The circular quantile residual

Abstract

Circular-linear regression is often used to model the relationship between a circular dependent variable and a set of linear predictor variables. It is used in many areas such as meteorology, biology, and medicine. For checking model adequacy, it is desirable to use residuals that are approximately standard normally distributed. Most of the residuals used in circular regression models do not meet this requirement and are used especially for outlier identification. Other residuals are limited to the von Mises regression models. An asymptotically standard normally distributed residual that can be used for any parametric circular-linear regression model is introduced. Monte Carlo simulation studies suggest that the distribution of this residual is well approximated by the standard normal distribution in small samples. To study the behavior of this residual, two regression models are introduced, and two applications are used to show that the proposed residual can detect model misspecification.