Extension of Basic Linear Mixed Effect Model to Incorporate Heterocedasticity

The linear mixed effect model allows considerable flexibility in the specification of the random effects structure but restricts the within group errors to be independent, identically distributed random variables with mean zero and constant variance. In this paper the linear mixed-effects model is extended to include heteroscedastic errors. In this paper several classes of variance functions to characterize heteroscedasticity are introduced. We describe how the lme() function can be used to fit the extended linear mixed effects model and illustrate its various capabilities through examples. Also we will show the estimation and computational methods of simple linear mixed effect models can be applied to the extended model.