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A mixture model-based approach to the clustering of exponential repeated data

Author

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  • Martinez, M.J.
  • Lavergne, C.
  • Trottier, C.

Abstract

The analysis of finite mixture models for exponential repeated data is considered. The mixture components correspond to different unknown groups of the statistical units. Dependency and variability of repeated data are taken into account through random effects. For each component, an exponential mixed model is thus defined. When considering parameter estimation in this mixture of exponential mixed models, the EM-algorithm cannot be directly used since the marginal distribution of each mixture component cannot be analytically derived. In this paper, we propose two parameter estimation methods. The first one uses a linearisation specific to the exponential distribution hypothesis within each component. The second approach uses a Metropolis-Hastings algorithm as a building block of a general MCEM-algorithm.

Suggested Citation

  • Martinez, M.J. & Lavergne, C. & Trottier, C., 2009. "A mixture model-based approach to the clustering of exponential repeated data," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1938-1951, October.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:1938-1951
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    References listed on IDEAS

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    1. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    2. Biernacki, Christophe & Celeux, Gilles & Govaert, Gerard, 2003. "Choosing starting values for the EM algorithm for getting the highest likelihood in multivariate Gaussian mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 561-575, January.
    3. Wilfried Seidel & Karl Mosler & Manfred Alker, 2000. "A Cautionary Note on Likelihood Ratio Tests in Mixture Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(3), pages 481-487, September.
    4. 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.
    5. Christian Lavergne & Marie-José Martinez & Catherine Trottier, 2008. "Empirical model selection in generalized linear mixed effects models," Computational Statistics, Springer, vol. 23(1), pages 99-109, January.
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    Cited by:

    1. Charlotte Articus & Jan Pablo Burgard, 2014. "A Finite Mixture Fay Herriot-type model for estimating regional rental prices in Germany," Research Papers in Economics 2014-14, University of Trier, Department of Economics.

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