Modeling of covariance structures of random effects and random errors in linear mixed models

Abstract

In this paper, we discuss how to model the mean and covariancestructures in linear mixed models (LMMs) simultaneously. We propose a data-driven method to modelcovariance structures of the random effects and random errors in the LMMs. Parameter estimation in the mean and covariances is considered by using EM algorithm, and standard errors of the parameter estimates are calculated through Louis’ (1982 Louis, T.A. (1982). Finding observed information using the EM algorithm. J. Royal Stat. Soc. B 44:98–130. Google Scholar]) information principle. Kenward’s (1987 Kenward, M.G. (1987). A method for comparing profiles of repeated measurements. Appl. Stat. 36:296–308.Crossref], Web of Science ®] , Google Scholar]) cattle data sets are analyzed for illustration,and comparison to the literature work is made through simulation studies. Our numerical analysis confirms the superiority of the proposed method to existing approaches in terms of Akaike information criterion.