Geographically Weighted Regression-Based Modeling on the Basis of Bandwidth and Autoregressive Coefficient Uncertainty Determined Using Akaike Weights

Geographical modeling has to be based on fundamental characteristics of geographical processes. To simultaneously consider the three fundamental characteristics in one model, the recently developed multi-scale geographically weighted regression with spatial autoregressive (MGWR-SAR) model uses SAR, spatially varying coefficients, and covariate-specific bandwidths to account for spatial autocorrelation, nonstationary regression relationships and multi-scale effects (i.e., different operational scales of different underlying processes, corresponding to different bandwidths of different coefficients), respectively. On the basis of bandwidth and autoregressive coefficient uncertainty determined using Akaike weights, we propose a method to test differences in operational scale among different MGWR-SAR coefficients, further identify the constant regression coefficients with the global operational scale, and test the significance of the autoregressive coefficient for model specification. After evaluating the proposed method using numerical experiments, we demonstrate its applicability in empirical analysis. A mixed MGWR-SAR model specified by our method outperforms the other five baseline models.