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

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 diffuse priors. Simulations show that even large numbers of closely spaced normal components can be identified with sufficiently large samples, while for latent classes with Bernoulli responses identification is more complex, though it again improves with increasing sample size. Copyright Sapienza Università di Roma 2015