Comparison of multiplicative heterogeneous variance adjustment models for genetic evaluations

Two heterogeneous variance adjustment methods and two variance models were compared in a simulation study. The method used for heterogeneous variance adjustment in the Nordic test-day model, which is a multiplicative method based on Meuwissen (J. Dairy Sci., 79, 1996, 310), was compared with a restricted multiplicative method where the fixed effects were not scaled. Both methods were tested with two different variance models, one with a herd-year and the other with a herd-year-month random effect. The simulation study was built on two field data sets from Swedish Red dairy cattle herds. For both data sets, 200 herds with test-day observations over a 12-year period were sampled. For one data set, herds were sampled randomly, while for the other, each herd was required to have at least 10 first-calving cows per year. The simulations supported the applicability of both methods and models, but the multiplicative mixed model was more sensitive in the case of small strata sizes. Estimation of variance components for the variance models resulted in different parameter estimates, depending on the applied heterogeneous variance adjustment method and variance model combination. Our analyses showed that the assumption of a first-order autoregressive correlation structure between random-effect levels is reasonable when within-herd heterogeneity is modelled by year classes, but less appropriate for within-herd heterogeneity by month classes. Of the studied alternatives, the multiplicative method and a variance model with a random herd-year effect were found most suitable for the Nordic test-day model for dairy cattle evaluation.