Spatial Homogeneity Pursuit of Regression Coefficients for Large Datasets
Spatial regression models have been widely used to describe the relationship between a response variable and some explanatory variables over a region of interest under the assumption that the responses are spatially correlated. Nearly all existing work assumes the regression coefficients to be constant or smoothly varying over the region. In this article, we propose a spatially clustered coefficient regression model to capture the spatially varying pattern, especially clustering pattern in the effect of explanatory variables. In many applications especially with large spatial datasets, it is of great interest to practitioners to identify such clusters that allow straightforward interpretations of local associations among variables. This method incorporates spatial neighboring information through a carefully constructed regularization to automatically detect change points in space and to achieve computational scalability. Numerical studies show that it works very effectively not only in capturing clustered coefficients, but also smoothly varying coefficients because of its strong local adaptivity. This flexibility allows the researchers to explore various spatial structures in regression coefficients. Theoretical properties of the new estimator are also established. The method is applied to explore the relationship between temperature and salinity of sea water in the Atlantic basin, which provides insightful information on the evolution of individual water masses and the pathway and strength of meridional overturning circulation in oceanography.
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