Inverse circular–circular regression

The problem of determining the values of the independent variable given a value of the dependent variable is commonly referred to as the inverse regression problem. This problem is also encountered in real life with circular data and we refer to it in that context as the inverse circular regression problem. For such a problem, we develop distance-based methods, and parametric methods, where we use the von Mises (vM) error distribution and the asymmetric generalized von Mises (AGvM) error distribution. We then present a goodness of fit comparison among distance-based and parametric methods, utilizing a new criterion called the relative circular prediction bias (RCPB) criterion, with real and simulated examples. Real data applications are given from the biological and environmental sciences.