In this paper, we discuss how to model the mean and covariance structures in linear mixed models (LMMs), simultaneously. We propose a data-driven method to model covariance 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) information principle. Kenward’s (1987) 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.