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

Abstract

A linear mixed model ($LMM$)$M :yy = mxXBETA+ mxZuu + EPS $ with general assumptions and its transformed model $T:mxTyy = mxTmxXBETA+ mxTmxZuu + mxTEPS $ 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 ($BLUP$s) of unknown vectors under two $LMM$s $M$and$T$ through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.