Constraints on Random Effects and Mixed Model Predictions

摘要

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 (2003) 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 (2010)'~([11]) weakened the conditions of his theorem, and obtained the same results as his. Wang (2010)~([12]) extended Mols's (2003) results to situation that X is deficient in rank. We give a series of results in this paper. They are all necessary and sufficient theorems.