Adjustment for Heterogeneous (Co)Variances in Test-Day Models by Transformation of Random Regressors

N. Gengler,* G.R. Wiggans, and A. Gillion

*National Fund for Scientific Research, B-1000 Brussels, Belgium
Animal Science Unit, Gembloux Agricultural University, B-5030 Gembloux, Belgium
Animal Improvement Programs Laboratory , Agricultural Research Service,
USDA, Beltsville, MD 20705-2350

Received December 31, 2003.
Accepted ? ?, 2004.
Corresponding author: N. Gengler; e-mail: gengler.n@fsagx.ac.be

2004 J. Dairy Sci. (?)
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ABSTRACT

A method of accounting for differences in (co)variance components of test-day milk records was developed based on transformation of regressors for random regression effects. Preliminary analysis indicated that genetic and nongenetic (co)variance structures differed by herd milk yield. Differences were found for phenotypic (co)variances and also for heritability, permanent environmental, and herd-time (co)variances. Heritabilities for test-day milk yield were higher (maximum of ~25%) for high-yield herds and lower (maximum of 15%) for low-yield herds. Permanent environmental variances had the opposite trend and averaged 10% lower in high-yield 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 end of lactation. Regressors for random regression effects were transformed to adjust for heterogeneity of test-day yield (co)variances. 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 (co)variance. The method suggests a number of innovative solutions to issues related to heterogeneous (co)variance structures, such as adjusted estimates in multibreed evaluation.

(Key words: heterogeneous (co)variance, (co)variance structure, test-day yield, random regression)

Abbreviation key: EM = expectation maximization, HV = heterogeneous (co)variance, RRM = random regression model.