Exploring Some Analytical Characteristics of Finite Mixture Models

Finite mixture models have become increasingly prevalent in criminology over the past two decades. Yet there is no consensus about the appropriate criterion for model selection with finite mixture specifications. In this paper, we use simulation evidence to examine model selection criteria. Our focus is on mixture models for event count data like those often encountered in criminology. We use two indices to measure model selection performance. First, we examine how often each criterion chooses the correct specification. Then, we investigate how closely the finite mixture models selected by these criteria approximate the true mixing distribution used to simulate the event count data. We consider three sets of simulations. In the first set, the underlying model is itself a three component Poisson-based finite mixture model. In the two other sets of simulations, the underlying distribution of the Poisson rate parameter follows a continuous distribution. The analysis shows that both AIC and BIC perform well under certain sets of circumstances likely to be encountered by criminologists.