On the Estimation of Variances Within Herd-Mean Production Groups

Abstract

In investigating heterogeneity of variance among herd groups, herds are often grouped according to their mean production, and variances are estimated within such groups using a sire model. Stratifying herds in this way may be a form of “selection” on sire progeny groups, resulting in herd production groups with a selected sample of sires, causing a “pseudoheterogeneity” of variance to be estimated. A selection effect was not found for balanced nested and cross-classified designs, For a balanced design, the only biased estimate of the sire variance is obtained for the limited case of selection directly on progeny group means, with the absence of any fixed effects other than a mean. For unbalanced designs, the bias depends on the distribution of regressions of progeny means on herd means and is likely to be negligible in most practical analyses in which there is substantial variation within herds due to environmental effects.