Page 96 - Linear Models for the Prediction of Animal Breeding Values 3rd Edition

Multivariate analysis Univariate analysis
Effects WWG PWG WWG PWG

Sex
Male 4.367 6.834 4.364 6.784
Female 3.657 6.007 3.648 5.873
Animal
1 0.130 0.266 0.077 0.273
2 −0.084 −0.075 −0.081 0.000
3 −0.098 −0.194 −0.058 −0.165
4 0.007 0.016 0.003 −0.025
5 −0.343 −0.555 −0.250 −0.463
6 0.192 0.440 0.098 0.517
7 −0.308 −0.483 −0.237 −0.460
8 0.201 0.349 0.143 0.392
9 −0.018 −0.119 0.010 −0.230

The differences for sex solutions for WWG from the multivariate and univariate
analyses are very similar to those in Section 5.2 since there are no missing records in
WWG. However, sex differences in the two analyses are different for PWG due to the
missing records. Again, most of the benefit in terms of breeding values from the mul-
tivariate analysis was observed in WWG, as explained in Section 5.2. However, for
the calves with missing records for PWG, there was a substantial change in their
proofs compared with the estimates from the univariate analysis. The proofs for these
calves for PWG are based on pedigree information only in the univariate analysis but
include information from the records for WWG in the multivariate analysis due to
the genetic and residual correlations between the two traits. Thus the inclusion of a
correlated trait in a multivariate analysis is of much benefit to animals with missing
records for the other trait.

5.4 Unequal Design Matrices

Unequal design matrices for different traits arise when traits in the multivariate analysis
are affected by different fixed or random effects – for instance, the multivariate analysis
of yields in different lactations as different traits. Due to the fact that calving in different
parities occur in different years, herd–year–season (HYS) effects associated with each
lactation are different, and an appropriate model should include different HYS for yield
in each parity. An example where random effects might be different for different traits is
the joint analysis for weaning weight and lean per cent in beef cattle. It might be consid-
ered that random maternal effect (see Chapter 7) is only important for weaning weight
and the model for the analysis will include maternal effects only for weaning weight.

5.4.1 Numerical example

Example 5.3
Using the fat yield data in Chapter 4 analysed with a repeatability model, the princi-
ples of a multivariate analysis with unequal design are illustrated below, considering

80 Chapter 5