Linear Mixed Models with Heterogeneous within-Cluster Variances

This paper describes an extension of linear mixed models to allow for heterogeneous within-cluster variances in the analysis of clustered data. Unbiased estimating equations based on quasilikelihood/pseudolikelihood and method of moments are introduced and are shown to give consistent estimators of the regression coefficients, variance components, and heterogeneity parameter under regularity conditions. Cluster-specific random effects and variances are predicted by the posterior modes. The method is illustrated through an analysis of menstrual diary data and its properties are evaluated in a simulation study.