Estimation of Variances and Covariances under Multiple Trait Models

Abstract

An algorithm is described for minimum variance quadratic unbiased estimation of additively genetic and environmental covariance matrices in the multiple trait model. This method has the undesirable property of producing solutions not in the parameter space. Presented are restricted maximum likelihood and maximum likelihood algorithms of the expectation-maximization type and guaranteed to converge in the parameter space. If selection has occurred with consequent alteration of the covariance structure of additive genetic values and errors, it appears that restricted maximum likelihood, maximum likelihood, and minimum variance quadratic unbiased estimators with good priors remove most of the bias due to selection in estimation of the parameters before selection commenced. These are the parameters needed for unbiased prediction of breeding values in a selection model. © 1984, American Dairy Science Association. All rights reserved.