Adjustment for heterogeneous covariance due to herd milk yield by transformation of test-day random regressions

A method of accounting for differences in covariance
components of test-day milk records was developed
based on transformation of regressions for random effects.
Preliminary analysis indicated that genetic and
nongenetic covariance structures differed by herd milk
yield. Differences were found for phenotypic covariances
and also for genetic, permanent environmental,
and herd-time covariances. Heritabilities for test-day
milk yield tended to be lower at the end and especially
at the start of lactation; they also were higher (maximum
of ∼25%) for high-yield herds and lower (maximum
of 15%) for low-yield herds. Permanent environmental
variances were on average 10% lower in highyield
herds. Relative herd-time variances were ∼10%
at start of lactation and then began to decrease regardless
of herd yield; high-yield herds increased in midlactation
followed by another decrease, and medium-yield
herds increased at the end of lactation. Regressors for
random regression effects were transformed to adjust
for heterogeneity of test-day yield covariances. Some
animal reranking occurred because of this transformation
of genetic and permanent environmental effects.
When genetic correlations between environments were
allowed to differ from 1, some additional animal reranking
occurred. Correlations of variances of genetic
and permanent-environmental regression solutions
within herd, test-day, and milking frequency class with
class mean milk yields were reduced with adjustment
for heterogeneous covariance. The method suggests a
number of innovative solutions to issues related to heterogeneous
covariance structures, such as adjusted estimates
in multibreed evaluation.