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Multiple-trait model with unequal design matrix

Model

When each trait has a different model, the design matrices are unequal. Even in this case, the matrix notation of the model and the mixed model equations are the same described as before.

BLUPF90 can handle a multiple-trait model with unequal design matrices in 2 ways. Both approaches provide the same results so the difference is only from a user’s preference ¹.

Files

The data are shown in the textbook at p.81, as a file data_mr05c.txt. This contains 2 different class effects and each trait takes an alternative one.

1. Animal ID (Cow)
2. Sire ID
3. Dam ID
4. HYS 1 (for Fat yield 1)
5. HYS 2 (for Fat yield 2)
6. Fat yield 1
7. Fat yield 2

The pedigree (pedigree_mr05c.txt) is from the previous example.

First, we show a parameter file to handle the unequal design matrices in one way.

DATAFILE
data_mr05c.txt
NUMBER_OF_TRAITS
2
NUMBER_OF_EFFECTS
2
OBSERVATION(S)
6 7
WEIGHT(S)

EFFECTS:
4 5 2 cross
1 1 8 cross
RANDOM_RESIDUAL VALUES
65.0 27.0
27.0 70.0
RANDOM_GROUP
2
RANDOM_TYPE
add_animal
FILE
pedigree_mr05c.txt
(CO)VARIANCES
35.0 28.0
28.0 30.0
OPTION solv_method FSPAK

Look at the first line in EFFECT: which refers to 2 different columns; column 4 for trait 1 and column 5 for trait 2. So you can put different effects together into the single statement. You should put the maximum number of levels among effects enumerated in this statement. For example, in this case, the maximum level in column 4 is 2 and the maximum number of level in column 5 is also 2 — so you can put 2 as the representative number of levels.

Solutions

This is identical to the textbook shown in p.82.

Another parameter file

BLUPF90 supports a different way to handle unequal design matrices. Consult the following parameter file with the same data and pedigree files.

DATAFILE
data_mr05c.txt
NUMBER_OF_TRAITS
2
NUMBER_OF_EFFECTS
3
OBSERVATION(S)
6 7
WEIGHT(S)

EFFECTS:
4 0 2 cross
0 5 2 cross
1 1 8 cross
RANDOM_RESIDUAL VALUES
65.0 27.0
27.0 70.0
RANDOM_GROUP
3
RANDOM_TYPE
add_animal
FILE
pedigree_mr05c.txt
(CO)VARIANCES
35.0 28.0
28.0 30.0
OPTION solv_method FSPAK

In this parameter file, the fixed effect for each trait is separately defined. The column number will be 0 for a trait which doesn’t need the effect. In this case, the first line describes the effect \(HYS_1\) and only the first trait needs this effect (so you should put 0 to the second trait). Note that the Gibbs sampling programs (including GIBBS2F90 and THRGIBBS1F90) accept only this style.

You can immediately find the results are identical to the previous ones. Some effects (\(HYS_1\) for trait 2 and \(HYS_2\) for trait 1) are not estimated because they are not defined in the parameter file.

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