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

Year 2021, Volume: 4 Issue: 3, 143 - 149, 30.09.2021

Melek Eriş Büyükkaya , Nesrin Güler , Melike Yiğit

https://doi.org/10.33401/fujma.889229

Abstract

A linear mixed model ($\LMM$) $\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 $ 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.

Keywords

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

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