Uncovering spatial process heterogeneity from graph-based deep spatial regression

One can never specify the true statistical form of a complex spatial process. Model misspecification, such as linearity and additivity, will lead to fundamentally flawed interpretations in the estimated coefficients, particularly in empirical geographic studies involving a large number of observations and complex data generation processes. Motivated to learn representative patterns of spatial process heterogeneity, we propose a deep explainable spatial regression (XSR) framework based on graph convolutional neural networks (GCN), which bypasses the conventional parametric statistical assumptions in spatial regression modeling and can generate deep spatially varying coefficients that depict the heterogeneity structure of spatial processes. We introduce an analytical framework to (1) perform deep spatial regression modeling in multivariate cross-sectional scenarios, (2) reconstruct spatial heterogeneity patterns from the learned deep coefficients, and (3) explain the effectiveness of heterogeneity through a simple diagnostic test. Experiments on Greater Boston house prices modeling demonstrate better fitting performance over spatial regression baselines. The spatial patterns of deep local coefficients consistently exhibit stronger explanatory power than those derived from geographically weighted regression, indicating a better representation of the true spatial process heterogeneity uncovered by graph-based deep spatial regression.