ASReml User Guide - VSN International
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1. 34 row AR1 56 15 col ID 1 2 0 19 28 row AR1 38 site test 2 site 0 coruh 66 13 13 13 GU test The LogL increases 22 4 P lt 0 01 to 288 484 P lt 0 01 and the components are site test CORRelat 3 0 418611 0 418611 6 36 OU site test CORRelat 3 0 991299 0 991289 T39 QY site test CORRelat 3 0 152347 0 152347 2 3 O09 site test CORRelat S 0 122776 0 122776 tole 0 U So the common correlation under this model is 0 42 down from 0 66 and the site variances are 0 99 0 15 and 0 12 respectively site 1 being particularly high This CORUH model would typically be the first model fitted In this case there is genetic variance at each site but sometimes that will not be the case Is the assumption of common correlation justified Finally we fit an unstructured model This is often equivalent to an XFA1 model for 3 sites but with more sites the XFA1 model might be more parsimonious The G structure code is shown in the code box The resulting LogL is 286 824 an in site test 2 crease of 1 66 with 2 df P gt 0 05 The initial 35 values were derived from the CORUH results for 16 15 example 0 16 0 42 x 0 99 x 0 15 14 06 12 test The fitted genetic variance matrix from the unstructured model is 991 157 132 157 072 078 132 078 122 What next Predicted values for the lines at each site are given in the pvs file by the predict statement predict site test check 7 Check 72. 001 IPART 3 xfa Site 1 Geno IPART 4 xfa Site 2 Geno IPART 23 45 Site 2 1 55 5 ARI 0 5 S2 0 132 12 4 AR1 0 35 Section 65 65 ARI 0 7 182 0 22 12 4 AR1 0 22 Section 55 5 ARI 0 74 S2 0 028 12 4 AR1 0 25 Section 55 5 ARI 0 78 S2 0 22 12 4 AR1 0 18 Section 55 5 ARI 0 68 S2 0 041 12 4 AR1 0 36 Section oP WNP IPART 2 Site Geno 2 Site 0 CORUH Starting values from PART 1 62 062 10 14 16 06 Geno IPART 3 xfa Site 1 Geno 2 xfa Site 1 0O XFA1 018 045 004 10 012 eth s24 gl sae 222 Geno IPART 4 xfa Site 2 Geno 2 xfa Site 2 0 XFA2 G5P5P5P 018 045 004 10 012 yak OE I 22D 22 5 01 Geno IPART 5 Site Geno 2 Site 0 US GP 0 5945E 01 0 4989E 01 0 1007 0 2145E 01 0 2443E 01 0 1443E 01 0 4640E 01 0 5285E 01 0 2272E 01 0 1503 0 4622E 01 0 5265E 01 0 2263E 01 0 4896E 01 0 6088E 01 Geno Part 1 ended after 10 iterations with a LogL of 2563 4 not having quite converged Part 2 starting from Part 1 estimates converged in 7 iterations to LogL 2586 7 These LogLs are not comparable because some fixed effects were dropped when fitting part 2 Both these fitted the genetic variance matrix assuming equal correlation among sites but different variances CORUH Factor Analytic models provide a parsimonious approach generalising the co variance structure Replacing CORUH with XFA1 in part 3 increased the LogL to 2611 71 a substantial gain The XFA2 model in part 4 increased the LogL
3. 1 732 The experiment variances range 0 00037 to 0 04671 with an average of 0 02491 Note that the weights have been scaled by this average value via transformation and back again in the model so that variances have their natural scale Following is code that fits 5 models to this data IWORK 1 NO CONTINUE RENAME ARG 111 2 DOPART 1 Title ALBUS_2stage trial year region variety yield rep weight ems KFAO2BURU 2002 NSW KIEV MUTANT 0 873 3 2136 562 0 0010000 trial A year I region A variety A yield rep weight 0 025 ems ALBUS csv SKIP 1 IMAXIT 40 PART 11 Initial Model Uniform correlation heterogenous variance Shows trials 51 and 85 have minimal variance fix 0001 yield wt weight mu trial r trial variety LogL 2783 33 fid 0 1520 025 trial variety 2 trial 0 CORUH 1 87 1 variety IPART 123 4 Sequence of Factor Analytic models XFA1 LogL 2911 52 increase of 128 18 XFA2 LogL 3039 34 then 3050 38 increase of 138 86 11 XFA3 LogL 3155 65 then 3158 increase of 105 XFA4 LogL 3201 99 then drift increase of 44 yield wt weight mu trial r xfa trial 1 var 214 0 52 0 025 xfa trial 1 var 2 xfa trial O XFA 1 IGP 50 01 0001 33 01 0001 2 01 87 07 87 07 87 07 87 07 variety The equal correlation model is fitted first in part 11 After 40 iterations it had converged with a LogL of 2783 3 with an average genetic correlation of 0 55 Continuing with XFA1 in par
4. have few sites and few replicates but many lines to compare Current late stage trials have more 3 4 replicates 10 15 sites and 30 50 entries of elite lines grown at most sites National analyses draw together results from multiple late stage trials using re sults from several years and regions many sites and many lines We will consider these three cases to discuss some features of ASReml These analyses should not be considered as definitive typical or recommended as they demonstrate just one approach They are chosen to demonstrate syntactical issues not statistical issues An early generation trial Early stage multi environment trials typically have many genotypes but limited seed Consequently within site replication of test lines is low 1 or 2 so that lines can be tested at more locations Traditionally grid plot designs have been used where standard reference check lines are highly replicated using a systematic grid but partial replicate designs are strongly advocated Cullis et al 2006 This example involves 6 check lines and 330 test lines grown at three locations The first 2 locations were laid out in a 12 x 34 arrangement 12 replicates of each check line and 1 of each test line The extra 6 plots were sown to a fill in variety which was also harvested The third location was laid out in a 15 x 28 arrangement and had 15 replicates of each check line The data file MET DAT is sorted row within column within site The distrib
5. is the mean effect for test Five site MET example This second example is also an early generation trial but with more sites 5 It demonstrates a set of five models typically fitted to current late stage trials There were 330 genotypes replicated twice at each site except 7 plots were sown to a fill in variety Notice there is no separate coding of check plot genotypes in this example IRE WORK 100 NO ARG 1 2345 DOPART 1 Title met a307 Plot Block Entry Column Row Genotype A Site A 5 Year I Environment A yield 0 001 met307 csv SKIP 1 IPART 1 SECTION Site Row Row Col Column generates standard spatial R structure tab Block Col Row Gen Site stats tabulates structural factors yield mu Site at Site lin Row at Site lin Col mv fixed model Ir at Site Row at Site Col at Site Block Site Geno random model Site 2 1 NB R structure is generated by ASReml so not here Site Geno 2 Site 0 CORUH b B 015 Geno IPART 2 5 Fits CORUH and US CONTINUE yield mu Site at Site 1 2 4 5 lin Row at Site 5 lin Col mv tr at Site 01 02 03 05 Row 003 003 0001 0008 at Site Col 06 2007 002 02 001 at Site 2 Block 05 Site Geno Starting values inserted from PART 1 IPART 3 4 Fits XFA1 and XFA2 CONTINUE yield mu Site at Site 1 2 4 5 lin Row at Site 5 lin Col mv tr at Site 2 Block 05 at Site 1 2 3 5 Row 003 003 0001 0008 at Site Col 06 007 002 02
6. to 2621 57 after 10 iterations not quite converged Finally fitting US in part 5 resulted in a LogL of 2622 06 This has only one more parameter than the XFA2 model which has 4 more free parameters than the XFA1 model Consequently the XFA2 model is the best fit In this case the unstructured variance matrix can be fitted but in general es pecially with more than five sites with high genetic correlations and with fewer genotypes the REML estimate of an unstructured variance matrix if it can be successfully estimated may not be a positive definite matrix The final genetic Second loading 0 10 0 05 0 00 0 05 0 10 0 15 0 10 0 15 T 0 20 0 25 0 30 0 35 First loading Figure 1 loadings variance matrix was Covariance Variance Correlation Matrix UnStructured Site Geno 0 05947 0 6092 0 7241 0 5229 0 7736 0 04755 0 1025 0 6013 0 5910 0 6717 0 02119 0 02310 0 01440 0 4829 0 7818 0 04943 0 07334 0 02247 0 1503 0 4438 0 04657 0 05308 0 02316 0 04247 0 06093 Recall the average correlation from the CORUH model was 0 626 It is convenient at this point to explore the XFA model which is akin to Principal Components analysis The underlying latent variables are called factors The XFA1 model assumes a single factor a set of genotype effects usually called genotype scores that explain the covariance among sites The XFA2 assumes two ge
7. variance and loadings as a table with a figure see page Further investigation must be done outside of ASReml using the variance parameters and the fitted effects
8. ASReml User Guide Release 3 0 July 2008 A R Gilmour NSW Department of Primary Industries Orange Australia B J Gogel Department of Primary Industries Brisbane Australia B R Cullis NSW Department of Primary Industries Wagga Wagga Australia R Thompson Rothamsted Research Harpenden United Kingdom ASReml User Guide Release 3 0 ASReml is a statistical package that fits linear mixed models using Residual Maximum Likelihood REML It is a joint venture between the Biometrics Pro gram 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 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 S J Welham and I M S White Author email addresses Arthur Gilmour dpi nsw gov au Beverley Gogel edelaide edu au Brian Cullis dpi nsw gov au Robin Thompson bbsrc ac uk Copyright Notice Copyright 2008 NSW Department of Primary Industries All rights reserved Except as permitted under the Copyright Act 1968 Commonwealth of Aus tralia no part of the publication may be reproduced by any process electronic or otherwise without specific written permission of the copyright owner Nei ther may information be stored electronically in any form
9. al models for the genetic variances and covariances of test lines across sites We are interested in the common effect of genotype across sites but also to know to what extent individual sites diverge from the common genotype rankings Our naive first model simply fits a common genetic effect primarily to show why this model is inadequate It implies the genetic variance is the same at all sites and the genetic correlation between sites is 1 Both assumptions are unlikely given that the residual variances range from 0 12 to 2 77 Adding site test to the random model allows for a common covariance less than the common variance It increases the LogL from 314 262 to 310 879 highly significant and gives components test 336 336 O0 86 727E O1 0 867727E 01 5 46 O P site test 1008 1008 0 440183E 01 0 440183E 01 2 62 Q P This represents a genetic correlation of 0 66 e E and an average genetic variance of 0 1308 0 08677 0 04418 up from 0 1031 However the residual site variances are quite different 20 fold so it is likely that the genetic variances differ between sites Our next model therefore fits a common correlation but heterogeneous variances We drop test from the list of model terms and put the CORUH structure on the site component of site test The ASReml code is yld site chk site Ir at site 3 row 02 at site col 90 40 036 site test site 2 1 12 col ARI 1271 1 2 2 19 34 row AR1 751 12 col ARI lt 25 1S2 0 84
10. imable because they include the mu term but note Site fixed effects The site specific residuals 6 are not included in the ASReml output but can be calculated with a predict state ment like for site 4 predict Geno AVE Site 0 0 0 1 0 347 0 171 ONLY xfa Site 2 Geno 10 Meta analysis of trial means When it comes to later stages of selection it is desirable to include as many experiments as possible representing different locations and seasons when com paring genotypes This will commonly be over 30 experiments after 3 years of evaluation and could easily be as many as 100 trials Furthermore few genotypes will be represented at all sites The combined analysis of experiments at the plot level discussed in the previous subsection is therefore not always feasible We describe a two step approach First each experiment is analysed separately under a spatial model and predicted genotype means are produced along with a set of weights see TWOSTAGEWEIGHTS on page Ideally these should be stored in a database so that they can be conveniently retrieved later for subsequent analysis We also store the site mean yield and the residual variance along with details of the spatial model fitted For this example we have extracted 2019 predicted lupin yields from the data base with their weights They represent 203 genotypes and 87 experiments conducted in 3 regions over 5 years The yields range from 0 09300 to 5 613 with an average of
11. notype factors The XFA2 model forms the across site variance matrix as TT with estimates from this example of 0 0172 0 0 0 0 186 0 088 0 0 043 0 0 0 237 0 055 v 0 0 0 004 0 and 0 089 0 049 0 0 0 0 000 0 0 347 171 0 0 0 0 008 0 188 0 133 The elements in the diagonal matrix W are known as specific variances and rep resent the variation in genotype effects that is site specific not associated with the factors The elements of IF are the loadings for the two factors at the five sites They represent the regression of the genotype effects for each site on the latent factors and plotting them maps the sites according to genetic similarity highlighting that site 4 is most divergent Figure 1 The XFA2 variance matrix as presented in the asr file slightly reformated is Covariance Variance Correlation Matrix XFA xfa Site 2 Geno 0 0594 0 6252 0 7120 0 5247 0 7762 0 7615 0 3627 0 0488 0 1024 0 6175 0 5883 0 6564 0 7391 0 1720 0 0208 0 0237 0 0144 0 4853 0 7850 0 7403 0 4089 0 0494 0 0727 0 0225 0 1490 0 4485 0 8983 0 4394 0 0467 0 0518 0 0233 0 0427 0 0609 0 7628 0 5387 0 1857 0 2365 0 0889 0 3468 0 1883 1 000 0 000 0 0884 0 0550 0 0491 0 1696 0 1330 0 000 1 000 The first 5 x 5 block is the variance matrix directly comparable to the US matrix displayed above with derived correlations in the upper right triangle The first 5 columns of the last 2 rows are the loadings I being the covariances of the genotype
12. s a set if as a set they appear relatively large Moving from XFA2 to XFA3 the LogL increased 105 3050 to 3155 with 74 extra parameters 87 loadings less 2 constraints on loadings and 11 more specific vari ances fixed at 0 0 which is about twice the 5 critical value However this model has trouble converging a problem we are still investigating The LogL increased 12 nicely to 3155 in 40 iterations Continuing it rose to 3157 drifted to 3144 rose again to 3158 and dropped away to 3154 A pragmatic option is to rerun the job using MAXIT to stop at the iteration with the highest LogL and accept that as the solution Proceeding to XFA4 is probably ambitious Starting from the 3155 XFA3 solution and using the default AILOAD f strategy the LogL increases to 3201 briefly but quickly starts decreasing In another run the first 3 loadings were held at their XFA3 values until approximate convergence at LogL of 3209 Then continuing with using AILOADINGS 20 the LogL rose to around 3235 with 51 specific variance at 0 0 before drifting away This is an increase of 80 which for 76 87 3 8 extra parameters is close to the 5 critical value The interpretation of results from a factor analytic model is not easy but is similar to interpreting results from a principal components analysis First users are re ferred to the section of the res file headed DISPLAY of variance partitioning for XFA structure in which lists the specific
13. s effects at the 5 sites with the latent factors Similarly the first 5 rows of the last 2 columns are the correlations of the genotypes effects at the 5 sites with the latent factors The final 2 x 2 identity matrix relates to the two factors The sln file also contains genotype effects for the five sites and two factors that is the genotype scores as well as genotype effects for the 5 sites For example xfa Site 2 Geno BLA3071 VV5866 0 1006 0 9392E O01 xfa Site 2 Geno MTA3071 VV5866 O 1237 0 1680 xfa Site 2 Geno PNA3071 VV5866 0 7299E 01 0 5347E 01 xfa Site 2 Geno RSA3071 VV5866 0 3641 0 1638 xfa Site 2 Geno WTA3071 VV5866 0 2089 0 8414E 01 xfa Site 2 Geno Factor_1 VV5866 0 2370 0 3487 xfa Site 2 Geno Factor_2 VV5866 1 661 0 5551 The genotype E BLUPS for each site are calculated as I s 8 where s is the score 237 1 661 the residuals 6 are not explicitly returned by ASReml and 6 is a lack of fit residual with variance given by W Note that 0 1006 0 186 0 088 0015 0 1237 0 237 0 055 _ 937 0885 Thus 0 0730 0 089 0 049 1 661 0127 0 3641 0 347 171 0022 0 2089 0 188 0 133 0325 The factors will be close to orthogonal if the user has not applied explicit con straints to the loadings or they can be rotated as shown in the next example to be orthogonal Plotting the genotype scores on the factor axes gives a two dimensional representation of them Plotting the loadings gives information on the
14. similarity of sites with respect to genotype ranking Plotting both together provides a biplot Note that biplots are only useful when the factors plotted ex plain a large proportion of the variation The average genotype ranking is given by predicting genotype effects BLUPs at the average loadings 0 213 0 031 Stability of genotype performance is assessed by evaluating them at the extreme sites The choice of weights to use to produce an index upon which to rank geno types is beyond our present purpose The following predict statements simply demonstrate how one might proceed predict Site Genotype predicts each Genotype at each site predict Genotype Average Site 1 1 1 0 1 4 predict Genotype AVE site 5 0 0 213 0 031 ONLY xfa Site 2 Geno Average all The first predict statement gives predicted means for each genotype at each site even though some genotypes might not have been grown at some sites While all sites are statistically distinct in this case given Figure 1 one might be inter ested in the average of the most similar sites excluding site 4 This is given in the second prediction Note that these first two predictions incorporate the Sitex Genotype BLUPs and so include the the site specific residuals 6 The third prediction is based on the genotype scores only and predicts the common genotype effects at the average environment the average of the loadings Note the ONLY qualifier Without it the predictions are not est
15. t 1 the LogL increases to 2911 52 in another 40 iter ations with 9 specific variances at 0 0 The factor explains 56 of the genotype variation Again using CONTINUE to start with the XFA1 values part 2 fits an XFA2 model After 40 iterations the LogL had reached 3039 and another 40 iter ations increased it to 3050 4 with 23 of the 87 specific variances fixed at 0 0 The second factor explains a further 18 of the genotype variation The parameters were still changing slightly but this provides two factors and permits a biplot of genotypes and experiments to be formed XFA models with two or more factors are often difficult to fit The main strategy for fitting these models is getting better starting values which is why these 5 models are fitted in sequence and using CONTINUE The AILOAD f qualifier may also help It is set by default when XFAk model parameters are initialized using CONTINUE from a previous XFA model fit with k 1 factors The strategy followed when the user does not supply explicit constraints and AILOAD f is set has three stages The first stage is to hold the first k 1 factor loadings fixed for a few iterations estimating the loadings for the kth factor and the specific variances The second stage is to estimate two factors and the specific variances until iteration f before updating all factors simultaneously in the third stage There is also an automatic procedure which shrinks the AI updates for the loadings a
16. un is 314 262 and the parameter estimates follow Results from analysis of yld Source Model terms Gamma Component Comp SE C Residual 1236 1213 at site 01 col 15 15 0 622124 0 622124 1 45 0 P at site 02 col 15 15 0 158966 0 158966 1 40 Q P at site 03 col 15 15 0 483343E 01 0 483343E 01 1 85 OP at site 3 row 34 34 0 235011E 01 0 235011E 01 Bott OP test 336 336 0 103063 0 103063 02 OP Variance 1 408 0 2 0 220 2 77228 8 80 OP Residual AR AutoR 12 0 195859 0 195859 3 64 OU Residual AR AutoR 34 0 650554 0 650554 16 80 OU Variance 2 408 0 0 992656 0 992656 9 20 0 P Residual AR AutoR 12 0 286849 0 286849 5 47 OU Residual AR AutoR 34 0 574471 0 574471 13 65 OU Variance 3 420 O 0 120457 0 120457 6 43 OP Residual AR AutoR 28 0 639281 0 639281 10 11 OU Wald F statistics Source of Variation NumDF F incr 8 site 3 1230 64 9 chk site 20 11 36 Practioners have taken two views on whether check or reference lines should be fitted as fixed effects or just treated as random effects in the set of genotypes It may effect the variance of the test genotype effects Comparison of test lines with check lines is easier if all are in the same random factor but this analysis takes the former approach Notice in passing that chk site has 20 rather than 18 degrees of freedom because of the fill in variety at the first 2 sites Our aim in this analysis is to get good predictions of test line effects To do this we can compare sever
17. uted data file has extra fields we will ignore The code for an initial combined analysis fitting a common random test effect follows This code incorporates the results from several preliminary runs involving separate spatial analyses of each site ignoring test These runs suggested a random row term was required for site 3 col terms for all sites AR1 was unnecessary for the col dimension of the R structure for site 3 and provided the inital values inserted in the code The SECTION site qualifier allows ASReml to check that the factor site does indeed correspond to the 3 sections in the R structure Notice in the 6 R structure lines that the field dimensions are explicitly given in the first field and the row col in the second field enables ASReml to sort check the plots in field order Early Generation MultiEnvironment Trial seq col 15 Actually 12 12 and 15 for the sites respectively row 34 Actually 34 34 and 28 for the sites respectively chks 7 O is fill in 1 6 are check lines 7 is test line test 336 0O is fill in or check 7 336 is test line geno 337 1 6 are checks 7 336 are test lines 337 is fill in yla i 01 site 3 met dat ISECTION site yld site chk site Ir at site 3 row 02 at site col 90 40 036 test predict chk site predict test site chks 7 site 2 12 col ARI 1271 1 2 2 19 34 row ARI 751 a2 col ARL 25 1 2 0 84 34 row AR1 56 15 col ID 1 2 0 19 28 row AR1 38 The LogL from this r
18. whatever without such permission Published by VSN International Ltd 5 The Waterhouse Waterhouse Street Hemel Hempstead HP1 1ES UK E mail 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 and Thompson R 2008 ASReml User Guide Release 3 0 VSN International Ltd Hemel Hempstead HP1 1ES UK ISBN 1 904375 23 5 0 1 Miulti environment trials Revised 08 In this section we explore some models that can be fitted to multi environment trials in particular showing the application of factor analytic models A multi environment trial is a series of experiments with treatments in common Our examples are drawn from field crops where the aim is to identify genotypes which consistently yield well over a region in several seasons The traditional approach involved analysing the experiments separately saving the means and then performing some analysis of the means This approach tends to ignore differences in experiment accuracy and to require each genotype be tested in each experiment limiting the experiments and or genotypes that can be considered together The methods described in this section build on spatial analysis incorporate trial accuracy and allow for unbalance in genotype representation For further reading see Smith et al 2001 2005 Multi environment trials have three basic forms Early generation trials
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