Selecting the Number of States in Hidden Markov Models: Pragmatic Solutions Illustrated Using Animal Movement
- 415 Downloads
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.
KeywordsAnimal movement Information criteria Selection bias Unsupervised learning
- Biernacki, C., Celeux, G. & Govaert, G. (2013), Assessing a mixture model for clustering with the integrated completed likelihood IEEE Transactions on pattern analysis and machine intelligence, 22, 719–725.Google Scholar
- DeRuiter, S.L., Langrock, R., Skirbutas, T., Goldbogen, J.A., Calambokidis, J., Friedlaender, A.S. & Southall, B.L. (in press), A multivariate mixed hidden Markov model for blue whale behaviour and responses to sound exposure. Annals of Applied Statistics, 11, 362–392.Google Scholar
- Leos-Barajas, V., Photopoulou, T., Langrock, R., Patterson, T.A., Watanabe, Y.Y., Murgatroyd, M. & Papastamatiou, Y.P. (in press), Analysis of animal accelerometer data using hidden Markov models. Methods in Ecology and Evolution, 8, 161–173.Google Scholar
- Li, M. & Bolker, B.M. (2017), Incorporating periodic variability in hidden Markov models for animal movement Movement Ecology, 5, DOI: 10.1186/s40462-016-0093-6.
- Patterson, T.A., Parton, A., Langrock, R., Blackwell, P.G., Thomas, L. & King, R. (2016), Statistical modelling of animal movement: a myopic review and a discussion of good practice. arXiv:1603.07511.