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) 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.

Keywords:

• Covariance modeling
• Expectation-Maximization (EM) algorithm
• Linear mixed models
• Longitudinal data

Mathematics Subject Classification:

• Primary: MSC62F99, Secondary: MSC62J99

Acknowledgments

We gratefully acknowledge very helpful and constructive comments and suggestions made by an associate editor and an anonymous referee which led to significant improvements to the paper.

Funding

This research was supported by the grants from the National Natural Science Foundation of China (11061036, 11561071) for Y. Fei and Y. T. Pan; and the Fundamental Research Funds for the Central Universities in UIBE (10QD34) for Y. Chen.