Inference and estimation of spatial autoregressive varying coefficient models using a geographical gaussian process GAM

Spatial autoregressive varying coefficient (SARSVC) model effectively explores both spatial autocorrelation and spatial heterogeneity in spatial data, yet its current estimation and inference are limited to locally weighted least squares and bootstrap methods. These methods suffer from inadequate explanation of complex processes and the high computational cost. We propose a novel method, termed GGP-GAM, which effectively estimates and identifies the SARSVC model by reformulating it as a generalized additive model (GAM) and calibrating each regression relationship with a geographical gaussian process (GGP). The residual sums of squares based statistics are formulated to recognize spatial heterogeneity in the spatial lag term and in the regression relationship, respectively. We then conduct simulation studies to evaluate the performance of the proposed estimation and identification methods and to examine the impact of multicollinearity among the explanatory variables. The simulation results demonstrate that the GGP-GAM framework delivers superior estimation accuracy, high computational efficiency, a well-controlled Type I error rate, satisfactory test power, and robustness against different model error distributions and multicollinearity levels for the SARSVC model. Finally, an empirical case study using the Boston housing price data set is provided to further demonstrate the applicability of the GGP-GAM method.