地理加权回归(GWR)是空间数据分析中用于探究回归关系空间非平稳性的经典统计方法。本文探讨了GWR的一种贝叶斯实现路径,全面讨论了基于尖峰-平板先验(spike-and-slab prior)的贝叶斯变量选择、基于范围先验(range prior)的带宽选择,以及采用修正偏差信息准则(modified deviance information criterion)和修正伪边际似然对数(modified logarithm of pseudo-marginal likelihood)进行模型评估的方法。本文还引入了图距离(graph distance)在面域数据建模中的应用。通过大量模拟研究,我们在小样本与大样本位置数量两种情景下检验了所提方法的经验表现,并与经典频率学派GWR进行了比较。结果表明,所提方法在不同情形下的变量选择与参数估计性能均令人满意。最后,我们将该方法应用于中国30个省份的省级宏观经济数据实证分析;估计与变量选择结果揭示了关于中国经济的若干合理洞见,且与既有研究及事实相符。
The geographically weighted regression (GWR) is a well-known statistical approach to explore spatial non-stationarity of the regression relationship in spatial data analysis. In this paper, we discuss a Bayesian recourse of GWR. Bayesian variable selection based on spike-and-slab prior, bandwidth selection based on range prior, and model assessment using a modified deviance information criterion and a modified logarithm of pseudo-marginal likelihood are fully discussed in this paper. Usage of the graph distance in modeling areal data is also introduced. Extensive simulation studies are carried out to examine the empirical performance of the proposed methods with both small and large number of location scenarios, and comparison with the classical frequentist GWR is made. The performance of variable selection and estimation of the proposed methodology under different circumstances are satisfactory. We further apply the proposed methodology in analysis of a province-level macroeconomic data of 30 selected provinces in China. The estimation and variable selection results reveal insights about China's economy that are convincing and agree with previous studies and facts.