A Bayesian regression model for circular data based on the projected normal distribution

Abstract

Inferences based on regression models for a directional response are usually problematic. This paper presents a Bayesian analysis of a regression model for circular data using the projected normal distribution. Inferences about the model are based on samples from the posterior densities which are obtained using the Gibbs sampler after the introduction of suitable latent variables. The problem of missing data in the response variable is also addressed in this context as is the use of a predictive criterion for model selection. The procedures are illustrated using two simulated datasets a dataset previously analysed in the literature and a real dataset concerning wind directions.