Fitting Nonlinear Mixed-Effects Models

Chapter Summary

This chapter describes the nonlinear modeling capabilities available in the nlme library. A brief review of the nonlinear least-squares function nls in S is presented and self-starting models for automatically producing starting values for the coefficients in a nonlinear model are introduced and illustrated. The nlsList function for fitting separate nonlinear regression models to data partitioned according to the levels of a grouping factor is described and its use for model building of nonlinear mixed-effects models illustrated.

Nonlinear mixed-effects models are fitted with the nlme function. Data from several real-life applications are used to illustrate the various capabilities available in nlme for fitting and analyzing single and multilevel NLME models. Variance functions and correlation structures to model the within group variance-covariance structure are used with nlme in the exact same way as with lme, the linear mixed-effects modeling function. Several examples are used to illustrate the use of varFunc and corStruct classes with nlme.

A new modeling function, gnls, for fitting the extended nonlinear model with heteroscedastic, correlated errors is introduced. The gnls function can be regarded as an extended version of nls which allows the use of varFunc and corStruct objects to model the error variance-covariance structure, or as a simplified version of nlme, without random effects. The hemodialyzer example is used to illustrate the use of gnls and its associated methods.