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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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    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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