IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v22y2017i3d10.1007_s13253-017-0283-8.html
   My bibliography  Save this article

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

Author

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-017-0283-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-017-0283-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. 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.
    4. C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
    5. Roger Pradel, 2005. "Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States," Biometrics, The International Biometric Society, vol. 61(2), pages 442-447, June.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Anton Gerunov, 2023. "Stock Returns Under Different Market Regimes: An Application of Markov Switching Models to 24 European Indices," Economic Studies journal, Bulgarian Academy of Sciences - Economic Research Institute, issue 1, pages 18-35.
    5. Tardy, Olivia & Lenglos, Christophe & Lai, Sandra & Berteaux, Dominique & Leighton, Patrick A., 2023. "Rabies transmission in the Arctic: An agent-based model reveals the effects of broad-scale movement strategies on contact risk between Arctic foxes," Ecological Modelling, Elsevier, vol. 476(C).
    6. De Gooijer, Jan G. & Henter, Gustav Eje & Yuan, Ao, 2022. "Kernel-based hidden Markov conditional densities," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    7. 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.
    8. Timo Adam & Roland Langrock & Christian H. Weiß, 2019. "Penalized estimation of flexible hidden Markov models for time series of counts," METRON, Springer;Sapienza Università di Roma, vol. 77(2), pages 87-104, August.
    9. Antonello Maruotti & Antonio Punzo, 2021. "Initialization of Hidden Markov and Semi‐Markov Models: A Critical Evaluation of Several Strategies," International Statistical Review, International Statistical Institute, vol. 89(3), pages 447-480, December.
    10. Geir D. Berentsen & Jan Bulla & Antonello Maruotti & Bård Støve, 2022. "Modelling clusters of corporate defaults: Regime‐switching models significantly reduce the contagion source," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(3), pages 698-722, June.
    11. Mevin B. Hooten & Ruth King & Roland Langrock, 2017. "Guest Editor’s Introduction to the Special Issue on “Animal Movement Modeling”," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(3), pages 224-231, September.
    12. Giorgio E. Montanari & Marco Doretti, 2019. "Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(1), pages 307-326, November.
    13. Chimienti, Marianna & Desforges, Jean-Pierre & Beumer, Larissa T. & Nabe-Nielsen, Jacob & van Beest, Floris M. & Schmidt, Niels Martin, 2020. "Energetics as common currency for integrating high resolution activity patterns into dynamic energy budget-individual based models," Ecological Modelling, Elsevier, vol. 434(C).
    14. Roland Langrock & Timo Adam & Vianey Leos‐Barajas & Sina Mews & David L. Miller & Yannis P. Papastamatiou, 2018. "Spline‐based nonparametric inference in general state‐switching models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 179-200, August.
    15. Adam, Timo & Mayr, Andreas & Kneib, Thomas, 2022. "Gradient boosting in Markov-switching generalized additive models for location, scale, and shape," Econometrics and Statistics, Elsevier, vol. 22(C), pages 3-16.
    16. Gianluca Mastrantonio, 2022. "The modelling of movement of multiple animals that share behavioural features," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 932-950, August.
    17. 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.
    18. Marc A. Scott & Jean-Marie Goff & Jacques-Antoine Gauthier, 2024. "History matters: the statistical modelling of the life course," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(1), pages 445-469, February.
    19. Maruotti, Antonello & Petrella, Lea & Sposito, Luca, 2021. "Hidden semi-Markov-switching quantile regression for time series," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    20. Valeriy Zakamulin, 2023. "Not all bull and bear markets are alike: insights from a five-state hidden semi-Markov model," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-25, March.
    21. Floriane Cardiec & Sophie Bertrand & Matthew J Witt & Kristian Metcalfe & Brendan J Godley & Catherine McClellan & Raul Vilela & Richard J Parnell & François le Loc’h, 2020. "“Too Big To Ignore”: A feasibility analysis of detecting fishing events in Gabonese small-scale fisheries," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Liu, Hefei & Song, Xinyuan, 2021. "Bayesian analysis of hidden Markov structural equation models with an unknown number of hidden states," Econometrics and Statistics, Elsevier, vol. 18(C), pages 29-43.
    3. Azar, Pablo D. & Micali, Silvio, 2018. "Computational principal agent problems," Theoretical Economics, Econometric Society, vol. 13(2), May.
    4. Angelica Gianfreda & Francesco Ravazzolo & Luca Rossini, 2023. "Large Time‐Varying Volatility Models for Hourly Electricity Prices," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 545-573, June.
    5. Tobias Fissler & Yannick Hoga, 2024. "How to Compare Copula Forecasts?," Papers 2410.04165, arXiv.org.
    6. Davide Pettenuzzo & Francesco Ravazzolo, 2016. "Optimal Portfolio Choice Under Decision‐Based Model Combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(7), pages 1312-1332, November.
    7. Rubio, F.J. & Steel, M.F.J., 2011. "Inference for grouped data with a truncated skew-Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3218-3231, December.
    8. Oliver, Lauren J. & Morgan, Byron J.T. & Durant, Sarah M. & Pettorelli, Nathalie, 2011. "Individual heterogeneity in recapture probability and survival estimates in cheetah," Ecological Modelling, Elsevier, vol. 222(3), pages 776-784.
    9. Hwang, Eunju, 2022. "Prediction intervals of the COVID-19 cases by HAR models with growth rates and vaccination rates in top eight affected countries: Bootstrap improvement," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    10. R de Fondeville & A C Davison, 2018. "High-dimensional peaks-over-threshold inference," Biometrika, Biometrika Trust, vol. 105(3), pages 575-592.
    11. Armantier, Olivier & Treich, Nicolas, 2013. "Eliciting beliefs: Proper scoring rules, incentives, stakes and hedging," European Economic Review, Elsevier, vol. 62(C), pages 17-40.
    12. 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.
    13. Finn Lindgren, 2015. "Comments on: Comparing and selecting spatial predictors using local criteria," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 35-44, March.
    14. Chuliá, Helena & Garrón, Ignacio & Uribe, Jorge M., 2024. "Daily growth at risk: Financial or real drivers? The answer is not always the same," International Journal of Forecasting, Elsevier, vol. 40(2), pages 762-776.
    15. Laura Liu & Hyungsik Roger Moon & Frank Schorfheide, 2023. "Forecasting with a panel Tobit model," Quantitative Economics, Econometric Society, vol. 14(1), pages 117-159, January.
    16. Warne, Anders, 2023. "DSGE model forecasting: rational expectations vs. adaptive learning," Working Paper Series 2768, European Central Bank.
    17. James Mitchell & Aubrey Poon & Dan Zhu, 2024. "Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 790-812, August.
    18. Rafael Frongillo, 2022. "Quantum Information Elicitation," Papers 2203.07469, arXiv.org.
    19. Karimi, Majid & Zaerpour, Nima, 2022. "Put your money where your forecast is: Supply chain collaborative forecasting with cost-function-based prediction markets," European Journal of Operational Research, Elsevier, vol. 300(3), pages 1035-1049.
    20. Peysakhovich, Alexander & Plagborg-Møller, Mikkel, 2012. "A note on proper scoring rules and risk aversion," Economics Letters, Elsevier, vol. 117(1), pages 357-361.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jagbes:v:22:y:2017:i:3:d:10.1007_s13253-017-0283-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.