An Alternative Estimation Approach for the Heterogeneity Linear Mixed Model

Abstract

In this article, an alternative estimation approach is proposed to fit linear mixed effects models where the random effects follow a finite mixture of normal distributions. This heterogeneity linear mixed model is an interesting tool since it relaxes the classical normality assumption and is also perfectly suitable for classification purposes, based on longitudinal profiles. Instead of fitting directly the heterogeneity linear mixed model, we propose to fit an equivalent mixture of linear mixed models under some restrictions which is computationally simpler. Unlike the former model, the latter can be maximized analytically using an EM-algorithm and the obtained parameter estimates can be easily used to compute the parameter estimates of interest.

Keywords:

• Heterogeneous model
• EM-algorithm
• Linear mixed model
• Mixture model
• Repeated measurements

Mathematics Subject Classification:

• 62J05
• 62H12