Detection of spatial heterogeneity based on spatial autoregressive varying coefficient models

Spatial autocorrelation and spatial heterogeneity are fundamental properties of geo-referenced data. Spatial autoregressive varying coefficient models have been proposed to simultaneously deal with spatial autocorrelation in the response variable and spatial heterogeneity in the regression relationship. Nevertheless, the identification of spatial heterogeneity in the spatial lag term and in the regression relationship remains to be studied, which is essential to model selection and deep understanding of the intrinsical characteristics of the regression relationship. In this article, based on the two-stage least squares estimation of the spatial autoregressive varying coefficient model and the related null models, two residual sums of squares based statistics are constructed and the bootstrap tests are proposed to detect spatial heterogeneity in the spatial lag term and in the regression relationship, respectively. Then, simulation studies are conducted to assess the performance of the tests. The results show that both tests are of valid size, satisfactory power, and robustness to the model error distribution. Furthermore, a real-life example based on the Boston housing price data is given to demonstrate the application of the proposed tests.