Regression analysis of correlated circular data based on the multivariate von Mises distribution

A regression model for correlated circular data is proposed by assuming that samples of angular measurements are drawn from a multivariate von Mises distribution with mean and concentration parameters that depend on covariates through link functions. The model can flexibly accommodate heteroscedasticity, unstructured correlation, and specific autoregressive correlation structures. Because the computation of the normalizing constant of the multivariate von Mises distribution is unfeasible, inference is based on a computationally tractable Monte Carlo approximation of the log-likelihood. These methods are illustrated by fitting a number of regression models in two case studies: a longitudinal study of animal orientation, involving multiple time series of directional observations, and a study of marine currents, involving a spatial series of sea current directions.