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Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement

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Listed:
  • Jennifer Pohle

    (Bielefeld University)

  • Roland Langrock

    (Bielefeld University)

  • Floris M. Beest

    (Aarhus University)

  • Niels Martin Schmidt

    (Aarhus University)

Abstract

We discuss the notorious problem of order selection in hidden Markov models, that is of selecting an adequate number of states, highlighting typical pitfalls and practical challenges arising when analyzing real data. Extensive simulations are used to demonstrate the reasons that render order selection particularly challenging in practice despite the conceptual simplicity of the task. In particular, we demonstrate why well-established formal procedures for model selection, such as those based on standard information criteria, tend to favor models with numbers of states that are undesirably large in situations where states shall be meaningful entities. We also offer a pragmatic step-by-step approach together with comprehensive advice for how practitioners can implement order selection. Our proposed strategy is illustrated with a real-data case study on muskox movement. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • Jennifer Pohle & Roland Langrock & Floris M. Beest & Niels Martin Schmidt, 2017. "Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 270-293, September.
    • Handle: RePEc:spr:jagbes:v:22:y:2017:i:3:d:10.1007_s13253-017-0283-8
    DOI: 10.1007/s13253-017-0283-8
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    References listed on IDEAS

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    1. Roland Langrock & Thomas Kneib & Alexander Sohn & Stacy L. DeRuiter, 2015. "Nonparametric inference in hidden Markov models using P-splines," Biometrics, The International Biometric Society, vol. 71(2), pages 520-528, June.
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    4. Gilles Celeux & Jean-Baptiste Durand, 2008. "Selecting hidden Markov model state number with cross-validated likelihood," Computational Statistics, Springer, vol. 23(4), pages 541-564, October.
    5. Femke Broekhuis & Steffen Grünewälder & John W. McNutt & David W. Macdonald, 2014. "Optimal hunting conditions drive circalunar behavior of a diurnal carnivore," Behavioral Ecology, International Society for Behavioral Ecology, vol. 25(5), pages 1268-1275.
    6. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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