Inference on state occupancy in covariate-driven hidden Markov models

Abstract

Hidden Markov models (HMMs) are popular tools for analysing animal behaviour based on movement, acceleration and other sensor data. In particular, these models allow to infer how the animal's decision-making process interacts with internal and external drivers, by relating the probabilities of switching between distinct behavioural states to covariates. A key challenge arising in the statistical analysis of behavioural data using covariate-driven HMMs is the models' interpretation, especially when there are more than two states, as then several functional relationships between state-switching probabilities and covariates need to be jointly interpreted. The model-implied probabilities of occupying the different states, as a function of a covariate of interest, constitute a much simpler summary statistic. A pragmatic approximation of the state occupancy distribution, namely the hypothetical stationary distribution of the model's underlying Markov chain for fixed covariate values, has in fact routinely been reported in HMM-based analyses of ecological data. However, for stochastically varying covariates with relatively little persistence, we show that this approximation can be severely biased, potentially invalidating ecological inference. We develop two alternative approaches for obtaining the state occupancy distribution as a function of a covariate of interest - one based on resampling of the covariate process, the other obtained by regression analysis of the empirical state probabilities. The practical application of these approaches is demonstrated in simulations and a case study on Gal\'apagos tortoise (Chelonoidis niger) movement data. Our methods enable practitioners to conduct unbiased inference on the relationship between animal behaviour and general types of covariates, thus allowing to uncover the factors influencing behavioural decisions made by animals.