Identical Predictions for Different Singular Mixed Models

Abstract

In linear mixed models theory one is assumed to know the structure of random effects covariance matrix. The suggestions are sometimes contradictious, especially if the model includes interactions between fixed effects and random effects. Mols [3] presented conditions under which two different random effects’ variance matrices will yield equal estimation and prediction results during the paper it is assumed that X is of full column rank. Wang [11] weakened the conditions of his theorem, and obtained the same results as his. Wang [12] extended Mols’s [3] results to situation that X is deficient in rank. Wang [13] gave a series of results it is assumed that X is possibly deficient in rank. They contain some necessary and sufficient theorems. We extend Wang’s [11-13] results to singular linear mixed models in this paper.