A new Bayesian approach for determining the number of components in a finite mixture

Abstract

This article evaluates a new Bayesian approach to determining the number of components in a finite mixture. We evaluate through simulation studies mixtures of normals and latent class mixtures of Bernoulli responses. For normal mixtures we use a "gold standard" set of population models based on a well-known "testbed" data set - the galaxy recession velocity data set of Roeder (J Am Stat Assoc 85:617-624, 1990). For Bernoulli latent class mixtures we consider models for psychiatric diagnosis Berkhof et al. (Stat Sin 13:423-442, 2003). The new approach is based on comparing models with different numbers of components through their posterior deviance distributions, based on non-informative or d..