测绘学报 ›› 2023, Vol. 52 ›› Issue (2): 307-317.doi: 10.11947/j.AGCS.2023.20210336

• 摄影测量学与遥感 • 上一篇    下一篇

地理加权回归建模结果不确定性度量与约束方法

刘宁1, 邹滨1, 张鸿辉2,3   

  1. 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
  • 收稿日期:2021-06-11 修回日期:2022-09-12 发布日期:2023-03-07
  • 通讯作者: 邹滨 E-mail:210010@csu.edu.cn
  • 作者简介:刘宁(1992-),男,博士生,研究方向为大气污染统计建模。E-mail:nliucsu@csu.edu.cn
  • 基金资助:
    国家自然科学基金(41871317;41871318)

Uncertainty measuring and constraining method for geographic weighted regression model results

LIU Ning1, ZOU Bin1, ZHANG Honghui2,3   

  1. 1. School of Geosciences and Info-physic, Central South University, Changsha 410083, China;
    2. Guangdong Guodi Planning Science Technology Co., Ltd., Guangzhou 510075, China;
    3. College of Resources and Environmental Sciences, Hunan Normal University, Changsha 410012, China
  • Received:2021-06-11 Revised:2022-09-12 Published:2023-03-07
  • Supported by:
    The National Natural Science Foundation of China (Nos. 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PM2.5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PM2.5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。

关键词: 地理加权回归模型, 不确定性度量, PM2.5浓度, 遥感制图

Abstract: 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 PM2.5 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 PM2.5 concentration mapping results. The proposed method can effectively guarantee the stability and effectiveness of GWR results.

Key words: geographic weighted regression, uncertainty measuring, PM2.5 concentration, remote sensing mapping

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