Quantitating Significance in Finite Mixture Models and Model-Based Clustering

• Activity Number: 507
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Ranjan Maitra*+ and Volodymyr Melnykov
• Companies: Iowa State University and North Dakota State University
• Keywords: EM algorithm ; information matrix ; matrix derivatives ; model selection ; model-based clustering ; MixSim

Abstract

A new method is proposed to quantify significance in finite mixture models using an approach that calculates the $p$-value for testing a simpler against a more complex model and that is able to provide inference in cases where the use of the likelihood ratio test is limited because of the failure of regularity conditions. The developed testing procedure thus allows for pairwise comparison of any two mixture models with failure to reject the null hypothesis implying insignificant likelihood improvement under the more complex model. This leads to a comprehensive tool called the quantitation map which displays significance and quantitatively summarizes all model comparisons. We apply this map to decide on the best among a set of candidate mixture models in several simulated and real-world datasets, with very encouraging results.