A Review of Conditions Under Which Blues and/or Blups in One Linear Mixed Model are also Blues and/or Blups in Another

Abstract

Abtsrcat The linear mixed model, with its combination of fixed and random parameters, plays a central role in many statistical applications. Here we review results on conditions for best linear unbiased estimates (BLUEs) of estimable functions of fixed parameters under one linear mixed model to remain BLUEs under a second model, which difiers from the first in covariance structure. Without making full rank assumptions for design matrices or covariance matrices, we also review results for the conditions under which best linear unbiased predictors (BLUPs) of random parameters under the first model remain BLUPs under the second model, and for the conditions under which both BLUEs and BLUPs under the first model remain the BLUEs and BLUPs under the second. We also provide a rather generous list of related references.