Abstract
A restricted maximum likelihood procedure is described to estimate variance and covariance components in a multivariate mixed model when records are missing for some traits. The algorithm combines features of an expectation-maximization algorithm to estimate the within random effects components with the method of scoring to estimate the between random effects components. The procedure is computationally less demanding per round of iteration than the method of scoring, although the number of iterates required to reach convergence is increased. A computing strategy is described for the example of estimating genetic parameters for first and later lactations of dairy cows.