Circular (Directional) regression

Oregon Convention Center 

Directional data has received increasing attention across a large number of scientific fields. In particular, such data assume some notion of an underlying circular distribution, which is characterized by some form of angular or degree direction. Naturally, modeling with such distributions when observed covariates are present necessitate the use of regression methods. However, circular variables have some specific characteristics which are different from linear variables, so traditional linear models need an appropriate transformation to become circular models. This paper extends the simple circular-circular regression model and the circular-linear model into multivariate circular-circular regression models, and models based on both circular and linear covariates. We further develop a degree-determination algorithm that is used in the aforementioned models. This algorithm makes use of classic dimension reduction methods (principal component analysis and partial least squares) applied to multivariate circular regression models. Performance of our methods are investigated and compared based on both simulated and real datasets.

Circular data

Regression model

Dimension reduction

Determination of degree of polynomial 

Section on Statistical Computing