Mixed-Effects Models in S and S-PLUS

Abstract

In this chapter the linear mixed-effects model of Chapters 2 and 4 is extended to include heteroscedastic, correlated within-group errors. We show how the estimation and computational methods of Chapter 2 can be extended to this more general linear mixed-effects model. We introduce several classes of variance functions to characterize heteroscedasticity and several classes of correlation structures to represent serial and spatial correlation, and describe how variance functions and correlations structures can be combined to flexibly model the within-group variance-covariance structure. We illustrate, through several examples, how the lme function is used to fit the extended linear mixed-effects model and describe a suite of S classes and methods to implement variance functions (varFunc) and correlation structures (corStruct). Any of these classes, or others defined by users, can be used with lme to fit extended linear mixed-effects models. An extended linear model with heteroscedastic, correlated errors is introduced and a new modeling function to fit it, gls, is described. This extended linear model can be thought of as an extended linear mixed-effects model with no random effects, and any of the varFunc and corStruct classes available with lme can also be used with gls. Several examples are used the illustrate the use of gls and its associated methods.