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

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  • 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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    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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    14. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov 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. 16(2), pages 457-485, June.
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    16. Michela Gnaldi & Simone Del Sarto, 2024. "Validating Corruption Risk Measures: A Key Step to Monitoring SDG Progress," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 175(3), pages 1045-1071, December.
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    18. Joseph D. Bailey & Edward A. Codling, 2021. "Emergence of the wrapped Cauchy distribution in mixed directional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 229-246, June.
    19. Lin, Yong & Huang, Mian, 2025. "Penalized composite likelihood estimation for hidden Markov models with unknown number of states," Statistics & Probability Letters, Elsevier, vol. 216(C).
    20. Kristina M Ceres & Ynte H Schukken & Yrjö T Gröhn, 2020. "Characterizing infectious disease progression through discrete states using hidden Markov models," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-14, November.
    21. Marius Ötting & Dimitris Karlis, 2023. "Football tracking data: a copula-based hidden Markov model for classification of tactics in football," Annals of Operations Research, Springer, vol. 325(1), pages 167-183, June.
    22. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    23. Ethan Lawler & Kim Whoriskey & William H. Aeberhard & Chris Field & Joanna Mills Flemming, 2019. "The Conditionally Autoregressive Hidden Markov Model (CarHMM): Inferring Behavioural States from Animal Tracking Data Exhibiting Conditional Autocorrelation," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(4), pages 651-668, December.
    24. De Gooijer, Jan G. & Henter, Gustav Eje & Yuan, Ao, 2022. "Kernel-based hidden Markov conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).

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