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

• Published in: Journal of agricultural, biological, and environmental statistics Vol. 22; no. 3; pp. 270 - 293
• Main Authors: Pohle, Jennifer, Langrock, Roland, van Beest, Floris M., Schmidt, Niels Martin
• Format: Journal Article
• Language: English
• Published: New York Springer 01-09-2017; Springer US; Springer Nature B.V
• Subjects: Agriculture; Biostatistics; Case studies; Computer simulation; Data processing; Health Sciences; Markov analysis; Markov chains; Markov processes; Mathematics and Statistics; Medicine; Monitoring/Environmental Analysis; Order picking; Statistics; Statistics for Life Sciences; Selection bias; Information criteria; Animal movement; Unsupervised learning
• ISSN: 1085-7117; 1537-2693
• DOI: 10.1007/s13253-017-0283-8

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.