Exact Prediction Error Variances for Full Model Computed from Reduced Model

Abstract

The coefficient matrix for mixed model equations is often too large to invert for obtaining prediction error variances and for computing estimates of variances and covariances. Reduced, but equivalent, models can be written that have many fewer elements in the u vector than in the full model. The resulting reduced coefficient matrix can then be inverted in some cases. This paper presents a method for computing a g-inverse of the full coefficient matrix by a set of linear functions of a g-inverse for the reduced model. Two examples are presented, a non-additive genetic model and an animal model.