Some Remarks on the Equalities of Predictors in Linear Mixed Models

Year 2021, Volume: 9 Issue: 4, 185 - 193, 31.12.2021

Melike Yiğit , Nesrin Güler , Melek Eriş Büyükkaya

https://doi.org/10.36753/mathenot.892258

Abstract

Consider a transformed linear mixed model (TLMM) obtained pre-multiplying a linear mixed model (LMM) M : y = Zα + Rγ + e by a given matrix. This work concerns the problem of the equalities of linear predictors under the considered two LMMs under general assumptions. We characterize the equalities between the best linear unbiased predictors (BLUPs) under the LMM and its TLMM by using various rank formulas of block matrices and elementary matrix operations.

Keywords

BLUP, equalities, linear mixed model, random vectors, transformed model

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