Cattle and Sheep Growth REDUCED RANK ESTIMATES OF THE GENETIC COVARIANCE MATRIX FOR LIVE ULTRA-SOUND SCAN TRAITS

Multivariate restricted maximum likelihood analyses for a large data set comprising eight traits were carried out, estimating the leading 3, 4, 5 and 6 genetic principal components only. Traits were eye muscle area, percentage intra-muscular fat, and fat depth at the 12/13th rib and P8 sites, treating records on bulls and heifers or steers as different traits. The resulting, reduced rank estimates of genetic covariance matrices for analyses fitting 5 or 6 principal components agreed closely with an estimate from pooled, bivariate analysis. It is shown that reduced rank estimation can result in substantial reduction in computational requirements, compared to standard analyses fitting unstructured covariance matrices, and thus facilitate higher-dimensional multivariate analyses.