Two Taylor-series approximation methods for nonlinear mixed models

Abstract

This paper considers a general class of nonlinear mixed models (NLMMs). In view of the often difficult numerical integrations involved in a full likelihood analysis of general NLMMs, we discuss two approximate inference procedures, both based on Taylor-series approximations to the integrated likelihood. The two methods differ in the Taylor-series expansion point for the random-effects parameters: the first method expands around zero (the expected value of the random effects) and the second around their empirical best linear unbiased predictors (EBLUPs). We present new algorithms for implementing both approximations and relate them to existing algorithms. Finally, we assess the performance of both methods through simulation, and conclude that the EBLUP-expansion method offers minor gains in accuracy over the zero-expansion method at the cost of higher computing times and instability.