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

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  • Salvatore D. Tomarchio
  • Antonio Punzo

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.

Suggested Citation

  • Salvatore D. Tomarchio & Antonio Punzo, 2025. "On the Number of Components for Matrix‐Variate Mixtures: A Comparison Among Information Criteria," International Statistical Review, International Statistical Institute, vol. 93(2), pages 222-245, August.
    • Handle: RePEc:bla:istatr:v:93:y:2025:i:2:p:222-245
    DOI: 10.1111/insr.12607
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    References listed on IDEAS

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    1. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
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    6. Tomarchio, Salvatore D. & Punzo, Antonio & Bagnato, Luca, 2020. "Two new matrix-variate distributions with application in model-based clustering," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
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    Cited by:

    1. Cappozzo, Andrea & Casa, Alessandro, 2025. "Model-based clustering for covariance matrices via penalized Wishart mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 212(C).
    2. Tomarchio, Salvatore D., 2025. "Heavy-tailed matrix-variate hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 211(C).

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