Inference on state occupancy in covariate‐driven hidden Markov models

Hidden Markov models (HMMs) are natural and popular tools for analysing animal behaviour based on movement, acceleration and other sensor data. In particular, these models make it possible 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 primarily of ecological data using covariate‐driven HMMs is the models' interpretation, especially when there are more than two states, as then many 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 the covariate of interest, constitute a more concise and hence useful 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—often referred to as the stationary state probabilities—has in fact routinely been reported in HMM‐based analyses of ecological data. However, for stochastically varying covariate processes with relatively little persistence, we show that this approximation can be severely biased, hence potentially invalidating ecological inference based on the approximate version of this important summary statistic of interest.

In this contribution, we develop three alternative approaches for obtaining the state occupancy distribution as a function of a covariate of interest—two based on resampling of the covariate process and the third obtained by regression analysis of the empirical state probabilities. The practical application of these approaches is demonstrated in simulations and a case study on Galápagos 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 us to uncover the factors influencing behavioural decisions made by animals.