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Abstract:
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A single regression model is unlikely to hold when the domain and dataset are large and complex. A finite mixture regression model can address this issue by clustering the data and providing multiple regression models explaining each homogenous group. However, in the case of spatial data, there are likely spatial dependencies that are not taken into account by the finite mixture model. Furthermore, the number of components selected can be too high in the presence of skewed data and/or outliers. 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 both simulated and real data.
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