Bayesian analysis for nonlinear mixed‐effects models under heavy‐tailed distributions

Abstract

A common assumption in nonlinear mixed-effects models is the normality of both random effects and within-subject errors. However, such assumptions make inferences vulnerable to the presence of outliers. More flexible distributions are therefore necessary for modeling both sources of variability in this class of models. In the present paper, I consider an extension of the nonlinear mixed-effects models in which random effects and within-subject errors are assumed to be distributed according to a rich class of parametric models that are often used for robust inference. The class of distributions I consider is the scale mixture of multivariate normal distributions that consist of a wide range of symmetric and continuous distributions. This class includes heavy-tailed multivariate distributions, such as the Student's t and slash and contaminated normal. With the scale mixture of multivariate normal distributions, robustification is achieved from the tail behavior of the different distributions. A Bayesian framework is adopted, and MCMC is used to carry out posterior analysis. Model comparison using different criteria was considered. The procedures are illustrated using a real dataset from a pharmacokinetic study. I contrast results from the normal and robust models and show how the implementation can be used to detect outliers.