Model-based clustering using a new mixture of circular regressions

Regression models, where the response variable is circular, are common in areas such as biology, geology and meteorology. A typical model assumes that the conditional distribution of the response follows a von-Mises distribution. However, this assumption is inadequate when the response variable is multimodal. For this reason, in this paper, a finite mixture of regressions model is proposed for the case of a circular response variable and a set of circular and/or linear covariates. Mixture models are very useful when the underlying population is multimodal. Despite the prevalence of multimodality in regression modelling of circular data, the use of mixtures of regressions has received no attention in the literature. This paper aims to close this knowledge gap. To estimate the proposed model, we develop a maximum likelihood estimation procedure via the Expectation-Maximization algorithm. An extensive simulation study is used to demonstrate the practical use and performance of the proposed model and estimation procedure. In addition, the model is shown to be useful as a model-based clustering tool. Lastly, the model is applied to a real dataset from a wind farm in South Africa which highlights its advantage compared to a competitive approach for model-based clustering of circular data.