Clustering Spatial Data with a Mixture of Skewed Regression Models

A single regression model is unlikely to hold throughout a large and complex spatial domain. A finite mixture of regression models can address this issue by clustering the data and assigning a regression model to explain each homogenous group. However, a typical finite mixture of regressions does not account for spatial dependencies. Furthermore, the number of components selected can be too high in the presence of skewed data and/or heavy tails. Here, we propose a mixture of regression models on a Markov random field with skewed distributions. The proposed model identifies the locations wherein the relationship between the predictors and the response is similar and estimates the model within each group as well as the number of groups. Overfitting is addressed by using skewed distributions, such as the skew-t or normal inverse Gaussian, in the error term of each regression model. Model estimation is carried out using an EM algorithm, and the performance of the estimators and model selection are illustrated through an extensive simulation study and two case studies.