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Order selection in finite mixture models: Complete or observed likelihood information criteria?


Hui, FKC and Warton, DI and Foster, SD, Order selection in finite mixture models: Complete or observed likelihood information criteria?, Biometrika, 102, (3) pp. 724-730. ISSN 0006-3444 (2014) [Refereed Article]

Copyright Statement

Copyright 2015 Biometrika Trust

DOI: doi:10.1093/biomet/asv027


Choosing the number of components in a finite mixture model is a challenging task. In this article, we study the behaviour of information criteria for selecting the mixture order, based on either the observed likelihood or the complete likelihood including component labels. We propose a new observed likelihood criterion called aicmix, which is shown to be order consistent. We further show that when there is a nontrivial level of classification uncertainty in the true model, complete likelihood criteria asymptotically underestimate the true number of components. A simulation study illustrates the potentially poor finite-sample performance of complete likelihood criteria, while aicmix and the Bayesian information criterion perform strongly regardless of the level of classification uncertainty.

Item Details

Item Type:Refereed Article
Keywords:complete likelihood, missing data, mixture of regression models, model selection, order consistency
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Stochastic analysis and modelling
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Foster, SD (Dr Scott Foster)
ID Code:119533
Year Published:2014
Web of Science® Times Cited:14
Deposited By:Directorate
Deposited On:2017-08-02
Last Modified:2017-09-15

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