Time-discretization approximation enriches continuous-time discrete-space models for animal movement

Abstract

Continuous time discrete state models are a valuable tool for explaining animal movement. However, data collection to fit such models over a specified window of time can be misaligned with the actual realization of the movement process. This necessitates approximate model fitting, at present, through approximate imputation distributions (AIDs). Here, we propose a direct time-discretization approximation to the likelihood. The approach employs familiar ideas from hidden Markov modeling. Computation is implemented through the induced infinitesimal generator matrix. Linearization of this matrix expedites computation time. Through simulation and a real data application involving whale movement, we demonstrate that this model fitting strategy can outperform AID approaches.