Sampling behaviour of reduced rank estimates of genetic covariance functions

A simulation study investigating relative errors and sampling variances of reduced rank estimates of genetic covariance functions from random regression analyses estimating the leading principal components only, is presented. The example considered pertains to covariance functions for growth of beef cattle. It is demonstrated that the leading principal components are estimated most accurately, and that reduced rank estimates yield estimates of covariance functions with similar errors than full rank estimates. Furthermore, it is shown that substantial repartitioning between genetic and permanent environmental covariances can occur if either is modelled with too few principal components. Results emphasize the need for a judicious choice among the possible combinations of rank of fit for different ovariance functions.