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

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<mark>Journal publication date</mark>21/08/2015
<mark>Journal</mark>Metron
Issue number2
Volume73
Number of pages21
Pages (from-to)155-175
Publication statusPublished
Early online date9/07/15
Original languageEnglish

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 (1990). For Bernoulli latent class mixtures we consider models for psychiatric diagnosis (Berkhof, van Mechelen and Gelman 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
atent classes with Bernoulli responses identification is more complex, though it again improves with increasing sample size.

Bibliographic note

(included in attached document) The final publication is available at Springer via http://dx.doi.org/10.1007/s40300-015-0068-1