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Dealing with label switching in mixture models under genuine multimodality

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  • Grn, Bettina
  • Leisch, Friedrich
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    Abstract

    The fitting of finite mixture models is an ill-defined estimation problem, as completely different parameterizations can induce similar mixture distributions. This leads to multiple modes in the likelihood, which is a problem for frequentist maximum likelihood estimation, and complicates statistical inference of Markov chain Monte Carlo draws in Bayesian estimation. For the analysis of the posterior density of these draws, a suitable separation into different modes is desirable. In addition, a unique labelling of the component specific estimates is necessary to solve the label switching problem. This paper presents and compares two approaches to achieve these goals: relabelling under multimodality and constrained clustering. The algorithmic details are discussed, and their application is demonstrated on artificial and real-world data.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 100 (2009)
    Issue (Month): 5 (May)
    Pages: 851-861

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:851-861

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    Keywords: 62H30 62F15 Constrained clustering Finite mixture models Label switching Multimodality;

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    References

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    1. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer, vol. 2(1), pages 193-218, December.
    2. Marin, Jean-Michel & Mengersen, Kerrie & Robert, Christian P., 2005. "Bayesian Modelling and Inference on Mixtures of Distributions," Economics Papers from University Paris Dauphine 123456789/6069, Paris Dauphine University.
    3. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    4. Hardy, Andre, 1996. "On the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 83-96, November.
    5. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer, vol. 66(2), pages 249-270, June.
    6. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    7. Robert Tibshirani & Guenther Walther & Trevor Hastie, 2001. "Estimating the number of clusters in a data set via the gap statistic," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 411-423.
    8. Chung H. & Loken E. & Schafer J.L., 2004. "Difficulties in Drawing Inferences With Finite-Mixture Models: A Simple Example With a Simple Solution," The American Statistician, American Statistical Association, vol. 58, pages 152-158, May.
    9. Jerome H. Friedman & Jacqueline J. Meulman, 2004. "Clustering objects on subsets of attributes (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 815-849.
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    Cited by:
    1. Christian AƟmann & Jens Boysen-Hogrefe & Markus Pape, 2014. "Bayesian Analysis of Dynamic Factor Models: An Ex-Post Approach towards the Rotation Problem," Kiel Working Papers 1902, Kiel Institute for the World Economy.
    2. Leonardo Grilli & Maria Iannario & Domenico Piccolo & Carla Rampichini, 2014. "Latent class CUB models," Advances in Data Analysis and Classification, Springer, vol. 8(1), pages 105-119, March.

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