A geographically weighted autoregressive model with an adaptive spatial weights matrix: Construction, estimation, and inference

Geographically weighted autoregressive (GWAR) models are a powerful tool for simultaneously modeling spatial autocorrelation and spatial heterogeneity. In these models, the spatial weights matrix characterizes the underlying autocorrelation structure of the response variable, and its correct specification is essential for valid estimation and inference. Studies of GWAR models typically assume the spatial weights matrix is a prespecified constant, limiting adaptability to capture the underlying autocorrelation structure. Using a binary spatial weights matrix and a distance-decay function with a scale parameter that governs the rate of spatial decay and the intensity of spatial autocorrelation, we construct an adaptive spatial weights matrix to formulate the GWAR model. The profile quasi-maximum likelihood procedure is employed to calibrate the model, and a bootstrap test is proposed to detect spatial autocorrelation. The simulation study shows that the estimation method yields accurate estimates of the scale parameter and regression coefficients, and the test has a valid type-I error and satisfactory power. The empirical analysis demonstrates that the proposed spatial weights matrix efficiently captures the spatial autocorrelation structure.