Abstract

Regression models with circular response variables are frequently encountered in fields like biology, geology, and meteorology. Typically, these models assume that the conditional distribution of the response variable follows a von Mises distribution. However, this assumption becomes insufficient when the response variable exhibits multimodality. To address this limitation, this paper proposes a finite mixture of regression models tailored for circular response variables, with both circular and/or linear covariates. Despite the frequent occurrence of multimodality in circular regression modeling, mixtures of regressions have not been explored in the literature. We introduce an Expectation-Maximization algorithm to estimate the proposed model. The model's effectiveness and estimation procedure are illustrated through an extensive simulation study. Additionally, we demonstrate its utility as a model-based clustering tool. Finally, the model is applied to analyze a real dataset from a wind farm in South Africa.