Abstract
The pseudo-expectation (PE) methods for estimating variance components in the mixed linear models are equivalent to the restricted maximum likelihood (REML) procedure in the balanced case, but are a variety of the approximations in the unbalanced case. In animal breeding applications, the PE methods are used, for instance, to quickly obtain an initial value in the REML estimation. In this article, we reveal that the PE approach can never be defined under the so-called individual animal model, when each animal has only one record. We then exploit the use of another sort of animal models, or the so-called reduced animal model, in the PE approach and present sets of the possible quadratic forms. It is shown that the current PE procedure actually performs numerically, as expected, but the sampling variance of the estimator is quite likely to be relatively large, and the similarity of the current estimate to the REML estimate would considerably be affected by the given data structure, definitely indicating the necessity of further theoretical investigation for the improved procedure.
