Approximation of Estimates of (Co)variance Components with Multiple-Trait Restricted Maximum Likelihood by Multiple Diagonalization for More Than One Random Effect

¹ University of Illinois, Urbana 61801
² Holstein Association, Brattleboro. VT 05301

Canonical transformation for REML can be applied to models with several random effects by simultaneously diagonalizing (co)variance matrices for all random effects. This procedure is an approximation when matrices cannot be diagonalized completely. The level of the approximation was studied with simulated data by comparing multiple diagonalization and exact REML estimates. For a range of diagonalization levels, the error of the estimates was 2 to 10 times lower than the fraction of non-diagonalizable (co)variances because 57 to 91% of these variances were recovered after the backtransformation step. To determine whether REML by multiple diagonalization is successful with real data, a study used 98,113 records of 44,765 Holstein cows for 14 conformation traits. Effects included in the model were herd classification, animal with unknown parent groups, and permanent environmental effects. Estimates of (co)-variance components were on average 5% higher for type compared with estimates from an earlier analysis using only first records, but the estimate for udder cleft increased 2.4 times. Correlations for the permanent environmental effect were within .1 of genetic correlations. Multi-trait REML by multiple diagonalization provides accurate multiple-trait estimates for repeatability models more efficiently than general model REML.

Key Words: variance components • restricted maximum likelihood • diagonalization algorithm • canonical transformation

Submitted on November 16, 1994
Accepted on April 3, 1995

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