A time-dependent extension of the projected Normal regression model for longitudinal circular data based on a hidden Markov heterogeneity structure

The modelling of animal movement is an important ecological andenvironmental issue. It is well-known that animals change their movementpatterns over time, according to observable and unobservable factors. To tracethe dynamics of behaviors, to identify factors in uencing these dynamics andunobserved characteristics driving intra-subjects correlations, we introduce atime-dependent mixed eects projected normal regression model. A set ofanimal-specic parameters following a hidden Markov chain is introduced todeal with unobserved heterogeneity. For the maximum likelihood estimationof the model parameters, we outline an Expectation-Maximization algorithm.A large-scale simulation study provides evidence on model behavior. The dataanalysis approach based on the proposed model is nally illustrated by anapplication to a dataset, which derives from a population of Talitrus saltatorfrom the beach of Castiglione della Pescaia (Italy).