User's Manual & Specifications - Australian Antarctic Division
Contents
1. Minimum from quadratic fit routine R1 9115 06 Func value 81 7234 Means of mixture components 294 001 360 379 Parameters of linear standard deviations Intercept 1 00941 Slope 0 504853E 01 Standard deviations of mixture components 15 8521 19 2033 Total density of each mixture component 135 183 9102 06 SD of each mixture component density 200 170 5799 84 CMIX Output File Format Summary results of the mean length and standard deviation for the component If the standard deviations have been found through a linear relationship between the SD and the mean then the parameters for that relationship are given Otherwise only the mean and standard deviation of the lengths in each component are given In all executions of the program the total density and standard deviation of the density for each component will be given Table of observed and expected mean densities Interval Observed Expected Lower C l Upper C l 265 000 0 000000 6 63820 0 000000 0 100000E 36 275 000 0 000000 16 8203 0 000000 0 100000E 36 285 000 27 8883 29 6301 0 000000 0 100000E 36 295 000 39 8717 39 8543 7 18659 223 849 305 000 60 7467 58 5455 6 52327 13772 4 315 000 123 821 136 221 18 4901 10894 5 325 000 414 407 360 987 37 0117 222581 335 000 798 009 797 416 127 341 63714 4 345 000 1244 24 1366 78 168 259 158029 355 000 2166 27 1799 44 242 037 466673 365 000 1467 45 1817 60 292 180 62100 2 38 CMIX User Manual CMIX Output File Format 372. densities estimated from net haul surveys Macdonald and Pitchers 1979 method assumes that length frequency data have no unusual statistical properties The usual method assumes that length frequency data are representative of a population with the frequencies in each length class having Poisson distributions This would be valid in the case where the animals in question are randomly and independently distributed and the frequencies consist of a complete enumeration of all the samples Unfortunately most net haul survey densities do not have these statistical properties The statistical distribution of net haul densities has to allow for an often substantial probability that a given haul will give a zero density estimate ie the net was empty The statistics of such distributions have been examined by Aitchison 1955 and Pennington 1983 has recommended using Aijtchison s delta distribution as the underlying statistical model when analysing net haul survey data This recommendation is followed in the method developed here The delta distribution consists of a discrete probability at the origin and a lognormal distribution for the non zero observations CMIX User Manual Understanding The CMIX Model Simulation studies de la Mare 1994b show that the sampling distribution of the mean for delta distributions is highly skewed with the numbers of observations typical in trawl surveys Simple transformations of the data or their mean do not le
3. Bounds Form 4 1 2 1 Method 1 Add Bounds From Spreadsheet Click on the corner of the Add Bounds From Spreadsheet tool to select data from any table within the current active worksheet Use the mouse to select the data by drawing a bounding box around the data You may not select empty cells or cells containing non numeric data 4 1 2 2 Method 2 Add Edit Bounds You manually enter the required bounds in the Add Edit Bounds frame The text box for entering a fixed mean value is only visible if the Would you like to fix the means checkbox has value Yes After entering bounds for a component you need to hit the Add Edit button to have the bounds added to the table Bounds do not need to be entered in order the wizard will re order them If bounds overlap the wizard will inform you and ask you to modify the bounds till they are correct To edit bounds that have already been added you need to click on the desired row of the bounds table and the selected bounds will appear in the Add Edit Bounds frame where they can be edited Note that edits will not appear updated in the bounds table until the Add Edit button has been hit 4 1 2 3 Method 3 Set von Bertalanffy Length Bounds Click the Set von Bertalanffy Length Bounds to let the wizard automatically calculate the bounds from user specified growth parameters using the von Bertalanffy equation Figure 7 will be displayed and needs to be comple
4. The following annotated output file is not presented in complete form The following line will be inserted at the points where lines of the file are skipped because the loss of information will not reduce the interpretation of the annotations dende skipped Mixtures input file for C gunnari at Heard Island 1993 NUMBER OF COMPONENTS IN MIXTURE 2 Bounds on the means of the components Component Low bound High bound 1 280 000 310 000 2 315 000 440 000 eee skipped End of haul data 1 The output file reports the input data so that the user can check that the inputs have been interpreted correctly This also provides a means of checking where the program might stop as a result of incorrect input data Table of densities for each length class Length Density S E Lower CL Upper C l 265 000 0 000000 0 000000 0 000000 0 100000E 36 275 000 0 000000 0 000000 0 000000 0 100000E 36 285 000 27 8883 27 8883 0 000000 0 100000E 36 295 000 39 8717 28 0657 7 18659 223 849 305 000 60 7467 54 9987 6 52327 13772 4 315 000 123 821 100 170 18 4901 10894 5 325 000 414 407 386 361 37 0117 222581 335 000 798 009 629 461 127 341 63714 4 345 000 1244 24 1023 69 168 259 158029 355 000 2166 27 1852 64 242 037 466673 365 000 1467 45 1077 89 292 180 62100 2 375 000 1773 21 1422 86 267 309 155819 385 000 678 933 488 063 145 398 24076 7 36 CMIX User Manual CMIX Output File Format 395 000 431 856 278 559 113 983 7893 69 405 000
5. f and FALSE all evaluate to FALSE Usually we would expect that the standard deviations for the components of a length density distribution will increase monotonically with the mean If the response field is TRUE the standard deviations of the mixture components are a linear function of the mean that is Oo a bu where o and u are the standard deviation and mean of component i respectively and a and bare constants which may be estimated from the data If the intercept a is held fixed at O then the mixture components will have a constant coefficient of variation estimated by the slope b If b is held fixed at O then the mixture components will have a constant standard deviation estimated by a These possibilities are allowed for in setting bounds and parameters in the next block Using the linear option ensures that the standard deviations behave in an orderly fashion If the response is FALSE the standard deviations can take any values within specified ranges given in the block after the next Any or all of the standard deviations can be forced to specified values in the block after that Both types of block are kept in the data file so that the user can change from one to the other without having to have two different versions of the data file However only one type of the following blocks is in effect depending on whether the response was TRUE or FALSE blank The following 8 parameters are only used if LINEARLY REL
6. may be unreliable EI CMIX User Manual von Bertalanffy Equation APPENDIX 1 von Bertalanffy Equation 1 1 The Equation The von Bertalanffy Equation Equation 1 11 is a commonly used to describe growth in fisheries modelling gak ie 1 12 where L is the expected size at age t L is the asymptotic length the length at which growth rate is theoretically zero K is the Brody growth rate parameter rate of growth towards asymptote 1 is the projected time age when length would have been zero on the modelled growth trajectory CMIX Wizard uses an adjusted form of the von Bertalanffy equation see Equation 4 12 to generate length bounds for input into CMIX see Section 4 1 2 3 The modified equation is used to correct for the time difference between the time of survey and the animals arbitrary birthday L L H p where ta t t 1 13 Here is the projected time age when length would have been zero on the modelled growth trajectory and 1 is the difference between t and r Where 1 is time between arbitrary birthday and January 1 arbitrary birthday is date when animals are assumed to enter the next age year and is time between date of survey and January 17 1 2 The Parameters Used By CMIX Excel Add in 27 CMIX User Manual von Bertalanffy Equation Day of Survey From Beginning of Year Time between date of survey and January 1 Birthday No of Days from Beginning of Year Time between birt
7. the density of the mixture components Name Distribution Contains a density vs length distribution plot Name_Density Plot Contains a observed and expected density vs length plot Note that this worksheet contains checkboxes underneath the plot to alter the series displayed You may choose to show or hide the confidence intervals standard error bars normal mixture distributions observed and expected densities It is essential to view the quality of the fit particularly when there is a possibility of fitting a component in a region where there are no or few density values for a range of length classes Length classes for which all observations have zero density make no contribution to the likelihood function Therefore a mixture component in such regions may be completely spurious and hence bias the estimate In such cases constraints on the range of length classes to be included in the fit as well as on the mixture components are required to attempt to produce a sensible fit The quality of fit plot is used as the principle method for performing adjustments to the values submiited as input to the program Name Residuals Contains a plot of the residuals Where Name is the name you assigned as the prefix to the CMIX worksheets You will need to check that the output from the run is valid Please see Section 6 2 which outlines methods to check the validity of output 299 CMIX User Manual CMIX And DOS Section 5 CMIX An
8. the log likelihood s for each length class Itis useful to designate the parameters of the mixture distribution as R t the parameter of primary interest and O a vector of the nuisance parameters consisting of Dr 3 Dp K and up47 Un The value of Dr used in calculating the mixture is derived from A t and the Dj as an P T RO E D 1 9 The likelihood function for fitting the mixture distribution can be written as d RR 0 Z Sup tal x p 4 6 O lt nei X n 0 lt 67 lt E p G 40 1 10 where djis the expected value of the density in length class j derived from equation 2 with the mixture distribution with parameters A t and 8 Note that estimating R t and o requires maximising h A t 8 which in turn requires maximising the likelihood function for the delta distribution in each length class All these maximisation s have to be carried out numerically The parameters pj and o are also nuisance parameters The maximisation s are carried out subject to the following constraints 0 lt R t lt 1 My SUSU gau Sau Saa lt lt i SH SH k lt k lt k where a superscript or represents a numerically specified constraint Apart from the well known advantages of statistical efficiency working with log likelihood allows asymptotic confidence intervals and variances to be calculated for the parameters In particular we are interested in a variance estimate for A t
9. the lower or upper ranges In this case the lower range can be truncated by skipping a number of length bins The upper range should be truncated by excluding those bins not required from the input file 6 5 Missing cohorts A better fit will result by leaving out cohorts known to be missing or in very low abundance This can be done simply by excluding them when nominating the characteristics of the components Although the components need to be numbered consecutively the characteristics do not have to represent consecutive cohorts e g age classes 6 6 Size of length bins and Poorly sampled length bins The time taken to fit a mixture and whether or not a successful minimisation is obtained can be affected by the amount of zero data present particularly if there is a vast array of length bins with zero data across many of the samples In this case reducing the range of the data discussed under bias or increasing the size of the length bins may yield a better result The size of length bins does not need to be constant across the range see the discussion under data input concerning bin intervals 6 7 Excluding messy data Messy data at each end of the range of lengths may disrupt the fit Restricting the range as described under bias may help in this case Another method for dealing with messy data is to allow for a component to have a larger or restricted standard deviation than might be expected from ordered growth eg
10. 115 340 107 372 10 4226 58818 9 415 000 14 4700 14 4700 0 000000 0 100000E 36 430 000 0 000000 0 000000 0 000000 0 100000E 36 445 000 0 000000 0 000000 0 000000 0 100000E 36 The densities of each length class is estimated with standard error and lower and upper confidence intervals and is the first table to be provided First minimisation PROGRESS REPORT EVERY 100 FUNCTION EVALUATIONS EVAL NO FUNC VALUE PARAMETERS 1 81 7253 287 598 360 445 19 1433 0 347428E 12 178 321 9156 41 2 81 7270 290 598 360 445 19 1433 0 347428E 12 178 321 9156 41 INITIAL EVIDENCE OF CONVERGENCE CENTROID OF LAST SIMPLEX 292 078 360 412 14 0210 0 143387E 01 157 671 9090 62 FUNCTION VALUE ATCENTROID 81 7237 INITIAL EVIDENCE OF CONVERGENCE CENTROID OF LAST SIMPLEX 292 074 360 412 14 0215 0 143405E 01 157 671 9091 31 FUNCTION VALUE AT CENTROID 81 7237 MINIMUM AT 294 001 360 379 1 00941 0 504853E 01 135 183 9102 06 MINIMUM FUNCTION VALUE 81 7234 END OF SEARCH Ke H k H H d de kkk kk K Ke Ke Summary results during the minimisation procedures are reported at the rate specified in the input file These can be reviewed Standard Error in estimate 5 200 170 2375 CMIX User Manual Standard Error in estimate 6 5799 84 Compare minimum found by quadratic fit with that found by minimisation If the the difference is large the standard error estimate is not reliable Minimum from minimisation routine R1 9102 06 Func value 81 7234
11. 5 000 1773 21 1408 41 267 309 155819 385 000 678 933 837 154 145 398 24076 7 395 000 431 856 381 673 113 983 7893 69 405 000 115 340 133 453 10 4226 58818 9 415 000 14 4700 35 7814 0 000000 0 100000E 36 430 000 0 000000 4 25730 0 000000 0 500000E 35 445 000 0 000000 0 139999 0 000000 0 100000E 36 Sum of the observed densities 9356 51 Sum of the expected densities 9235 07 If the sums differ by a large amount the fit may be unreliable 39 CMIX User Manual Trouble Shooting APPENDIX 4 Trouble Shooting If the program ends before providing a full output then the following steps might help Check the Output file to determine at what stage in the process the program stopped If the problem is with the input file then check vi vii the formatting of the input file see Appendix 2 that the number of components in mixture specified in line 2 of the file matches the number of components in the lists below that the number of components for the means equals the number of components for the standard deviation NB even if the standard deviations are linearly related to the means i e TRUE and the block listing the standard deviations components is not used the number of components for the mean and standard deviations must be equal This is because the two methods for estimating the standard deviations of the components was retained in the one input file to minimise the changes to the input file necessary to explore diffe
12. 6 6 Size of length bins and Poorly sampled length bie 25 6 7 Excluding messy data sae oes coe aesthetic aot lee Bead 25 6 8 R1 The proportion of sample in first mixture component 26 6 9 EIPORIMCSSA GSS EE 26 APPENDIX 1 von Bertalanffy Equation cccsssscsscsssesseeseesseesseesseeneseeeeneeseeensenseeaes 27 TA The Equa OR E 27 1 2 The Parameters Used By CMIX Excel Add In ssscsccessesseeeseesseentenseeeneenees 27 APPENDIX 2 CMIX Input File Format csccsssesseesseeseeeseeeseeneeseseeneeseeeeneeseenenensneaes 28 APPENDIX 3 CMIX Output File Format cccssssssscessesseeeseesseenseesseeneenseeeneeseeeenenseeaes 36 APPENDIX A Trouble Shooting sscssceceessesseesneeseesenensnenseensneneensseeneeneeneneeseenenensneaes 40 APPENDIX 5 CMIX Excel Add In WorkSheets csssssscsssesseestessseeneenseeeneeseeensensneees 41 NOUN Li EE 43 Re trerences eege kee Eeer ee Meed 44 CMIX User Manual Introduction Section 1 Introduction 1 1 Introduction This manual outlines the use of CMIX which is a FORTRAN program designed to fit mixture distributions to length density data obtained from net surveys using maximum likelihood estimation The current version of CMIX is distributed with a CMIX Excel Add In to streamline data input and visualise output The user s manual introduces CMIX and the analytical method that it employs see Section 2 The manual desc
13. ALSE Unless the bounds are selected such as to impose restrictions on the values of the standard deviation estimates it is possible that the standard deviation for a high mean will be numerically smaller than for a low mean blank Components with standard deviations to be held constant 1 is end of list Component Fixed std dev Only if LINEAR is false 1 As was the case for the means specified mixture components can have their standard deviations fixed There is a bug in the program so that the component number and the SD to be held constant must be put on separate lines Also if you have the same number of components in the fixed mean block as you have in the block above i e the bounds around the mean then you need to delete the blank line after the last line in the fixed mean block If you have an uneven number of components in the two blocks then you do not need to delete this line blank MINIMISATION YES This parameter specifies whether estimates are to be made by minimising the residual function over he parameter space If FALSE the residual function is evaluated once at the starting values of the parameters PLOT FITTED FUNCTION AND DATA YES The program will plot the fit of the mixture distribution to the data It is essential to view the goodness of fit particularly when there is a possibility of fitting a component in a region where there are no or few density values for a range of length classes Length clas
14. ATED is TRUE LOWER BOUND ON LINEAR INTERCEPT 1 UPPER BOUND ON LINEAR INTERCEPT 50 LOWER BOUND ON LINEAR SLOPE 0 0 UPPER BOUND ON LINEAR SLOPE 0 4 STARTING VALUE FOR INTERCEPT SEARCH 15 STEP LENGTH FOR INTERCEPT 1 STARTING VALUE FOR SLOPE SEARCH 0 07 STEP LENGTH FOR SLOPE 0 01 This block controls the estimation of the parameters for the linear relationship describing the standard deviations of the mixture distribution Obviously they only have any effect when the response to the linear relationship was TRUE The lower bound on the linear slope should be gt O if the constraint is to be enforced that the mixture standard deviations increase with the mean CMIX User Manual Example CMIX Input File When the starting value for the intercept and its step length are both set to zero the estimated slope is a constant coefficient of variation for the mixture components When the starting value and step length for the slope search are both set to zero the estimated intercept is a constant standard deviation for the mixture components The slope and intercept cannot both be simultaneously fixed at zero although either or both can be fixed at non zero values blank Bounds on the standard deviations of the components Only if LINEAR is false Component Low bound High bound 1 5 50 2 5 50 This block specifies the bounds to be respected in searching for the estimates of the standard deviations of the mixture components when linear is F
15. MIX Excel Add In Figure 8 Plot of von Bertalanffy Length Bounds 4 1 3 Standard Deviation Settings The Standard Deviation tab Figure 9 provides a means to set the data required to determine the estimates for the standard deviations The user can specify whether the standard deviations are linearly or independent functions of the mean by selecting the relevant option from the drop down list Data for both the Linear and Independent tabs need to be completed irrespective of whether you choose the standard deviations to be linearly related to or independent of the mean This is a requirement of CMIX Both types of input are kept in the CMIX input file so that the user can change from one to the other without having to have two different versions of the data file However only the option selected Linear or Independent is evaluated Defaults are automatically set for both forms so the minimum amount of changes can be performed 4 1 3 1 Linear Standard Deviation Settings Usually we would expect that the standard deviations for the components of a length density distribution will increase monotonically with the mean If the linear tab is selected then the standard deviations of the mixture components are a linear function of the mean that is Oo a bu where o and u are the standard deviation and mean of component i respectively and a and b are constants which may be estimated from the data If the intercept a is held fix
16. This is estimated from the second derivative of a quadratic function Cox and Hinkley 1974 passing through the points ann dan aal Lo r Reo pen dan R 8 1 41 where is small In determining these points R t is fixed as specified but the vector of nuisance parameters is re estimated by re maximising the likelihood function Thus the estimate obtained is for the marginal variance of R t Although asymptotic variance estimates are not always accurate for non normal sampling distributions they should be adequate for providing relative weights for the subsequent estimation of the distribution statistics of R t estimates CMIX User Manual Section 3 The package is distributed as an MS DOS executable program called CMIX EXE together with the Excel Add In CMIX_Excel_Add In xla A setup program is supplied to install these files onto any windows operating system In order to install and operate the Excel Add In It is recommended to have any Windows operating system except for Windows XP as CMIX wont run under this version At least a 386 processor 16 MB RAM 3 1 Installing CMIX and Excel Add in Complete the following steps to install CMIX and the Excel Add In Before continuing with the following installation procedure please make sure you have uninstalled any previous versions of the Add In See Section 3 2 Uninstalling CMIX and Excel Add In Double click the setup exe file supplied in
17. This parameter can be used to specify whether the length frequency data are to be truncated to the left In this example the specification means that the first 6 intervals are not used in fitting This means that the intervals less than 260mm will not be used in fitting the mixture distribution Specifying zero means that all the intervals will be used Bin interval boundaries mm 40 50 60 70 80 90 260 270 280 290 33 CMIX User Manual Example CMIX Input File 300 310 320 330 340 350 360 370 380 390 400 410 420 440 450 This block specifies the boundaries between the length intervals in the length density distribution The boundaries do not need to be all the same width but a length interval is defined between each pair of values In the example above there is one very wide interval between 90 and 260mm This feature can be used to save entering a large number of zeros in the haul by haul data in cases where there are large gaps between mixture components Obviously there will be one more datum entered in this block of interval boundaries than there are intervals in the data blocks below There is no requirement to use measurements in mm blank Gunnari Ridge haul no 19 1 0 0 0 0 0 0 0 0 0 71 90 0 0 143 80 287 61 503 32 934 73 790 92 790 92 143 80 71 90 0 0 0 0 This block and those that follow are the basic length density data from each single haul in the survey The first line in the block can be used
18. User s Manual amp Specifications CMIX User Manual Version Information Version Information Citation de la Mare W 1994 Estimating Krill recruitment and its variability CCAMLR Science 1 55 69 Copies available from authors or from CCAMLR Secretariat Current Version CMIX EXE 1997 Marine and Ecological Research Australian Antarctic Division CMIX User Interface Ronai B and Lamb T Australian Antarctic Division User s Manual Last Modified 28 9 02 Written by de la Mare W Constable A van Wijk E Lamb T Hayes D and Ronai B Australian Antarctic Division Contact Person Andrew J Constable User s Manual amp Antarctic Marine Living Resources Group Specifications Australian Antarctic Division Cie Channel Highway Kingston Tasmania 7050 Australia Ph 61 3 6232 3558 Email andrew constable aad gov au Australian Antarctic Division CMIX User Manual Introduction Contents Section Rn e TO d deer tence de denetieagn enda 1 1 1 aide ler WOM EE 1 1 2 OMIX gege 1 1 3 Excel ele E 00 are nee eee eee eee eee eee 2 Section 2 Understanding The CMIX Model scsccsssssseeesesseesseesseensensseeneenseeenensneas 3 2 1 VGA ler ler E 3 2 2 The Model See de la Mare o04a ENEE NENNEN 3 Section 3 STAM ALON isi clestiessuieddetadceiuiasavasetshanadeuieiadscinsiscscuninasiaasetnsaihanetetaennrantcenenas 8 3 1 Installing CMIX and Excel Add mn 8 3 2 Uninstalling CMIX and Excel Ad
19. accepted examining the output will usually reveal the nature of the problem Following is an annotated data file for the CMIX program Each line of a data file is printed in BOLD type Where the function of the parameter is not obvious explanatory notes about it are given Mixtures input file for C gunnari at Heard Island 1993 The first line of the input file is available for an annotation identifying the data file and any other details the user would like for identification purposes Free format text blank CMIX User Manual Example CMIX Input File All lines marked as blank must be included in the data file as blank lines NUMBER OF COMPONENTS IN MIXTURE 2 blank This is the number of components to be included in the mixture distribution maximum 10 Bounds on the means of the components Component Low bound High bound 1 2 blank 280 310 315 440 The first two lines in this block are explanatory header lines The following numeric lines specify the bounds within which the means for each mixture component can be fitted Each line consists of three tems separated by spaces The first item is the mixture component number The next two items are the upper and lower bounds respectively There must be one line for each component in ascending order The bounds for the components must not overlap The bounds are not allowed to be negative or greater than 10000 The program checks that these conditions are compl
20. ad to summary statistics which capture all the features of the sampling distribution The likelihood for the sampling distribution of the mean cannot be expressed in terms of summary statistics and so the full data set has to be used in calculating the likelihood of given parameter values The delta distribution has the following probability function x p 2 6 1 p I x l 459 4 1 4 f x p N O p D Pane 0 0 where p is the proportion of observations of x which are gt 0 and o are the parameters of the lognormal distribution of the non zero observations l is an indicator function which takes the value 1 when x 0 and 0 otherwise and lg takes the value O when x 0 and 1 when x gt O The first term is a discrete probability mass at the origin and the second term is a probability density Figure 3 shows a schematic depiction of Equation 4 4 e N z 5 o B E a o Ei 4 6 catch number Figure 3 Aitchesons Delta consisting of the log normal distribution which shows the probability or likelihood of the number in a particular haul This distribution includes a non negative point at 0 which represents the case when a particular haul results in no catch This scenario has p 0 9 The log likelihood of a vector of observations x x7 XN from a delta distribution is given by CMIX User Manual Understanding The CMIX Model Y nx Al m In L x x p 2 0 N m In 1 p
21. atically display the output in Excel see Section 4 4 x Please select worksheet to use as CMIX input file Run CMIX Cancel Figure 14 Run CMIX form 4 3 Display CMIX Output The Display CMIX Output tool can be used to display output for any CMIX output file or output worksheet A form will be displayed asking you to choose between displaying the files in the existing workbook or in a new workbook The form shown in Figure 15 will be displayed where you can either browse for an output file using the browse button or select an output worksheet from the drop down list Hit the Display Output button and the output will automatically be imported into Excel as various worksheets containing graphical displays of the output see Section 4 4 Display CMIX Output x Please select worksheet to use as CMIX output file Display Cancel Figure 15 Display CMIX Output Form 21 CMIX User Manual 4 4 Output Using CMIX Excel Add In Once CMIX has finished execution and the DOS window running CMIX has been closed either manually or automatically the output will be imported to Excel and presented graphically Five output worksheets will be imported into your current Excel workbook with names Name Output Contains the output file from CMIX loaded as an Excel worksheet Name Results Contains the results of the CMIX run such as the calculated length means of the mixture components and
22. d DOS 5 1 Running CMIX From DOS Command Prompt The CMIX executable file is located in the installation directory chosen during the setup process See Section 3 The command line for executing the program from a MS DOS command prompt is cmix lt input file gt lt output file gt The program prompts for input and output filenames if they are not specified in the command line You will need to make sure that the input file has been placed in the same directory as the CMIX executable For details on the format of the input and output files please see Appendices 2 3 and 4 An example input file will have been installed during the setup process and can be found in nstallation Directory Examples Input dat CMIX also tputs a plot file written in HGRAPH archive format and is given the default filename PLOT05 DAT 5 2 Plotting CMIX Output From DOS Command Prompt The MSDOS version of the program can also plot various graphs on a screen HPGL compatible plotter or IBM EPSON graphics compatible printer Plotting is done using subroutines from the HGRAPH library by Heartland Software Inc 234 S Franklin Ames IOWA 50010 USA The CMIX program produces a plot file of the mixtures with default name PLOT05 DAT This default file is overwritten each time CMIX is run so if you want to keep the file rename it The file can be plotted using the program vtrans exe which is located in the CMIX installation directory The
23. d In 9 Section A Using CMIX Excel Add ln ccsssscsscesneesseesneeseeeeeenseensennsnensenseeeneenseeeneesees 10 4 1 Using CMIX WA E 10 4 1 1 Setting Input RE EE 10 4 1 2 Setting Mixture Component Bounds ccc 11 4 1 2 1 Method 1 Add Bounds From Gpreadeheet AAA 12 4 1 2 2 Method 2 Add Edit 0 8 48 E 12 4 1 2 3 Method 3 Set von Bertalanffy Length Bounde 12 4 1 3 Standard Deviation Settings s seseesseeeeneeeeenseenenenenetnnennrnnrnnnnnnnnnnnnnnnnnnnnnne nnn 14 4 1 3 1 Linear Standard Deviation SettiNJS ccciiiciciiiiiiiiiiiiiiiiiiinen 14 4 1 3 2 Independent of Mean Standard Deviation Gettmgs AA 16 4 1 4 Selecting Haul ege euuerEseEiEeNEENEeCNEEdEEEEEESEEEEEENEEEEEEEEEEEEEdEEEEESEEEEENEg 18 4 1 5 Final CMIX Settings and Parameters eccsceseceeseeeeeeeeeeeeeeeeeeeeeseaneeeseeaneees 19 4 2 Ster 21 4 3 Display CMIX QUT EE 21 4 4 OTN eeh 22 SECTION 5 CMIX And DOS wisscisisissessesesscsdisstnsctantessatatanussascdsdessctannnsbauinaedsbunntanstisieansaisnathie 23 5 1 Running CMIX From DOS Command Prompt 23 5 2 Plotting CMIX Output From DOS Command Prompt ee 23 Section 6 Tips When Fitting Mixtures scscsssssssssesseeseeeseeeseenseensensenseeneenseeeneesees 24 6 1 Mpu DF EE 24 CMIX User Manual Introduction CSC Relft fg EI 24 6 3 leegen 24 6 4 Bias in length densities arising from gear selectivity or sampling pattern 25 6 5 Missing COMMONS EE 25
24. e CMIX Excel Add In is deselected and then close Excel From the Windows Start menu select Settings gt gt Control Panel gt gt Add Remove Programs Select CMIX from list and hit the Add Remove button The un installation procedure will begin If prompted do not remove any components that are designated as shared components as this may affect the operation of other software V In Excel choose the menu options Tools gt gt Add Ins and click on the CMIX Excel Add In name When prompted select Remove From List and then close Excel If CMIX and the CMIX Excel Add In were installed manually use the following procedure to uninstall the software In Excel choose the menu options Tools gt gt Add Ins and make sure the CMIX Excel Add In is deselected and then close Excel Locate the files CMIX EXE and CMIX_Excel_Add In xla on your local system and delete them V In Excel choose the menu options Tools gt gt Add Ins and click on the CMIX Excel Add In name When prompted select Remove From List and then close Excel CMIX User Manual Using CMIX Excel Add In Section 4 Using CMIX Excel Add in This section illustrates how you can use the CMIX Excel Add In easily to run CMIX and display CMIX output The Add In is essentially a toolbar containing 3 tools CMIX Wizard Run CMIX and Display CMIX Output Figure 4 oN CMIX Wizard 348 Run CMIX B Display CMIX Output Figure 4 CMIX E
25. e 1 CMIX Excel Add In Toolbar Schematic CMIX User Manual Understanding The CMIX Model Section 2 Understanding The CMIX Model 2 1 Introduction This Section aims to give a brief overview of the theory behind the model used in the CMIX routines 2 2 The Model See de la Mare 1994a The aim of the method is to estimate the proportion of recruits in samples from populations The proportion of recruits also known as the gross recruitment rate A t is the ratio of numbers in age class t to the numbers in that age class and above that is RS 1 1 A l gt where A is the number of animals in age class i and nis the age of the oldest animals in the population present in non negligible numbers Thus we need only be able to separate one young age class from all the others it is not necessary to be able to distinguish between the older age classes Figure 2 shows a schematic mixture generated from four nominal age classes with length at age distributions C1 to C4 It is clear that there is little prospect of accurately decomposing the mixture for age classes 3 and above However this is not necessary for calculating R t Length arbitrary units Figure 2 Schematic diagram of a mixture distribution generated from four length at age distributions C1 to C4 and their sum CMIX User Manual Understanding The CMIX Model The model assumes that the length distributions follow a normal distributions with a constant coefficie
26. e any values within specified ranges given in this form Any or all of the standard deviations can be forced to specified values in this form Figure 10 shows this form and descriptions of the input required follows 16 CMIX User Manual Using CMIX Excel Add In Standard Deviation Settings HH xj Are mixture standard deviations linearly related to the mean Ta Linear Independent Component Low Bound High Bound Fix Std Dew Add Edit Bounds Component Low Bound Independent Parameters High Bound Fixed Std Dev Add Edit Remove Reset All Figure 10 Setting Independent Standard Deviation Settings Default low and high bounds are always present for the number of components specified on the Bounds tab of 5 and 50 respectively These may be edited as you require by selecting the relevant row from the bounds table You may edit the values in the Add Edit bounds frame The table will be updated upon hitting the Add Edit button NOTE Unless the bounds are selected such as to impose restrictions on the values of the standard deviation estimates it is possible that the standard deviation for a high mean will be numerically smaller than for a low mean 17 CMIX User Manual Using CMIX Excel Add In 4 1 4 Selecting Haul Data The user can select the haul data using the Haul Data form shown in Figure 11 A description of the import process follows CMIX Wizard Input Bounds Sta
27. e few function calls before convergence is reported combined with obvious variation remaining between values of the residual function indicates the stopping criterion is too large Frequency for Convergence Testing l Simplex Expansion Coefficient Number of Leading Intervals to Skip This is a minimisation routine technical parameter which only applies if quadratic surface fitting is enabled Adjusting it can improve the correspondence between the minima of the fitted quadratic and the minimum found by the search This parameter can be used to specify whether the length frequency data are to be truncated to the left In this example the specification means that the first 6 intervals are not used in fitting This means that the intervals less than 260mm will not be used in fitting the mixture distribution Specifying zero means that all the intervals will be used CMIX User Manual Using CMIX Excel Add In 4 2 Run CMIX The Run CMIX tool can be used to run CMIX on an input file or an input worksheet if changes do not need to be made to the data Firstly a form will be displayed asking you to choose between displaying files in the existing workbook or in a new workbook Then the form shown in Figure 14 will be displayed where you can either browse for an input file using the browse button or select an input worksheet from the drop down list Hit the Run CMIX button and CMIX will run on the input data selected and autom
28. ed at 0 then the mixture components will 14 CMIX User Manual Using CMIX Excel Add In have a constant coefficient of variation estimated by the slope b If b is held fixed at O then the mixture components will have a constant standard deviation estimated by a These possibilities are allowed for when setting bounds and parameters Using the linear option ensures that the standard deviations behave in an orderly fashion Figure 9 and Figure 10 is the standard deviations setting tab with the linear and the Independent tab selected respectively The input for both tabs is described below together with some suggestions for reasonable starting values for parameters CMIX Wizard J xj Input Bounds Standard Deviation Haul Data Settings Are mixture standard deviations linearly related to the mean Linear Independent 1 Upper Bound On Linear Intercept 50 Lower Bound On Linear Slope 0 0 Upper Bound On Linear Slope 0 4 Starting Value For Intercept Search Step Length For Intercept Starting Value For Slope Search Step Length For Slope Cancel lt lt Back Next gt gt Figure 9 Setting Linear Standard Deviation Settings Table 1 Linear Parameters 15 CMIX User Manual Using CMIX Excel Add In Lower Bound on Linear Intercept The lower bound desired for fitting the relationship between the SD and the mean Upper bound on Linear Intercept The highest bound desired Lower Bound on Linear Slo
29. for a haul identifier After the 40th character is the data block number This starts at 1 and increases strictly sequentially for each haul This is used to help ensure that any formatting errors in the data blocks will be detected The data can be placed over as many lines as required The first blank line terminates the individual haul block blank Gunnari Ridge haul no 55 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13 75 13 75 0 13 75 13 75 0 0 0 0 0 blank Gunnari Ridge haul no 56 3 0 0 0 0 0 0 0 0 0 0 0 20 44 0 40 88 40 88 40 88 81 76 81 76 122 64 81 76 40 88 0 0 0 blank Gunnari Ridge haul no 57 4 0 0 0 0 0 0 0 0 0 0 0 0 0 303 88 694 58 1041 86 1953 49 2648 07 2431 01 1693 03 651 16 86 82 0 0 blank Gunnari Ridge haul no 58 5 0 0 0 0 0 0 0 0 0 0 29 82 89 45 0 0 0 0 59 64 29 82 29 82 59 64 0 0 0 0 blank Gunnari Ridge haul no 114 6 0 0 0 0 0 0 0 0 167 33 167 33 334 66 669 33 2342 64 5019 95 5521 94 8199 25 4685 28 4350 62 1171 32 836 66 0 0 0 0 CMIX User Manual Example CMIX Input File blank End of haul data 1 This line must be present to indicate the end of the haul by haul data After this line the user may type any additional information they wish to record about the data file or anything else for that matter These lines are not read by the program e g blank Data are numbers of fish per square kilometre 35 CMIX User Manual CMIX Output File Format APPENDIX 3 CMIX Output File Format
30. g the lines of ERROR COULD NOT CONVERGE If this occurs then change the expected configuration of the mixtures or increase the maximum number of function calls that the program can use 6 3 Achieving a Good Fit Experience has shown that a good fit can often be obtained if you have a good understanding of the growth parameters Using the von Bertalannfy growth curve remember to take into account the difference between your sampling time and the birthday of the fish see Section 4 1 2 3 and Appendix 1 expected mean lengths at age can be determined Try fixing the mean lengths and allow the standard deviations to be linearly related to the means This often results in a better fit than setting the bounds around the expected mean The standard deviations around the mean should increase with increasing mean length 24 CMIX User Manual Tips When Fitting Mixtures When fixing means and allowing the standard deviations to be linearly related the following settings are a good starting point STARTING VALUE FOR INTERCEPT SEARCH 1 STEP LENGTH FOR INTERCEPT 0 STARTING VALUE FOR SLOPE SEARCH 0 05 6 4 Bias in length densities arising from gear selectivity or sampling pattern The sampling program may sample only a portion of the population If that is the case then some cohorts may not be sampled at all and or gear may selectively sample a specific size range Such information can be used to restrict the data used in the input file truncate
31. h CMIX For information on the correct structure of a CMIX input file please see Appendix 2 All data contained in the input file will automatically be loaded into the wizard ready for editing V To load an existing input file from a worksheet in the current Excel workbook select the required worksheet from the drop down list All data contained in the worksheet will be automatically loaded into the wizard ready for editing Note that the prefix used for the input worksheet will be used to name worksheets displaying output resulting from the CMIX run at a later point 4 1 2 Setting Mixture Component Bounds The Mixture Component Bounds tab Figure 6 specifies the bounds within which the means for each mixture component can be fitted You can choose whether to fix one or more of the means The bounds still need to be specified if you decide to fix the means There are 3 methods for setting the mixture component bounds as seen in Figure 6 CMIX Wizard Input Bounds Standard Deviation Haul Data Settings Add Bounds From Spreadsheet Would you like to fix the means No Sheet1 I 20 k 21 J Component Low Bound High Bound Fixed Mean Add Edit Bounds Component E Low Bound High Bound lt lt Method 2 Add Edit Remove Reset All Set von Bertalanffy Length Bounds Cancel lt lt Back MNext gt gt 11 CMIX User Manual Using CMIX Excel Add In Figure 6 Mixture Component
32. hday can be arbitrary and January 1 Arbitrary Birthday is date when animals are assumed to enter the next age year To Birthday Enter the time at which length is zero on the modelled growth trajectory K Growth Rate Enter the von Bertalanffy growth coefficient Linitinity MM Enter the maximum size in sample or population Proportion between Cohort Lengths Enter the value for the proportion between cohort lengths for use in generating bounds First Cohort Age Place here the age of the first cohort Number of Cohorts Required Enter the number of cohorts required APPENDIX 2 CMIX Input File Format CMIX requires a carefully formatted input file Sample data files are included on the distribution CD It is suggested that CMIX Excel Add In and CMIX Wizard be utilised in creating input files for CMIX as it already handles the complex formatting of the input file The input file must have the format of an MS DOS filename consisting of at most 8 characters followed by DATT extension Range checking is carried out on input data It is essential to have the correct number of data items and in the correct order With the combination of range checking and type checking it is extremely unlikely that the program will run if the number and order of items is incorrect In some places the types of items depend on the selection of an option The input is copied across to the output file and if you strike problems with getting the data file
33. ied with Components with means to be held constant 1 is end of list Component Fixed mean 1 0 This block enables the user to specify if any of the component means are to be held at a fixed value The first element on the line is the component number and the second element is the value of the mean The component number has to fall in the range of 1 to the number specified in the number of components line at the start of the file The fixed value has to fall within the bounds specified for that component In this particular example no means are to be held fixed because the only entry in the list is the end of list marker 1 0 There is a bug in the program If you have the same number of components in the fixed mean block as you have in the block above i e the bounds around the mean then you need to delete the blank line after the last line in the fixed mean block If you have an uneven number of components in the two blocks then you do not need to delete this line 29 CMIX User Manual Example CMIX Input File blank MIX Std Devs LINEARLY RELATED TRUE This line specifies whether the standard deviations for the mixture components are to be restricted to being linearly related Valid responses are YES NO TRUE or FALSE and depend only on the first letter and are case independent Thus responses yes true y and TRUE for example all evaluate to TRUE Similarly NO
34. m from the bounds The program also allows for various parameters to be held at fixed values For those parameters where the user does not have direct control of the step length such as the means and standard deviations the fixed values can be achieved by directly specifying those values in the data file For those parameters where the user does have direct control of the step length such as the parameters of a linear relationship between the mean and standard deviation fixed values can be achieved by setting the step length to zero Be warned this program calculates estimates by brute force computations can take several hours for large data files 1 3 Excel Add In A visual basic Add In for Excel CMIX_Excel_Add In xla is available which can be used to create CMIX Input files run CMIX and display CMIX output CMIX requires a detailed and precise input file format which users can find difficult to build CMIX Wizard a part of the excel Add In can be used to create the CMIX input files run CMIX and display the CMIX output The Excel Add In tool bar is shown in Figure 1 along with a schematic diagram of its options The toolbar contains three options CMIX Wizard Run CMIX and Display CMIX Output For a more detailed description see Section 4 CMIX v x N CMIX Wizard E Run CMIX kr Display CMIX Output Locate Input File or Ee Worksheet Locate Output File Or Worksheet Create Input File Display Output Figur
35. mber of Function Calls Minimum Reporting Frequency Stopping Criteria Using CMIX Excel Add In Figure 13 Settings Tab This parameter specifies whether estimates are to be made by minimising the residual function over the parameter space If not selected the residual function is evaluated once at the starting values of the parameters This parameter specifies the maximum number of function calls allowed in searching for the best fit to the data The value given here of 10 000 should be adequate in most cases The minimisation routine will report the parameters and residual function value at the regular intervals specified here This output is useful for checking that the procedure has converged reliably and on a minimum in the range covered in a given run A specified value less than zero inhibits reporting This is a technical parameter of the minimisation routine and controls how little the values of the residual function should vary with changes in the estimated parameters before the minimisation will end In other words the minimisation will end when the change in the residual function is smaller than or equal to the magnitude of the stopping criterion Failure of the procedure to converge even though the function reports indicate that convergence has occurred i e the residual function values in the final function calls are more or less the same is symptomatic that the stopping criterion is too small Conversely if there ar
36. mln p gt 1n6 er Z 1 5 Y nee Ela 2 T7 x gt 0 where N is the total number of observations and m is the number of non zero observations The last two terms are additive constants which can be ignored when maximising the likelihood function to calculate estimates In the method described here it is the densities for a given length class in each haul which constitute the xj Using Aitchison s 1955 brmulae the maximum likelihood estimate of the mean value of density in the j length class is d Sc CsN DER N x dr m 1 1 6 d 0 m 0 where y and s are the sample mean and sample variance of the log of the non zero observations and 1 aie t CAC P p Y gt Ual m lt m m 1 m 3 m 2j 3 j FQ Using a likelihood ratio approach Cox and Hinkley 1974 asymptotic confidence intervals on the mean density can be found as the roots of the following function p L A LY ik or 2 Y nz ON m X gt 0 m X gt 0 EI L x p A 07 1 8 o r k 0 lt o oi Es PG eee 0 lt pst n sa L x p o where is the critical value of the x distribution with one degree of freedom at the probability level The maximum likelihood estimates of the parameters of the mixture Sup x Supremum A supremum operator will take the asymptotic maximum of a function 6 CMIX User Manual Understanding The CMIX Model distribution are obtained by maximising the sums of
37. ndard Deviation Haul Data Settings Select Haul Data Sheet1 a 9 G 33 zj Haul data must be contained in a table with one column of bin bounds and subsequent columns of individual haul data for each bin interval The last bin must contain no haul data Bin Bound 0 0 0 0 0 0 0 0 1 oo OO oO co OO OH oo oo OO OO OH Les H BD H Bn BL BL BL Be CO OO OO OO OH J Merge Bins Cancel lt lt Back Next gt gt Figure 11 CMIX Wizard Haul Data Tab The Select Haul Data tool alows the user to select data from any table in the current worksheet Figure 12 The first column contains the bin interval boundary data and subsequent columns the haul data There is no limit on the number of bins or hauls The bin boundaries do not need to be all the same width The last bin however must contain no haul data as the bin boundaries in the table are lower bounds and the last bin bound closes off the last bin Haul data can be merged over several bins by using the Merge Bins button Select the rows of haul data in the table you wish to be merged and hit the Merge Bins button The haul data for each bin selected will be summed and placed in one new bin with the bounds of the bin ranging from the lowest to the highest bin selected This step is irreversible It is a useful function for grouping bins comprising of zeros or very low densities which can prevent the analysis from successfully minimising It is importa
38. nt of variation k the expected density in length class j is the sum of n distributions in the length interval of the j class given by EEE gt w where lj and lj 1 are the length bounds of the j length interval D is the total density of animals aged in the population denotes the cumulative standard normal function uj is the mean of the length distribution for animals of age The values of the Dj uj and k are estimated by finding the values for them which result in the dj having a good fit to the distribution of observed densities at length from surveys The assumption of a constant coefficient of variation is reasonable since it implies that older animals exhibit a greater range of lengths This assumption has the advantage of reducing the number of parameters to be estimated in fitting the model and ensures an orderly relationship between the variance estimated for each mixture component The estimated value of R t for the survey is given by R t a 1 3 D i t Only D and the sum of the Dj need to be estimated accurately The values of uj k and the individual D j j so are nuisance parameters We need be only concerned that their values provide a good fit to the data we are not particularly interested in their values except that they should be consistent with what is known about the biology of your organism The major problem for the analysis is that the existing methods are not applicable to
39. nt that all hauls are included in the input data even those where no fish were caught in any of the length bins 18 CMIX User Manual Using CMIX Excel Add In 28 27 19 43 EE Sheet1 B424 H 47 E 34 haul1 haul2 haul3 haul4 haul5 haul6 ojojojojojojojojojojo ojojojojojojolojojojojo N o r lt 0 40 88 303 88 D 40 88 694 56 13 75 40 88 1041 86 13 75 81 76 _ 1953 49 D 81 76 2648 07 13 75 122 64 2431 01 13 75 81 76 _ 1693 03 0 40 88 651 16 0 86 82 CO 0 D 0 D 0 0 0 0 D 0 D 0 0 0 Figure 12 Selecting Haul Data From An Excel Worksheet 4 1 5 Final CMIX Settings and Parameters The Settings Form Figure 13 accepts the instructions for visual output and sets some technical parameters See Table 2 for parameter descriptions From here the user can instruct CMIX Wizard to run CMIX and the output is automatically displayed upon completion See Section 4 4 for output details CMIX Wizard j x Input Bounds Standard Deviation Haul Data Settings Maximum Number OF Function Calls 10000 Minim Reporting Frequency 1 Stopping Criteria 1 E 6 oo Frequency For Convergence Testing 5 1 6 Simplex Expansion Coefficient Number Of Leading Intervals To Skip Display Input And Output in Current Workbook C Display Input nd Output in New workbook Run CMIX lt lt Back Cancel 19 CMIX User Manual Table 2 Parameters Minimisation Fit Quadratic Surface Maximum Nu
40. on value at the regular intervals specified here This output is useful for checking that the procedure has converged reliably and on a minimum in the range covered in a given run A specified value less than zero inhibits reporting STOPPING CRITERIA 1 E 6 This is a technical parameter of the minimisation routine and controls how little the values of the residual function should vary with changes in the estimated parameters before the minimisation will end In other words the minimisation will end when the change in the residual function is smaller than or equal to the magnitude of the stopping criterion Failure of the procedure to converge even though the function reports indicate that convergence has occurred i e the residual function values in the final function calls are more or less the same is symptomatic that the stopping criterion is too small Conversely if there are few function calls before convergence is reported combined with obvious variation remaining between values of the residual function indicates the stopping criterion is too large FREQUENCY FOR CONVERGENCE TESTING 5 FIT QUADRATIC SURFACE NO SIMPLEX EXPANSION COEFFICIENT 1 This is a minimisation routine technical parameter which only applies if quadratic surface fitting is enabled Adjusting it can improve the correspondence between the minima of the fitted quadratic and the minimum found by the search blank NUMBER OF LEADING INTERVALS TO SKIP 6
41. pe The lower bound on linear slope should be gt 0 if the constraint is to be enforced that the mixture standard deviations increase with the mean Set lower bound 0 if SD is to be constant Upper Bound on Linear Slope Upper bound on slope must be greater than the lowest bound Starting Value for Intercept Search Enter a starting value for Intercept search A reasonable starting point is 1 Enter the step length for intercept A good starting value is 0 1 If you don t want the starting value to change set to 0 0 Starting Value for Slope Search Enter a starting value for slope search a reasonable starting value is 0 05 If you don t want the starting value to change set to 0 0 Step Length for Slope Enter the step length for the slope a reasonable starting value is 0 005 If you don t want the starting value to change set to 0 0 NOTE When the starting value for the intercept and its step length are both set to zero the estimated slope is a constant coefficient of variation for the mixture components When the starting value and step length for the slope search are both set to zero the estimated intercept is a constant standard deviation for the mixture components The slope and intercept cannot both be simultaneously fixed at zero although either or both can be fixed at non zero values 4 1 3 2 Independent of Mean Standard Deviation Settings If the Independent tab is selected the standard deviations can tak
42. program prompts for the name of the file to plot and then iunit which specifies the output device iunit O plots to screen iunit 1 plots to screen iunit 2 plots to plotter iunit 3 plots to printer in portrait mode iunit 4 plots to printer in landscape mode e g input file name Plot05 dat iunit 1 23 CMIX User Manual Tips When Fitting Mixtures Section 6 Tips When Fitting Mixtures 6 1 Input Data Be very careful to format the input file correctly Using the Excel Add In will assist in producing the correct input for CMIX Include all valid samples data blocks including those with no catch 6 2 Output data Always check that the program has run to completion by carefully checking the results in the output file which is displayed by the Excel Add In as an appended worksheet e Check that in the Excel worksheet Name Results the sum of the observed densities should not differ by a large amount to the sum of the expected densities If you are getting a large difference between your observed and expected densities then alter the expected configuration of the mixtures Check that the program has been able to converge successfully during the minimisation procedure You can check this by scrolling up a number of pages in the Excel worksheet name_Output until you find the line END OF SEARCH This means the program has run successfully If the program couldn t converge it will tell you something alon
43. rent options see annotations to the input file that there is one extra bin boundary than there are data points that there is a blank line between the last block of data and the End of data 1 line that the number of leading zeros to skip is correct that the number of each data block is given consecutively beginning at 1 AQ CMIX User Manual APPENDIX 5 nl Lath ied Comde La a ied COl Din rei dra Pred ied ere Ee r LDR P n eg CMIX Excel Add In Worksheets CMIX Excel Add In Worksheets Figure 16 CMIX Input File Worksheet aa Zem 3 D I SI REKTHNS TCD en MEET eyy4cur NETEP EELEE EEI E bd we CS g m m m LE HESI ra 7 mm m E m x ox we Lal i o ap et ap ma am en au KEN mm ams mg vg mam w em ice ikiia wun id mwin seras b ata s D Mni tHomas D b eita s rupp Pires op zm mm zm at Te au mm am mat tu mmi am o ap al uN a mm 91 nn ap a mr r nn w Figure 17 CMIX Output File Worksheet 41 CMIX User Manual CMIX Excel Add In Worksheets 16a mu E o DE LILES LES HS PE Tobit Gere fore Figure 18 CMIX Distribution Worksheet Figure 19 CMIX Density Plot Worksheet 42 CMIX User Manual CMIX Excel Add In Worksheets Figure 20 CMIX Results Worksheet 43 CMIX User Manual Notes Your Notes CMIX User Manual References References Aitchison J 1955 On the distribution of a positive random
44. ribes the use of the CMIX Excel Add In and the format of both the input and output files CMIX can be used with without the CMIX Excel Add In 1 2 CMIX CMIX fits a mixture distribution to length density distributions see Section 1 derived from net survey data The function of the program is similar to the well known method of MacDonald and Pitcher 1979 However the mixture distribution is fitted using a maximum likelihood estimator that assumes that the length density data have an Aitcheson delta distribution Aitcheson 1955 see equation 4 4 This distribution is more suitable for describing densities estimated from net haul surveys because it provides for the possibility that a given survey haul will be empty The delta distribution includes a log normal distribution for the non zero density observations and a finite probability for a zero density estimate The current version of CMIX allows only for a mixture of normal distributions each with characteristic means and standard deviations of length The mixture distribution is parameterised so as to allow 1 Estimation of the density of fish in each mixture component cohort 2 Estimation of the proportion of recruits in the sample where recruits are taken to be represented by the first mixture component The program reads a data file which includes a specification of the distribution mixture to be fitted in terms of the number of mixture components boundary values on the means of tho
45. se components and possible restrictions on the standard deviations for the mixture components The standard deviations can be specified to be independent or linearly related Example By restricting the linear relationship it is possible to include constant standard deviations and constant coefficients of variation for the mixture components The data must be given as the haul by haul densities in each length interval Any hauls which included zero densities for all length intervals still need to be included in the data file because the zeros still contribute information about the mean density for each class Estimates are obtained by non linear minimisation of a residual function which is log likelinood The minimisation involves a search over the parameter values for the set of values which gives the minimum value of the residual function The minimisation routine 1 The procedure to implement R1 calculations will be detailed in the second version 1 CMIX User Manual Introduction requires for each parameter of the mixture distribution a starting value a step length to be used in searching and a set of bounds in which the search will be confined In the case where the mixture distribution standard deviations are linearly related all these values are specified directly by the user In the case of the mixture component means only the search bounds are specified suitable starting points and step lengths are calculated by the progra
46. ses for which all observations have zero density make no contribution to the likelinood function Therefore a mixture component in such regions may be completely spurious and hence bias the recruitment 31 CMIX User Manual Example CMIX Input File proportion In such cases constraints on the range of length classes to be included in the fit as well as on the mixture components are required to attempt to produce a sensible fit The goodness of fit plot is the principle method for using the program for these interactive adjustments PLOT RESIDUAL FUNCTION OVER P1 NO PLOT ON SCREEN YES PLOT ON PLOTTER NO PLOT ON PRINTER NO PLOT TO FILE YES Output devices for graphs If plots have been enabled If plots are saved to files they are automatically named PLOT DAT with the representing a two digit number which increases from 05 as the number of plots generated by the program during a fit increases If these files are to be retained they must be renamed to prevent them being overwritten by the next run of the program They can be viewed with the VTRANS program see below MAXIMUM NUMBER OF FUNCTION CALLS 10000 This parameter specifies the maximum number of function calls allowed in searching for the best fit to the data The value given here should be adequate in most cases 32 CMIX User Manual Example CMIX Input File MINIM REPORTING FREQUENCY 100 The minimisation routine will report the parameters and residual functi
47. such as arising from biases combined with a different mean size to take account of this Changing bin sizes as well as collapsing all the messy data into a single bin might help this as well See the discussion under data input concerning bin intervals 25 CMIX User Manual Tips When Fitting Mixtures 6 8 R1 The proportion of sample in first mixture component 6 9 Error Messages Most of the errors arising from using CMIX result from errors in formatting the input file see above It is hoped that the use of CMIX Wizard will dramatically reduce the number of errors users encounter Some points to note Input files must have DATT extension If you look in the output file it will show you when the program stopped and give you a clue where to make changes in the input file either formatting or input values Error 151 means that CMIX can t find the input file it could be missing named incorrectly or have more than 8 characters in the name If you get the error Root bracketed for ZBRENT then part of the minimisation was unable to be completed It is likely that you are asking too much of the program given the expected mixture distributions set up in the input file combined with the amount of data available you are likely to have too many zeros in your input data and you may not get a reliable result Although you can press the ENTER key several times to force the program continue this is not recommended as the result
48. ted with suitable parameters Click on the Enter New Values button to begin entering a new set of parameters See section 4 3 von Bertalanffy Equation for information about how the von Bertalanffy equation is used to estimate bounds and for information on the parameters used see Appendix 1 The Length vs Age plot generated using the von Bertalanffy equation can be viewed also Figure 8 Upon clicking the Set Bounds button if the parameters have been set correctly the wizard takes you back to the Mixture Component Bounds Form where the von Bertalanffy generated Bounds have been set automatically If the means on the bounds form were chosen to be fixed the fixed means are set along with the bounds User defined default von Bertalanffy parameters can be stored within the wizard for subsequent uses of the Add In Every time the Add In is closed or Excel is closed the default parameters are saved with the Add In for use at a later date To save a set of parameters give it a name in the Save Current Values As textbox and click the Save button To use a default set of values 12 CMIX User Manual Using CMIX Excel Add In choose a set from the Use Stored Values drop down list Be careful of not Create von Bertalanffy Length Bounds losing default von Bertalanffy parameters if you re install the software Figure 7 Create von Bertalanffy Length Bounds Form 13 CMIX User Manual Using C
49. the base directory of the CD This should handle the whole installation process on your PC The default installation directory is C Program Files CMIX It is recommended that you do not change the installation directory from this default directory Various ActiveX controls and Dynamic Linked Libraries DLL s are supplied in conjunction with this installation The setup process will prompt you if there are newer controls or DLL s on your system than those being installed Do not overwrite your system files in these cases Once the required files have been installed on some systems Excel is automatically launched and the CMIX Excel Add In is loaded You should see the CMIX Excel Add In menu bar which can be dragged to any location If Excel is not launched after completing the setup double click on the file Installation Directory install xls to have the Add In loaded for you The Add In will now be available to use with any Excel workbook If you wish to turn the Add In on or off at any stage on the Excel file menu choose Tools gt gt Add Ins and deselect or select the CMIX Excel Add In checkbox Installation Installation CMIX User Manual Installation 3 2 Uninstalling CMIX and Excel Add In If CMIX and the CMIX Excel Add In have been installed using the setup exe installation program use the following procedure to uninstall the software V In Excel choose the menu options Tools gt gt Add Ins and make sure th
50. variable having a discrete probability mass at the origin J Am Stat Assoc 50 901 908 de la Mare W K 1994a Estimating krill recruitment and its variability CCAMLR Science 1 55 69 de la Mare W K 1994b Modelling krill recruitment CCAMLR Science 1 MacDonald P D M and Pitcher T J 1979 Age groups from size frequency data a versatile and efficient method for analysing distribution mixtures J Fish Res Board Can 36 987 1001 Cox D R and Hinkley D V 1974 Theoretical Statistics Chapman and Hall London Pennington M 1983 Efficient estimators of abundance for fish and plankton surveys Biometircs 39 281 286 45
51. xcel Add In Toolbar 4 1 Using CMIX Wizard This section illustrates the use of CMIX Wizard to create input data suitable for running through CMIX CMIX requires a carefully formatted input file thus it is recommended that you use CMIX Wizard to create and edit your CMIX input files 4 1 1 Setting Input Details The first tab of the CMIX Wizard form Figure 5 may be used to create a new input file to run through to CMIX or to load an existing CMIX input file CMIX Wizard x Input Bounds Standard Deviation Haul Data Settings CMIX is a program for fitting mixture distributions to length density data obtained from net surveys using maximum likelihood estimation This wizard can be used as a tool to create suitable input Browse system for an existing CMIX run CMIX and display output CMIX input file CMIX Input Worksheet Icefishl z Si Data Description CMIX Input File Description About CMIX Cancel Next gt gt Figure 5 CMIX Wizard Input Tab 10 CMIX User Manual Using CMIX Excel Add In To create a new input file simply type in a new name for the worksheet that the input data will be loaded into The wizard will automatically append the name with Input Also enter a description for the input file you will be creating V To load an existing input file you may use the browse button to search for the input file The input file MUST contain data in the correct format suitable for running throug
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