Bayesian estimation and hypothesis tests for a circular Generalized Linear Model

Abstract

Motivated by a study from cognitive psychology, we develop a Generalized Linear Model for circular data within the Bayesian framework, using the von Mises distribution. Although circular data arise in a wide variety of scientific fields, the number of methods for their analysis is limited. Our model allows inclusion of both continuous and categorical covariates. In a frequentist setting, this type of model is plagued by the likelihood surface of its regression coefficients, which is not logarithmically concave. In a Bayesian context, a weakly informative prior solves this issue, while for other parametersnoninformative 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. The analyses are available in the package CircGLMBayes. 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.