Latent class model with conditional dependency per modes to cluster categorical data

Matthieu Marbac (), Christophe Biernacki and Vincent Vandewalle
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Matthieu Marbac: McMaster University
Christophe Biernacki: University Lille 1 and CNRS and Inria Lille
Vincent Vandewalle: EA 2694 University Lille 2 and Inria Lille

Advances in Data Analysis and Classification, 2016, vol. 10, issue 2, No 5, 183-207

Abstract: Abstract We propose a parsimonious extension of the classical latent class model to cluster categorical data by relaxing the conditional independence assumption. Under this new mixture model, named conditional modes model (CMM), variables are grouped into conditionally independent blocks. Each block follows a parsimonious multinomial distribution where the few free parameters model the probabilities of the most likely levels, while the remaining probability mass is uniformly spread over the other levels of the block. Thus, when the conditional independence assumption holds, this model defines parsimonious versions of the standard latent class model. Moreover, when this assumption is violated, the proposed model brings out the main intra-class dependencies between variables, summarizing thus each class with relatively few characteristic levels. The model selection is carried out by an hybrid MCMC algorithm that does not require preliminary parameter estimation. Then, the maximum likelihood estimation is performed via an EM algorithm only for the best model. The model properties are illustrated on simulated data and on three real data sets by using the associated R package CoModes. The results show that this model allows to reduce biases involved by the conditional independence assumption while providing meaningful parameters.

Keywords: Categorical data; Clustering; Integrated complete-data likelihood; MCMC algorithm; Mixture models; Model selection; 62H30; 62F15; 62-07; 62F07 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11634-016-0250-1

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