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covariance_structure_of_correlated_random_effects_for_multiple_traits

The documentation is bit confusing on how to declare several correlated effects for several traits. Whereas renumf90 does this automatically for maternal effects models, it is not so obvious if one does it by itself. Llibertat Tusell and I put this together.

For instance terminal crosses models (e.g. |here) use:

• trait_pure: y = herd-year-season + u + e (animal)
• trait_crossbred : y = herd-year-season + s + e (sire of crossbred)

Thus we have two traits, purebred and crossbred performance, but effect u only affects purebreds and effect s only affects crossbreds. Data file has “animal” in column 4 and “sire” in column 5. Effect hys has respectively 12 and 25 levels.

1 0  12 cross
0 2  25 cross
4 0  3084 cross
0 5  3084 cross
...
RANDOM_GROUP
3 4
RANDOM_TYPE
FILE
../SNPgr/ped.txt
(CO)VARIANCES
10 0 0 5
0 0 0 0
5 0 0 12

Where we have a 4×4 matrix for covariances. In fact this corresponds to

Effect 3Effect 3Effect 4Effect 4
Trait 1 Trait2Trait1 Trait2
Effect 3Trait 1Var(u) 0 0Cov(u,s)
Effect 3Trait 2 0 0 0 0
Effect 4Trait 10 0 0 0
Effect 4Trait 2Cov(s,u) 0 0Var(s)