOINTS and PVAL fac v y forms a factor with a level for each combination of values from v and y The values are reported in the res file 95 6 6 Alphabetic list of model functions Table 6 2 Alphabetic list of model functions and descriptions model function action giv f n g f n grm f n h f ide f i f inv v r leg v n lin f 1 f log v r mal mal f mbf f c mbf f associates the nth giv G inverse with the factor This is used when there is a known except for scale G structure other than the additive inverse genetic relationship matrix The G inverse is supplied in a file whose name has the file extension giv described in Section 9 6 grm and giv are formally equivalent with grm standing for generalized relationship Matrix h f requests ASReml to fit the model term for factor f using Helmert constraints Neither Sum to zero nor Helmert constraints generate interpretable effects if singu larities occur ASReml runs more efficiently if no co
495. w to construct the trial means including the appropriate region and location effects and which trials means to then average to form the location table However for region means we have a choice We can average the trial means in Table 10 4 according to region obtaining region means of 11 83 and 11 33 or we can average the location means in Table 10 5 to get region means of 12 and 11 The former is the default in ASReml produced by predict region ASSOCIATE region location trial ASAVERAGE trial or equivalently by predict region ASSOCIATE region location trial Again this is base averaging By contrast predict region ASSOC region location trial ASAVE location trial or predict region ASSOC region location trial ASAVE location produces sequential averaging giving region means of 12 and 11 respectively Similarly an overall sequential mean of 11 5 is given by predict mu ASSOC region location trial ASAVE region location while predict mu ASSOC region location trial ASAVE region gives a value of 11 58 being the average of region means 11 83 and 11 33 obtained by averaging trials within regions from Table 10 4 and predict mu ASSOCIATE region location trial ASAVE location predicts mu as 11 38 the average of the 8 location means in Table 10 5 Further discussion of associated factors The user may specify their own weights using file input if necessary Thus predict region ASAVERAGE location 1 2 3 6 1 1 1 2 1 6
496. wes in 1981 and 12 Booroola by Romney rams from froup 3 over Perendale ewes in 1981 This data was analysed by Gilmour 1984 and Gilmour et al 1987 The data file LAMB DAT contains grouped data for the 68 combinations of Sex and Sire for two footshape classes FS1 all four feet are normal FS2 one foot is deformed and two indicator variables for the presence of disease conditions Scald and Rot No scald or rot was present in group 4 lambs and these responses have been set to missing The genetic relationships among sires are ignored in this analysis although it would just require a sire relationship matrix to include them Our first analysis is of the incidence of foot rot on the Normal scale as a weighted analysis to mimic analysis of the ungrouped data Using 56 of the 68 records ignoring Group 4 there are 1960 56 x 35 00 observations and so we use the DF 1904 1960 56 qualifier to get the correct residual degrees of freedom for this analysis of the proportion with footrot The YSS 62 54249 qualifier adds 62 54249 67 4 45751 to the Total Sum of Squares so that it includes the extra variation associated with the extra degrees of freedom There were 67 56 x 1 196 cases of foot rot so the Total uncorrected Sum of Squares for a binary variable should be 67 However the weighted sum of squares for the pRot values is only 4 45751 for example the first record contributes 1 39 1 39 x 39 instead of 1 0 4 45751 was discovered
497. where Gmm is the variance matrix for the measured traits corresponding to C in the example Gom is the genetic covariance matrix between the objective traits and the measured traits and a is the vector of economic values for the objective traits The results are given in a sli selection index file This directive should be placed after the model specification 194 11 Command file Running the job 11 1 Introduction The command line its options and arguments are discussed in this chapter Command line options enable more workspace to be accessed to run the job control some graphics output and control advanced processing options Command line arguments are substituted into the job at run time As Windows likes to hide the command line most command line options can be set on an optional initial line of the as file we call the top job control line to distinguish it from the other job control lines discussed in Chapter 6 If the first line of the as file contains a qualifier other than DOPATH it is interpreted as setting command line options and the Title is taken as the next line 11 2 The command line 11 2 1 Normal run The basic command to run ASReml is path ASRem1 basename as c e path provides the path to the ASReml program usually called asreml exe in a PC en vironment In a UNIX environment ASReml is usually run through a shell script called ASReml if the ASReml program is in the search path then path is n
498. whole matrix presented lower triangle rowwise with each row beginning on a new line e a sparse format file must be free format 1 1 1 with three numbers per line namely i s row column value E E defining the lower triangle row wise of the 5 5 1 0666667 matrix 6 5 0 2666667 6 6 1 0666667 7 7 1 0666667 e the file must be sorted column within row 8 7 0 2666667 8 8 1 0666667 e every diagonal element must be repre ae sented missing off diagonal elements are 10 10 1 0666667 assumed to be zero cells 11 11 1 0666667 12 11 0 2666667 e the file is used by associating it with a fac 12 12 1 0666667 tor in the model The number and order of the rows must agree with the size and order of the associated factor e the SKIP n qualifier tells ASReml to skip n header lines in the file The giv file presented in the code I 0 box gives the G inverse matrix on tige snag the right E 0 4 8 0267 1 067 The easiest way to ensure the variable is coded to match the order of the GRM file is to supply a list of level names in the variable definition For example genotype A L Gorder txt would code the variable genotype to agree with the order of level names present in the file Gorder txt which would be the order used in creating the GRM GIV matrix If the file has a grm file extension ASReml will invert the GRM matrix If it is not Positive Definite the job will abort unless an appropriate qualifier ND PSD or NSD is
499. written to the ass file if the SUM qualifier is specified It includes cell counts for factors histograms of variates and simple correlations among variates eigen analysis res file When ASReml reports a variance matrix to the asr file it res file also reports an eigen analysis of the matrix eigen values and eigen vectors to the res file elapsed time asr file this can be determined by comparing the start time with the asl file finishing time The execution times for parts of the Iteration process are writ ten to the as1 file if the DEBUG LOGFILE command line qual ifiers are invoked fixed and random sln file if BRIEF 1 is invoked the effects that were included in the effects dense portion of the solution are also printed in the asr file with their standard error a t statistic for testing that effect and a t statistic for testing it against the preceding effect in that factor heritability pvc file placed in the pvc file when postprocessing with a pin file histogram of resid res file and graphics file uals intermediate re asl file given if the DL command line option is used sults mean variance re res file for non spatial analyses ASReml prints the slope of the regres lationship sion of log abs residual against log predicted value This regression is expected to be near zero if the variance is independent of the mean A power of the mean data transfor mation might be indicated otherwise T
500. ws within columns in this case Important It is assumed that the joint indexing of the components uniquely defines the experimental units if field is a variable it can be plot coordinates provided the plots are in a regular grid Thus in this example 11 lat AR1 0 3 22 long AR1 0 3 is valid because lat gives column position and long gives row position and the positions are on a regular grid The autoregressive correlation values will still be on an plot index basis 1 2 3 not on a distance basis 10m 20m 30m if the data is sorted appropriately for the order the models are specified set field to O model specifies the variance model for the term for example 22 row AR1 0 3 chooses a first order autoregressive model for the row error process all the variance models available in ASReml are listed in Table 7 3 120 7 4 Variance structures these models have associated variance parameters a error variance component 0 for the example see Section 7 3 is automatically esti mated for each section the default model is ID initial_values are initial or starting values for the variance parameters and must be sup plied for example 22 row ARI 0 3 chooses an autoregressive model for the row error process see Table 7 1 with a starting value of 0 3 for the row correlation qualifiers tell ASReml to modify the variance model in some way the qualifiers are de scribed in Table 7 4 add
501. xF Lambda DenDF mu 1 1 245 1409 245 1409 1 0000 5 0000 variety 3 2 1 4853 1 4853 1 0000 10 0000 LinNitr 1 1 110 3282 110 3232 1 0000 45 0000 nitrogen 4 2 1 3669 1 3669 1 0000 45 0000 variety LinNitr 2 2 0 4753 0 4753 1 0000 45 0000 variety nitrogen 12 4 0 2166 0 2166 1 0000 45 0000 Conditional F statistics calculation of Denominator degrees of freedom Source Size NumDF F value LambdaxF Lambda DenDF mu 1 1 327 5462 327 5462 1 0000 6 0475 variety 3 2 1 4853 1 4853 1 0000 10 0000 LinNitr 1 1 110 3232 110 3232 1 0000 45 0000 nitrogen 4 2 1 3669 1 3669 1 0000 45 0000 variety LinNitr E 2 0 4753 0 4753 1 0000 45 0000 variety nitrogen 12 4 0 2166 0 2166 1 0000 45 0000 14 4 2 The as1 file The asl file is primarily used for low level debugging It is produced when the LOGFILE qualifier is specified and contains lowlevel debugging information information when the DEBUG qualifier is given However when a job running on a Unix system crashes with a Segmentation fault the output buffers are not flushed so the output files do not reflect the latest program output In this case use the Unix script screen log command before running ASReml with the DEBUG qualifier but without the LOGFILE qualifier to capture all the debugging information in the file screen log The debug information pertains particularly to the first iteration and includes timing infor mation reported in lines beginning gt gt gt gt gt gt gt gt gt gt gt gt
502. xperimental units The ASReml input file is presented below split plot example blocks 6 Coded 1 6 in first data field of oats asd nitrogen A 4 Coded alphabetically subplots Coded 1 4 variety A 3 Coded alphabetically wplots Coded 1 3 yield 212 16 2 Split plot design Oats Table 16 1 A split plot field trial of oat varieties and nitrogen application nitrogen block variety 0 0cwt 0 2cwt 0 4cwt 0 6cwt GR 111 130 157 174 I M 117 114 161 141 V 105 140 118 156 GR 61 91 97 100 Il M 70 108 126 149 V 96 124 121 144 GR 68 64 112 86 III M 60 102 89 96 V 89 129 132 124 GR 74 89 81 122 IV M 64 103 132 133 V 70 89 104 117 GR 62 90 100 116 V M 80 82 94 126 V 63 70 109 99 GR 53 74 118 113 Vi M 89 82 86 104 V 97 99 119 121 oats asd SKIP 2 yield mu variety nitrogen variety nitrogen r blocks blocks wplots predict nitrogen Print table of predicted nitrogen means predict variety predict variety nitrogen SED The data fields were blocks wplots subplots variety nitrogen and yield The first five variables are factors that describe the stratification or experiment design and treat ments The standard split plot analysis is achieved by fitting the model terms blocks and blocks wplots as random effects The blocks wplots subplots term is not listed in the model because this interaction corresponds to the experimental units and is automatically included as
503. xploited The equations for mv and any terms that follow are always included in the sparse set of equations Missing values are handled in three possible ways during analysis see Section 6 9 In the simplest case records containing missing values in the response variable are deleted For multivariate including some repeated measures analysis records with missing values are not deleted but ASReml drops the missing observation and uses the appropriate unstructured R inverse matrix For regular spatial analysis we prefer to retain separability and therefore estimate the missing value s by including the special term mv in the model out n out n t establishes a binary variable which is out i 1 if data relates to observation i trait 1 else is 0 out i t 1 if data relates to observation i trait t else is 0 The intention is that this be used to test remove single observations for example to remove the influence of an outlier or influential point Possible outliers will be evident in the plot of residuals versus fitted values see the res file and the appropriate record numbers for the out term are reported in the res file Note that i relates to the data analysed and will not be the same as the record number as obtained by counting data lines in the data file if there were missing observations in the data and they have not been estimated To drop records based on the record number in the data file use the D transformation in ass
504. y need to be predefined e g Tr male Tr female and Tr female at f n defines a binary variable which is 1 if the factor f has level n for the record For f n example to fit a row factor only for site 3 use the expression at site 3 row The string is equivalent to at for this function at f at f is expanded to a series of terms like at f 7 where i takes the values 01 Qf to the number of levels of factor f Since this command is interpreted before the data is read it is necessary to declare the number of levels correctly in the field definition This extended form may only be used as the first term in an interaction at f i 7 k is expanded to a series of terms at f i at f 7 at f k Sim at f m n ilarly at f 2 X at f j X at f k X can be written as at f i j7 k X pro Q f m n vided at f i j k is written as the first component of the interaction Any number of levels may be listed Contiguous sets of values can be specified as 7 7 cos u r forms cosine from v with period r Omit r if v is radians If v is degrees r is 360 con f apply sum to zero constraints to factor f It is not appropriate for random factors c f and fixed factors with missing cells ASReml assumes you specify the correct number of levels for each factor The formal effect of the con function is to form a model term with the highest level formally equal to minus the sum of the preceding terms With sum to zero constraints a missing treatment le
505. y of applications of the general linear mixed model available in ASReml One approach would be to use likelihood ratio methods see Welham and Thompson 1997 although their approach is not easily implemented Wald type test procedures are generally favoured for conducting tests concerning T The traditional Wald statistic to test the hypothesis Hy Lr l for given L r xp andl r x 1 is given by W LF DUNXH X L Y HL 1 2 24 and asymptotically this statistic has a chi square distribution on r degrees of freedom These are marginal tests so that there is an adjustment for all other terms in the fixed part of the model It is also anti conservative if p values are constructed because it assumes the variance parameters are known The small sample behaviour of such statistics has been considered by Kenward and Roger 1997 in some detail They presented a scaled Wald statistic together with an F approximation to its sampling distribution which they showed performed well in a range though limited in terms of the range of variance models available in ASReml of settings In the following we describe the facilities now available in ASReml for conducting inference concerning terms which are the in dense fixed effects model component of the general linear mixed model These facilities are not available for any terms in the sparse model These include facilities for computing two types of Wald F statistics and partial implementation of th

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