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Choosing the number of clusters in a finite mixture model using an exact integrated completed likelihood criterion

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  • Marco Bertoletti
  • Nial Friel
  • Riccardo Rastelli

Abstract

The integrated completed likelihood (ICL) criterion has proven to be a very popular approach in model-based clustering through automatically choosing the number of clusters in a mixture model. This approach effectively maximises the complete data likelihood, thereby including the allocation of observations to clusters in the model selection criterion. However for practical implementation one needs to introduce an approximation in order to estimate the ICL. Our contribution here is to illustrate that through the use of conjugate priors one can derive an exact expression for ICL and so avoiding any approximation. Moreover, we illustrate how one can find both the number of clusters and the best allocation of observations in one algorithmic framework. The performance of our algorithm is presented on several simulated and real examples. Copyright Sapienza Università di Roma 2015

Suggested Citation

  • Marco Bertoletti & Nial Friel & Riccardo Rastelli, 2015. "Choosing the number of clusters in a finite mixture model using an exact integrated completed likelihood criterion," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 177-199, August.
    • Handle: RePEc:spr:metron:v:73:y:2015:i:2:p:177-199
    DOI: 10.1007/s40300-015-0064-5
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. McDaid, Aaron F. & Murphy, Thomas Brendan & Friel, Nial & Hurley, Neil J., 2013. "Improved Bayesian inference for the stochastic block model with application to large networks," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 12-31.
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    1. Marco Alfó & Francesco Bartolucci, 2015. "Latent variable models for the analysis of socio-economic data," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 151-154, August.
    2. M. Corneli & E. Erosheva & X. Qian & M. Lorenzi, 2025. "A Bayesian approach for clustering and exact finite-sample model selection in longitudinal data mixtures," Computational Statistics, Springer, vol. 40(1), pages 509-545, January.
    3. Engel, Christoph, 2020. "Estimating heterogeneous reactions to experimental treatments," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 124-147.
    4. Lorenzoni, Valentina & Triulzi, Isotta & Martinucci, Irene & Toncelli, Letizia & Natilli, Michela & Barale, Roberto & Turchetti, Giuseppe, 2021. "Understanding eating choices among university students: A study using data from cafeteria cashiers’ transactions," Health Policy, Elsevier, vol. 125(5), pages 665-673.
    5. Etienne Côme & Nicolas Jouvin & Pierre Latouche & Charles Bouveyron, 2021. "Hierarchical clustering with discrete latent variable models and the integrated classification likelihood," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 957-986, December.

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