Theory and Computational Methods for Nonlinear Mixed-Effects Models

Chapter Summary

This chapter presents the theoretical foundations of the nonlinear mixed-effects model for single- and multilevel grouped data, including the general model formulation and its underlying distributional assumptions. Efficient computational methods for maximum likelihood estimation in the NLME model are described and discussed. Different approximations to the NLME model log-likelihood with varying degrees of accuracy and computational complexity are derived.

The basic NLME model with independent, homoscedastic within-group errors is extended to allow correlated, heteroscedastic within-group errors and efficient computational methods are described for maximum likelihood estimation of its parameters.

An extended class of nonlinear regression models, with correlated and heteroscedastic errors, but with no random effects, is presented. An efficient maximum likelihood estimation algorithm is described and approximate inference results for the parameters in this extended nonlinear regression are presented.