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

Eriş Büyükkaya M., Güler N., Yiğit M.

Fundamental journal of mathematics and applications (Online), vol.4, no.3, pp.143-149, 2021 (Peer-Reviewed Journal) identifier

Abstract

A linear mixed model (\LMM" role="presentation" >\LMM\LMM) \M:\yy=\mxX\BETA+\mxZ\uu+\EPS" role="presentation" >\M:\yy=\mxX\BETA+\mxZ\uu+\EPS\M:\yy=\mxX\BETA+\mxZ\uu+\EPS with general assumptions and its transformed model \T:\mxT\yy=\mxT\mxX\BETA+\mxT\mxZ\uu+\mxT\EPS" role="presentation" >\T:\mxT\yy=\mxT\mxX\BETA+\mxT\mxZ\uu+\mxT\EPS\T:\mxT\yy=\mxT\mxX\BETA+\mxT\mxZ\uu+\mxT\EPS are considered. This work concerns the comparison problem of predictors under \M" role="presentation" >\M\M and \T" role="presentation" >\T\T. Our aim is to establish equality relations between the best linear unbiased predictors (\BLUP" role="presentation" >\BLUP\BLUPs) of unknown vectors under two \LMM" role="presentation" >\LMM\LMMs \M" role="presentation" >\M\M and \T" role="presentation" >\T\T through their covariance matrices by using various rank formulas of block matrices and elementary matrix operations.

Keywords  BLUP, covariance matrix, linear mixed model, rank, transformed model