Estimation of Components of Variance by Method 3 and Henderson's New Method

Abstract

An algorithm for Method 3 for estimation of components of variance in a mixed model including fixed [cattle] herd-year-season, genetic groups and random sires nested within groups is presented. Computational aspects of the algorithm are discussed and compared with those of a new method of Henderson''s. The new method involves equating quadratic forms based on approximate best linear unbiased prediction solutions to their expected values. Relative computing effort for the 2 methods depended on the ease of eliminating equations for fixed effects and on the number of traits. Numerical estimates from the 2 methods were similar. When the method 3 estimate of the sire component of variance was not close to zero, the new method rapidly converged during iteration even when the a priori variance component ratio was not close to the final estimate.