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Dealing with label switching in mixture models under genuine multimodality

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  • Grn, Bettina
  • Leisch, Friedrich

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.

Suggested Citation

  • Grn, Bettina & Leisch, Friedrich, 2009. "Dealing with label switching in mixture models under genuine multimodality," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 851-861, May.
  • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:851-861
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    References listed on IDEAS

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    1. 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.
    2. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    3. Hardy, Andre, 1996. "On the number of clusters," Computational Statistics & Data Analysis, Elsevier, vol. 23(1), pages 83-96, November.
    4. Leisch, Friedrich, 2006. "A toolbox for K-centroids cluster analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 526-544, November.
    5. 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.
    6. Michael Brusco & J. Cradit, 2001. "A variable-selection heuristic for K-means clustering," Psychometrika, Springer;The Psychometric Society, vol. 66(2), pages 249-270, June.
    7. 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.
    8. repec:dau:papers:123456789/6069 is not listed on IDEAS
    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, November.
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    Cited by:

    1. Leonardo Grilli & Maria Iannario & Domenico Piccolo & Carla Rampichini, 2014. "Latent class CUB models," 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. 8(1), pages 105-119, March.
    2. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 2016. "Bayesian analysis of static and dynamic factor models: An ex-post approach towards the rotation problem," Journal of Econometrics, Elsevier, vol. 192(1), pages 190-206.
    3. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    4. Aßmann, Christian & Boysen-Hogrefe, Jens & Pape, Markus, 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 (IfW Kiel).
    5. Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2021. "Bayes estimates of multimodal density features using DNA and Economic Data," Tinbergen Institute Discussion Papers 21-017/III, Tinbergen Institute.

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