Inertia and rank approach in transformed linear mixed models for comparison of BLUPs
Nesrin Güler, Melek Eriş Büyükkaya
Abstract
This paper is concerned with comparison problems of predictors between a linear mixed model (LMM) that includes both fixed and random effects and its transformed model under general assumptions. Our aim is to establish a variety of equalities and inequalities for comparing covariance matrices of the best linear unbiased predictors (BLUPs) of unknown vectors under the models by using various inertia and rank formulas of block matrices. We also give some results for special transformed models such as submodels of original LMMs by applying the results obtained for general cases.
Topics & Concepts
Rank (graph theory)MathematicsGeneralized linear mixed modelMixed modelBest linear unbiased predictionVariety (cybernetics)CovarianceLinear modelInertiaBlock (permutation group theory)Random effects modelApplied mathematicsStatisticsArtificial intelligenceComputer scienceCombinatoricsSelection (genetic algorithm)Internal medicineClassical mechanicsMeta-analysisMedicinePhysicsMatrix Theory and AlgorithmsStatistical and numerical algorithmsScientific Research and Discoveries