On the Number of Components for Matrix-Variate Mixtures: A Comparison Among Information Criteria

Abstract

This study explores the crucial task of determining the optimal number of components in mixture models, known as mixture order, when considering matrix-variate data. Despite the growing interest in this data type among practitioners and researchers, the effectiveness of information criteria in selecting the mixture order remains largely unexplored in this branch of the literature. Although the Bayesian information criterion (BIC) is commonly utilised, its effectiveness is only marginally tested in this context, and several other potentially valuable criteria exist. An extensive simulation study evaluates the performance of 10 information criteria across various data structures, specifically focusing on matrix-variate normal mixtures.