A Bayesian approach to inequality constrained linear mixed models: estimation and model selection

Abstract

Constrained parameter problems arise in a wide variety of applications. This article deals with estimation and model selection in linear mixed models with inequality constraints on the parameters. It is shown that different theories can be translated into statistical models by putting constraints on the model parameters yielding a set of competing models. A new approach based on the principle of encompassing priors is proposed and used to compute Bayes factors and subsequently posterior model probabilities. Model selection is based on posterior model probabilities. The approach is illustrated using a longitudinal data set.