地理加权回归建模结果不确定性度量与约束方法

doi:10.11947/j.AGCS.2023.20210336

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

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. 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 Honghui^2,3

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/Abstract

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。

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

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 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.

Key words: geographic weighted regression, uncertainty measuring, PM_2.5 concentration, remote sensing mapping

中图分类号:

P227

刘宁, 邹滨, 张鸿辉. 地理加权回归建模结果不确定性度量与约束方法[J]. 测绘学报, 2023, 52(2): 307-317.

LIU Ning, ZOU Bin, ZHANG Honghui. Uncertainty measuring and constraining method for geographic weighted regression model results[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(2): 307-317.

参考文献

[1] BRUNSDON C, FOTHERINGHAM S, CHARLTON M. Geographically weighted regression[J]. Journal of the Royal Statistical Society:Series D (the Statistician), 1998, 47(3):431-443.
[2] HURVICH C M, SIMONOFF J S, TSAI C L. Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion[J]. Journal of the Royal Statistical Society:Series B (Statistical Methodology), 1998, 60(2):271-293.
[3] BOWMAN A W. An alternative method of cross-validation for the smoothing of density estimates[J]. Biometrika, 1984, 71(2):353-360.
[4] MA Zongwei, HU Xuefei, HUANG Lei, et al. Estimating ground-level PM_2.5 in China using satellite remote sensing[J]. Environmental Science & Technology, 2014, 48(13):7436-7444.
[5] 汤庆园, 徐伟, 艾福利. 基于地理加权回归的上海市房价空间分异及其影响因子研究[J]. 经济地理, 2012, 32(2):52-58. TANG Qingyuan, XU Wei, AI Fuli. A GWR-based study on spatial pattern and structural determinants of Shanghai's housing price[J]. Economic Geography, 2012, 32(2):52-58.
[6] DUAN Sibo, LI Zhaoliang. Spatial downscaling of MODIS land surface temperatures using geographically weighted regression:case study in Northern China[J]. IEEE Transactions on Geoscience and Remote Sensing, 2016, 54(11):6458-6469.
[7] 卢宾宾, 葛咏, 秦昆, 等. 地理加权回归分析技术综述[J]. 武汉大学学报(信息科学版), 2020, 45(9):1356-1366. LU Binbin, GE Yong, QIN Kun, et al. A review on geographically weighted regression[J]. Geomatics and Information Science of Wuhan University, 2020, 45(9):1356-1366.
[8] 胡炜, 刘永学, 林勇军. 基于GWR的住宅地价相对修正方法研究:以深圳市为例[J]. 中国土地科学, 2017, 31(9):62-69, 2, 97. HU Wei, LIU Yongxue, LIN Yongjun. Study on the correcting method of residential land price based on GWR:a case study of Shenzhen city[J]. China Land Sciences, 2017, 31(9):62-69, 2, 97.
[9] WHEELER D, TIEFELSDORF M. Multicollinearity and correlation among local regression coefficients in geographically weighted regression[J]. Journal of Geographical Systems, 2005, 7(2):161-187.
[10] SAMKAR H, ALPU O. Ridge regression based on some robust estimators[J]. Journal of Modern Applied Statistical Methods, 2010, 9(2):495-501.
[11] GUJARATI D, PORTER D. Basic econometrics[M]. New York:McGraw-Hill Education, 2008.
[12] LLOYD C D. Analysing population characteristics using geographically weighted principal components analysis:a case study of Northern Ireland in 2001[J]. Computers, Environment and Urban Systems, 2010, 34(5):389-399.
[13] STEWART F A, YANG W, KANG W. Multiscale geographically weighted regression (MGWR)[J]. Annals of the American Association of Geographers, 2017, 107(6):1247-1265.
[14] YU H, STEWART F A, LI Z, et al. On the measurement of bias in geographically weighted regression models[J]. Spatial Statistics, 2020, 38:100453.
[15] POURMOHAMMADI P, STRAGER M P, DOUGHERTY M J, et al. Analysis of land development drivers using geographically weighted ridge regression[J]. Remote Sensing, 2021, 13(7):1307.
[16] BELSLEY D A, KUH E, WELSCH R E. Regression diagnostics:identifying influential data and sources of collinearity[M]. New York:John Wiley & Sons, 1980.
[17] FOX J, MONETTE G. Generalized collinearity diagnostics[J]. Journal of the American Statistical Association, 1992, 87(417):178-183.
[18] JEUDY L M A. Generalyzed variance-covariance propagation law formulae and application to explicit least-squares adjustments[J]. Bulletin Géodésique, 1988, 62(2):113-124.
[19] SONG Yingchun, XIA Yuguo, XIE Xuemei. Adjustment model and algorithm based on ellipsoid uncertainty[J]. Journal of Geodesy and Geoinformation Science, 2020, 3(3):59-66.
[20] OSHAN T, LI Z, KANG W, et al.MGWR:a python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale[J]. ISPRS International Journal of Geo-Information, 2019, 8(6):269.
[21] YU H, STEWART F A, LI Z, et al. Inference in multiscale geographically weighted regression[J]. Geographical Analysis, 2020, 52(1):87-106.
[22] RODRIGUEZ J D, PEREZ A, LOZANO J A. Sensitivity analysis of k-fold cross validation in prediction error estimation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(3):569-575.
[23] 归庆明, 姚绍文, 顾勇为, 等. 诊断复共线性的条件指标-方差分解比法[J]. 测绘学报, 2006,35(3):210-214. GUI Qingming, YAO Shaowen, GU Yongwei, et al. A new method to diagnose multicollinearity based on condition index and variance decomposition proportion(CIVDP)[J]. Acta Geodaetica et Cartographica Sinica, 2006, 35(3):210-214.
[24] LI Tongwen, SHEN Huanfeng, ZENG Chao, et al. A validation approach considering the uneven distribution of ground stations for satellite-based PM_2.5 estimation[J]. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2020, 13:1312-1321.
[25] WANG Jun. Intercomparison between satellite-derived aerosol optical thickness and PM_2.5 mass:implications for air quality studies[J]. Geophysical Research Letters, 2003, 30(21):2095.
[26] ZHANG Tianhao, GONG Wei, WANG Wei, et al. Ground level PM_2.5 estimates over China using satellite-based geographically weighted regression (GWR) models are improved by including NO₂ and enhanced vegetation index (EVI)[J]. International Journal of Environmental Research and Public Health, 2016, 13(12):1215.

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

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价