地理加权回归建模结果不确定性度量与约束方法  

Uncertainty measuring and constraining method for geographic weighted regression model results

作　　者：刘宁[1] 邹滨[1] 张鸿辉 LIU Ning;ZOU Bin;ZHANG Honghui(School of Geosciences and Info-physic,Central South University,Changsha 410083,China;Guangdong Guodi Planning Science Technology Co.,Ltd.,Guangzhou 510075,China;College of Resources and Environmental Sciences,Hunan Normal University,Changsha 410012,China)

机构地区：[1]中南大学地球科学与信息物理学院,湖南长沙410083 [2]广东国地规划科技股份有限公司,广东广州510075 [3]湖南师范大学资源与环境科学学院,湖南长沙410012

出　　处：《测绘学报》2023年第2期307-317,共11页Acta Geodaetica et Cartographica Sinica

基　　金：国家自然科学基金(41871317,41871318)。

摘　　要：作为一种经典局部加权最小二乘方法,地理加权回归建模一直受样本空间稀疏及预测变量局部共线性等因素困扰,导致建模结果不确定性呈现空间异质。通过协方差传播定律构建后验标准差精度评价指标,本文提出了一种地理加权回归建模结果不确定性度量与约束方法,并基于地表PM 2.5浓度遥感制图实例开展了验证。试验结果表明:不确定性约束后,不同参数下地理加权回归模型的拟合精度、基于样本/站点/区域的十折交叉验证精度均有改善;局部共线性导致的模型回归系数符号偏差问题得到了改正;模型预测结果奇异值及负值能被有效甄别,有效提升了地表PM 2.5浓度制图结果的可靠性。该不确定性度量与约束方法可有效保证地理加权回归模型估算结果的稳定性和有效性。As a classical local weighting least-square method,the geographic weighted regression(GWR)model always suffers from the space sparsity of samples and the local multicollinearity of predictors,which results in the uncertainties of the model results show spatial heterogeneity.By constructing accuracy evaluation metric of posterior standard error based on the covariance propagation law,this study proposed an uncertainty measuring and constraining method for geographic weighted regression model and validated this method using the instance of ground PM 2.5 concentration remote sensing mapping.After uncertainty constraint,the results show the fitted accuracy and sample-based/site-based/regional-based cross validation accuracy for GWR model with different parameters are all improved;the sign error of regression coefficients caused by local multicollinearity are also corrected;the outlier and negative values in the GWR predicted values can also be effectively detected which improve the reliability of the ground PM 2.5 concentration mapping results.The proposed method can effectively guarantee the stability and effectiveness of GWR results.

关 键 词：地理加权回归模型 不确定性度量 PM 2.5浓度 遥感制图 

分 类 号：P227[天文地球—大地测量学与测量工程]