Exploring Some Analytical Characteristics of Finite Mixture Models |
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Authors: | Robert Brame Daniel S Nagin Larry Wasserman |
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Institution: | (1) Department of Criminology and Criminal Justice, University of South Carolina, Columbia, SC 29208, USA;(2) H. John Heinz III School of Public Policy and Management, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA;(3) Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA |
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Abstract: | 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.
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Keywords: | finite mixture models semi-parametric trajectories AIC BIC simulations |
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