Spatial non-stationarity test of regression relationships in the multiscale geographically weighted regression model

By allowing covariate-specific bandwidths for estimating spatially varying coefficients, the multiscale geographically weighted regression (MGWR) model can simultaneously explore spatial non-stationarity and multiple operational scales of the corresponding geographical processes. Treating the constant coefficients as an extreme situation which corresponds to the global scale and infinite covariate bandwidth, the traditional linear regression, GWR and mixed GWR models are special cases of the MGWR model. An appropriately-specified GWR-based model would be beneficial to the understanding of the general underlying processes, especially for their operational scales. To specify an appropriate model, the key issue is to determine how many MGWR coefficient(s) should be constant. Along the traditional statistical line of thought, we propose a residual-based bootstrap method to test spatial non-stationarity of the MGWR coefficients, which can underpin our understanding of the characteristics of regression relationships in statistics. The simulation experiment validates the proposed test, and demonstrates that it is of valid Type I error and satisfactory power, and is robust to different types of model error distributions. The applicability of the proposed test is demonstrated in a real-world case study on the Shanghai housing prices.