Rank Approach for Equality Relations of BLUPs in Linear Mixed Model and its Transformed Model

Abstract

A linear mixed model (LMM) M : y = Xβ + Zu + ε with general assumptions and its transformed model T : Ty = TXβ + TZu + Tε are considered. This work concerns the comparison problem of predictors under M and T . Our aim is to establish equality relations between the best linear unbiased predictors (BLUPs) of unknown vectors under two LMMs M and T through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.