Mixture of linear mixed models using multivariate t distribution

Abstract

Linear mixed models are widely used when multiple correlated measurements are made on each unit of interest. In many applications, the units may form several distinct clusters, and such heterogeneity can be more appropriately modelled by a finite mixture linear mixed model. The classical estimation approach, in which both the random effects and the error parts are assumed to follow normal distribution, is sensitive to outliers, and failure to accommodate outliers may greatly jeopardize the model estimation and inference. We propose a new mixture linear mixed model using multivariate t distribution. For each mixture component, we assume the response and the random effects jointly follow a multivariate t distribution, to conveniently robustify the estimation procedure. An efficient expectation conditional maximization algorithm is developed for conducting maximum likelihood estimation. The degrees of freedom parameters of the t distributions are chosen data adaptively, for achieving flexible trade-off between estimation robustness and efficiency. Simulation studies and an application on analysing lung growth longitudinal data showcase the efficacy of the proposed approach.

Keywords:

• ECM algorithm
• linear mixed models
• longitudinal data
• mixture models
• multivariate t distribution

Acknowledgments

The authors thank the editor, the associate editor, and reviewers for their constructive comments that have led to a dramatic improvement of the earlier version of this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

Yao's research is supported by NSF grant DMS-1461677.