Tests for spatial dependence and heterogeneity in spatially autoregressive varying coefficient models with application to Boston house price analysis

Spatially autoregressive varying coefficient models are a powerful tool for simultaneously dealing with spatial dependence and spatial heterogeneity in spatial data analysis. Different methods have been developed for estimating the models. Nevertheless, little work has been devoted to their statistical inference issues. In this paper, two generalized-likelihood-ratio-statistic-based bootstrap tests are developed to detect spatial autocorrelation in the response variable and to identify constant coefficients in the regression functions, respectively. The simulation studies show that both tests are of accurate size and satisfactory power. The Boston house price data are finally analyzed to demonstrate the application of the proposed tests in the detection of spatial dependence and heterogeneity.