Bayesian Estimation and Hypothesis Tests for a Circular GLM

Abstract

Circular data are data measured in angles or directions. Although they occur in a wide variety of scientific fields, the number of methods for their analysis is limited. We develop a GLM-like model for circular data within the Bayesian framework, using the von Mises distribution. The model allows inclusion of both continuous and categorical covariates. In a frequentist setting, this model is plagued by the likelihood surface of its regression coefficients, which is not log-concave. In a Bayesian context, a weakly informative prior solves this issue, while for other paramaters noninformative priors are available. In addition to an MCMC sampling algorithm, we develop Bayesian hypothesis tests based on the Bayes factor for both equality and inequality constrained hypotheses. In a simulation study, it can be seen that our method performs well. Finally, we apply this model to a dataset from experimental psychology, and show that it provides valuable insight for applied researchers. Extensions to dependent observations are within reach by means of the multivariate von Mises distribution.