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Penalized factor mixture analysis for variable selection in clustered data

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  • Galimberti, Giuliano
  • Montanari, Angela
  • Viroli, Cinzia

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.

Suggested Citation

  • Galimberti, Giuliano & Montanari, Angela & Viroli, Cinzia, 2009. "Penalized factor mixture analysis for variable selection in clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4301-4310, October.
    • Handle: RePEc:eee:csdana:v:53:y:2009:i:12:p:4301-4310
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    References listed on IDEAS

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    2. McLachlan, G. J. & Peel, D. & Bean, R. W., 2003. "Modelling high-dimensional data by mixtures of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 379-388, January.
    3. Peter D. Hoff, 2005. "Subset Clustering of Binary Sequences, with an Application to Genomic Abnormality Data," Biometrics, The International Biometric Society, vol. 61(4), pages 1027-1036, December.
    4. Chris Fraley & Adrian E. Raftery, 2003. "Enhanced Model-Based Clustering, Density Estimation, and Discriminant Analysis Software: MCLUST," Journal of Classification, Springer;The Classification Society, vol. 20(2), pages 263-286, September.
    5. Raftery, Adrian E. & Dean, Nema, 2006. "Variable Selection for Model-Based Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 168-178, March.
    6. Chris Fraley & Adrian E. Raftery, 1999. "MCLUST: Software for Model-Based Cluster Analysis," Journal of Classification, Springer;The Classification Society, vol. 16(2), pages 297-306, July.
    7. Khalili, Abbas & Chen, Jiahua, 2007. "Variable Selection in Finite Mixture of Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1025-1038, September.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. Fraley C. & Raftery A.E., 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 611-631, June.
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    Cited by:

    1. Gilles Celeux & Cathy Maugis-Rabusseau & Mohammed Sedki, 2019. "Variable selection in model-based clustering and discriminant analysis with a regularization approach," 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. 13(1), pages 259-278, March.
    2. Bouveyron, Charles & Brunet-Saumard, Camille, 2014. "Model-based clustering of high-dimensional data: A review," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 52-78.
    3. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    4. Ahonen, Ilmari & Nevalainen, Jaakko & Larocque, Denis, 2019. "Prediction with a flexible finite mixture-of-regressions," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 212-224.
    5. Ouysse, Rachida & Kohn, Robert, 2010. "Bayesian variable selection and model averaging in the arbitrage pricing theory model," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3249-3268, December.
    6. Charles Bouveyron & Camille Brunet-Saumard, 2014. "Discriminative variable selection for clustering with the sparse Fisher-EM algorithm," Computational Statistics, Springer, vol. 29(3), pages 489-513, June.

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