Assessing a Bayesian Embedding Approach to Circular Regression Models

Circular data is different from linear data and its analysis also requires methods different from conventional methods. In this study a Bayesian embedding approach to estimating circular regression models is investigated, by means of simulation studies, in terms of performance, efficiency, and flexibility. A new Markov chain Monte Carlo (MCMC) sampling method is proposed and contrasted to an existing method. An empirical example of a regression model predicting teachers' scores on the interpersonal circumplex will be used throughout. Performance and efficiency are better for the newly proposed sampler and reasonable to good in most situations. Furthermore, the method in general is deemed very flexible. Additional research should be done that provides an overview of what circular data looks like in practice, investigates the interpretation of the circular effects and examines how we might conduct a way of hypothesis testing or model checking for the embedding approach.