Bayesian approach to circular-linear regression with application

Circular data is measured in degrees or radians on a circle. It is a common data type that exists everywhere in the real world. However, it has different statistical properties compared to linear data. The majority of existing circular-linear regression models employ classic solutions such as maximum likelihood estimation; however, it is easy to fall into the local maximum trap. There have been numerous approaches to circular-linear regression models, but relatively few have employed the Bayesian approach. This study investigates the intrinsic approach to implementing circular-linear regression from the Bayesian perspective, which assumes the residuals are distributed as von Mises distribution. The model is then applied to real data comprising German political parties’ economic and social policy preferences, demonstrating model fitting, inference, and prediction. The results show that each party has its own preferred direction, and some economic and social indicators have less influence on the overall results.