Penalized factor mixture analysis for variable selection in clustered data

Authors:
Giuliano Galimberti;Angela Montanari;Cinzia Viroli
Affiliations:
Dipartimento di Scienze Statistiche, Alma Mater Studiorum - Universití di Bologna, via Belle Arti 41, 40126 Bologna, Italy;Dipartimento di Scienze Statistiche, Alma Mater Studiorum - Universití di Bologna, via Belle Arti 41, 40126 Bologna, Italy;Dipartimento di Scienze Statistiche, Alma Mater Studiorum - Universití di Bologna, via Belle Arti 41, 40126 Bologna, Italy
Venue:
Computational Statistics & Data Analysis
Year:
2009

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Abstract

A model-based clustering approach which contextually performs dimension reduction and variable selection is presented. Dimension reduction is achieved by assuming that the data have been generated by a linear factor model with latent variables modeled as Gaussian mixtures. Variable selection is performed by shrinking the factor loadings though a penalized likelihood method with an L1 penalty. A maximum likelihood estimation procedure via the EM algorithm is developed and a modified BIC criterion to select the penalization parameter is illustrated. The effectiveness of the proposed model is explored in a Monte Carlo simulation study and in a real example.