Bayesian Approach for Nonlinear Random Effects Models

In this paper we propose a general model determination strategy based on Bayesian methods for the nonlinear mixed effects models. Adopting an exploratory data analysis viewpoint we develop diagnostic tools based on conditional predictive ordinates which conveniently tie in with Markov Chain Monte Carlo (MCMC) fitting of models. Sampling based methods are used to carry out these diagnostics. Two examples are presented to illustrate the effectiveness of these criteria. The first one is the famous Langmuir equation, commonly used in pharmacokinetic models wheras the second model is used in growth curve model for longitudinal data problem. Key words: Longitudinal data, Metropolis-within-Gibbs algorithm, noninformative prior, nonlinear models, predictive distributions, pseudo Bayes factor, random effects models. * D.K. Dey is Professor, Department of Statistics , University of Connecticut, Storrs, CT 062693120, and H. Chang is a Consultant at Coopers Lybrand L.L.P., One International Plac...