Regressing over Linear-Circular Data Using a Mixture of Linear-Linear Regression Models

Regression over circular response data requires special methods due to the periodic nature of this data type. In previous works, researchers tried to use the concept of projecting real-line distributions on unit circles or using transformation methods to transform circular response to real-line and wise versa; however, their methods only work for simple data and in some cases they are really complicated and slow. In this research circular responses are treated as the output of the modulo operation on unobserved linear responses. A mixture of multiple linear-linear regression models is used to implement this idea. We used Gaussian Mixture method to model the data and Gibbs sampling to tune the parameters. The idea itself would be a new way to look at the linear-circular regression problem and can be used as the foundation of the other methods to be developed in future.