where

The design matrix for Trait has a level (column) for each trait.

Trait.Cov fits the covariate Cov for each variate. ASReml internally rearranges the data so that

Orange Wether Trial 1984-8 SheepID !I TRIAL BloodLine !I TEAM * YEAR * GFW YLD FDIAM wether.dat !skip 1 GFW FDIAM ~ Trait Trait.YEAR, # Fixed model !r Trait.TEAM Trait.SheepID # Random model predict YEAR Trait 1 2 2 # Variance header 1485 0 ID # units structure Trait 0 US # traits structure 3*0 Trait.TEAM 2 # First G header Trait 0 US !GP 3*0 TEAM 0 ID Trait.SheepID 2 # Second G header Trait 0 US !GP 3*0 SheepID 0 ID

independent records and

an unstructured variance matrix across traits;

1485 0 ID, could be replaced by

0 or

0 0 ID ; this tells ASReml to fill in the number of units and is a useful option when the exact number of units in the data is not known to the user,

3 * 0

Three initial values for the matrix are required being the lower triangle of the (symmetric) matrix specified row-wise.

Finding reasonable initial values can be a problem. If initial values are written on the next line in the form

ASReml will take half of the phenotypic variance matrix of the data as an initial value.

the use of 3*0 in lieu of estimates of initial values; ASReml again substitutes a proportion of the observed variance covariance matrix of the data.

ASReml 1.63o [01 Jun 2005] Orange Wether Trial 1984-88 Build: j [01 Jul 2005] 32 bit 13 Jul 2005 09:38:00.928 32.00 Mbyte Windows wether Licensed to: Arthur Gilmour Folder: C:\data\asr\UG2\manex TAG !I BloodLine !I QUALIFIERS: !SKIP 1 Reading wether.dat FREE FORMAT skipping 1 lines Bivariate analysis of GFW and FDIAM Using 1485 records of 1485 read Model term Size #miss #zero MinNon0 Mean MaxNon0 1 TAG 521 0 0 1 261.0956 521 2 TRIAL 0 0 3.000 3.000 3.000 3 BloodLine 27 0 0 1 13.4323 27 4 TEAM 35 0 0 1 18.0067 35 5 YEAR 3 0 0 1 2.0391 3 6 GFW Variate 0 0 4.100 7.478 11.20 7 YLD 0 0 60.30 75.11 88.60 8 FDIAM Variate 0 0 15.90 22.29 30.60 9 Trait 2 10 Trait.YEAR 6 9 Trait : 2 5 YEAR : 3 11 Trait.TEAM 70 9 Trait : 2 4 TEAM : 35 12 Trait.TAG 1042 9 Trait : 2 1 TAG : 521 1485 identity 2 UnStructure 0.2000 0.2000 0.4000 2970 records assumed sorted 2 within 1485 2 UnStructure 0.4000 0.3000 1.3000 35 identity Structure for Trait.TEAM has 70 levels defined 2 UnStructure 0.2000 0.2000 2.0000 521 identity Structure for Trait.TAG has 1042 levels defined Forming 1120 equations: 8 dense. Initial updates will be shrunk by factor 0.316 Notice: Algebraic ANOVA Denominator DF calculation is not available Empirical derivatives will be used. NOTICE: 2 singularities detected in design matrix. 1 LogL=-886.521 S2= 1.0000 2964 df 2 LogL=-818.508 S2= 1.0000 2964 df 3 LogL=-755.911 S2= 1.0000 2964 df 4 LogL=-725.374 S2= 1.0000 2964 df 5 LogL=-723.475 S2= 1.0000 2964 df 6 LogL=-723.462 S2= 1.0000 2964 df 7 LogL=-723.462 S2= 1.0000 2964 df 8 LogL=-723.462 S2= 1.0000 2964 df Source Model terms Gamma Component Comp/SE \verb Residual UnStru 2 1 0.128890 0.128890 12.40 0 U Residual UnStru 2 2 0.440601 0.440601 21.93 0 U Trait.TEAM UnStru 1 1 0.374493 0.374493 3.89 0 U Trait.TEAM UnStru 2 1 0.388740 0.388740 2.60 0 U Trait.TEAM UnStru 2 2 1.36533 1.36533 3.74 0 U Trait.TAG UnStru 1 1 0.257159 0.257159 12.09 0 U Trait.TAG UnStru 2 1 0.219557 0.219557 5.55 0 U Trait.TAG UnStru 2 2 1.92082 1.92082 14.35 0 U Covariance/Variance/Correlation Matrix UnStructured 0.4360 is the correlation Trait.TEAM 0.1984 0.4360 0.1289 0.4406 Covariance/Variance/Correlation Matrix UnStructured 0.3745 0.5436 0.3887 1.365 Covariance/Variance/Correlation Matrix UnStructured 0.2572 0.3124 0.2196 1.921 Wald F statistics Source of Variation NumDF DenDF F-inc Prob 9 Trait 2 33.0 5761.58 <.001 10 Trait.YEAR 4 1162.2 1094.90 <.001 Notice: The DenDF values are calculated ignoring fixed/boundary/singular variance parameters using empirical derivatives. Solution Standard Error T-value T-prev 10 Trait.YEAR 2 -0.102262 0.290190E-01 -3.52 3 1.06636 0.290831E-01 36.67 42.07 5 1.17407 0.433905E-01 27.06 6 2.53439 0.434880E-01 58.28 32.85 9 Trait 1 7.13717 0.107933 66.13 2 21.0569 0.209095 100.71 78.16 11 Trait.TEAM 70 effects fitted 12 Trait.TAG 1042 effects fitted SLOPES FOR LOG(ABS(RES)) on LOG(PV) for Section 1 1.00 1.54 10 possible outliers: see .res file Finished: 13 Jul 2005 09:38:05.725 LogL Converged