Joint estimation of breeding values and heterogeneous variances of large data files

A method is presented to estimate breeding values that corrects for phenotypic heterogeneous variances within herd-year. Heritabilities are assumed to be homogeneous. A multiplicative mixed model is used that simultaneously estimates breeding values and heterogeneity factors. Information on the other herd-years within a herd is used to improve the accuracy of the estimation of variances within herd-year by applying an autoregressive model to the herd-year variances. Estimates for the phenotypic heterogeneous variances account for differences among breed and genetic groups, relationships between animals, and reductions in variance from selection. This type of estimate avoids selection that favors animals from inferior breeds and genetic groups, from herds with closely related animals, and from later parities. The method is computationally feasible for the large data files used in the dairy industry. Computation time is about twice that needed without correction for heterogeneity. When applied to the Dutch national dairy data, the mean difference between the parent average and the EBV of progeny-tested bulls was reduced by 38% when heterogeneous variances were considered. Also, the variance of EBV minus parent average was reduced by 18%. The coefficient of variation of the heterogeneous variances was approximately 0.32. Variances hardly differed over the years within a herd (i.e., were homogeneous within herds). The latter suggests a simplified model with variances estimated within herds.