区域地理加权回归分析方法

Regionally geographically weighted regression method

地理加权回归方法是建立在“临近相关”假设前提下的一种有效探测空间连续异质性方法,但地理空间中存在“临近异质”的空间离散情况。地理加权回归算法无法充分拟合这种非线性特征,导致其在解算离散异质性时面临区域临界处拟合不充分的问题,影响了模型的准确性和可靠性。本文提出区域地理加权回归分析方法,通过构建区域空间权重计算策略有效筛选观测点,修正空间核函数,构建区域空间权重,实现空间权重的优化。以武汉市住宅销售价格为例,从区域影响因子有效性、模型性能及模型拟合效果3个角度进行分析。结果表明,区域影响因子的引入,对固定型带宽和调整型带宽下的模型精度均有显著提升;从武汉城区住宅销售价格实例看,受教育因素影响的区域影响因子对模型精度提升最好;同时在固定型带宽下模型R2提升21.84%,MSE提升37.09%。说明在考虑区域影响因素后,模型的精度得到了提高,证明了方法的有效性。

Geographically weighted regression(GWR)serves as a potent approach to discern spatially continuous heterogeneity,premised on the assumption of proximity correlation.However,in practical applications,particularly within the socio-economic domain,the presence of“near-heterogeneous”spatial discrete is frequently observed.Consequently,the challenge of concurrently detecting spatially discrete and continuous heterogeneity to enhance the estimative precision of GWR warrants further investigation.In this study,we introduce a regionally geographic weighted regression(RGWR)analysis methodology,which effectively filters observation points by devising a regional spatial weight computation strategy,refining the spatial kernel function,optimizing spatial weights,and mitigating the impact of“near-heterogeneous”observation points.We utilize housing sales prices in Wuhan as the empirical case,examining the data from three perspectives:regional factor effectiveness,model performance,and model fit.The findings reveal that incorporating regional impact factors considerably enhances model accuracy under both fixed and adaptive bandwidths.Specifically,the regional impact factors stemming from educational determinants yield the most substantial improvement in model accuracy.Simultaneously,under fixed bandwidth conditions,the model's R2 value increases by 21.84%,while the MSE rises by 37.09%.This evidence underscores the model's heightened accuracy upon considering regional influence factors,thereby substantiating the effectiveness of the proposed method.