-
摘要: 空间数据关系中的异质性或非平稳性特征是近期空间统计或相关应用领域的研究热点之一，而局部空间统计分析技术的提出与发展是其关键环节。地理加权回归分析技术（geographically weighted regression，GWR）通过关于位置的局部加权回归分析模型求解，以随着空间位置不同而变化的参数估计结果，量化反映空间数据关系中的异质性或非平稳性特征。GWR技术已在众多领域内广泛应用，逐渐成为重要的空间关系异质性建模工具之一。针对GWR模型解算、结果解读、模型检验等基础技术环节进行了系统总结，分别分析回顾了其对应的相关研究进展以及应用过程中存在的问题。同时，系统梳理了近年来GWR技术的主要拓展与延伸，重点阐述了其在采用灵活的距离度量选择、参数的多尺度估计以及时空数据建模方面的GWR技术扩展研究。此外，还简要介绍了现有的主要GWR技术软件工具，以期为读者和用户提供相对全面的GWR技术信息参考与知识总结。Abstract: Spatial heterogeneity or non-stationarity in data relationships is one of the hot topics in spatial statistics or relative application fields, while the development of local techniques forms an essential part for the relative studies. Geographically weighted regression (GWR) provides spatially varying coefficient estimates via location-specific weighted regression model calibrations, to explore spatial heterogeneities or non-stationarities, quantitatively. It has been widely used in a number of fields, and become one of the most important tools for exploring spatial heterogeneities in data relationships. We summarized the GWR basics in model calibration, result interpretation, model diagnostics, reviewed its research progress and problems in its applications, respectively. Meanwhile, we sorted out the important extensions of the basic GWR technique, particularly in applying flexible distance metric choices in GWR model calibration, multiscale parameter estimates and spatiotemporal data modeling. In addition, we also introduced the main GWR tools or software accordingly to provide the users or readers comprehensive reference and knowledge on the GWR technique.
-
-
![]()
图 3 不同类型带宽作用示意图
Figure 3. Schematic Diagram of Different Types of Bandwidth Definitions
表 1 GWR技术文章发表量英文和中文期刊（前10位）
Table 1 Publication Sources of GWR-Related Articles (Top 10)
英文期刊 数量/篇 中文期刊 数量/篇 Applied Geography 70 测绘科学 6 Sustainability 40 农业工程学报 5 Plos One 38 统计与信息论坛 5 International Journal of Environmental Research and Public Health 34 测绘通报 4 Remote Sensing 33 经济地理 4 Science of the Total Environment 31 长江流域资源与环境 4 ISPRS International Journal of Geo-information 29 测绘与空间地理信息 3 Geographical Analysis 26 地理研究 3 International Journal of Geographical Information Science 26 甘肃科学学报 3 Journal of Transport Geography 26 国土与自然资源研究 3 
下载: 导出CSV
-
[1] Fotheringham A S, Brunsdon C. Local Forms of Spatial Analysis[J]. Geographical Analysis, 1999, 31(4): 340-358 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1111/j.1538-4632.1999.tb00989.x
[2] Goodchild M F. The Validity and Usefulness of Laws in Geographic Information Science and Geography[J]. Annals of the Association of American Geographers, 2004, 94(2): 300-303 doi: 10.1111/j.1467-8306.2004.09402008.x
[3] Páez A. Local Analysis of Spatial Relationships: A Comparison of GWR and the Expansion Method[C]. The 5th International Conference on Computational Science and Its Applications, Singapore, 2005
[4] Swamy P A V B, Conway R K, Leblanc M R. The Stochastic Coefficients Approach to Econometric Modeling, Part 1: A Critique of Fixed Coefficients Models[R]. US: Board of Governors of the Federal Reserve System, 1988
[5] Gamerman D, Moreira A R B, Rue H.Space-Varying Regression Models: Specifications and Simulation[J]. Computational Statistics & Data Analysis, 2003, 42(3): 513-533 http://www.sciencedirect.com/science/article/pii/S0167947302002116
[6] Cleveland W S. Robust Locally Weighted Regression and Smoothing Scatterplots[J]. Journal of the American Statistical Association, 1979, 74(368): 829-836 doi: 10.1080/01621459.1979.10481038
[7] Brunsdon C, Fotheringham A S, Charlton M E. Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity[J]. Geographical Analysis, 1996, 28(4): 281-298
[8] Páez A, Wheeler D. Geographically Weighted Regression[M]// Kitchin R, Thrift N. International Encyclopedia of Human Geography.Oxford: Elsevier, 2009: 407-414
[9] Aria M, Cuccurullo C. Bibliometrix: An R-Tool for Comprehensive Science Mapping Analysis[J]. Journal of Informetrics, 2017, 11(4): 959-975 doi: 10.1016/j.joi.2017.08.007
[10] 玄海燕, 李琪, 张运虎.基于地理加权回归的我国各市人口总数的空间特征分析[J].生物数学学报, 2016, 31(2): 223-228 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=swsxxb201602009 Xuan Haiyan, Li Qi, Zhang Yunhu. Spatial Characteristics Analysis of Total Population in Various Cities Based on Geographically Weighted Regression[J]. Journal of Biomathematic, 2016, 31(2): 223-228 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=swsxxb201602009
[11] 赵阳阳, 刘纪平, 张福浩, 等.贪心算法的地理加权回归特征变量选择方法[J].测绘科学, 2016, 41(7): 41-46 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chkx201607009 Zhao Yangyang, Liu Jiping, Zhang Fuhao, et al.An Approach of Characteristics Variable Selection of Geographically Weighted Regression Based on Greedy Algorithm[J]. Science of Surveying and Mapping, 2016, 41(7): 41-46 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chkx201607009
[12] Tobler W R. A Computer Movie Simulating Urban Growth in the Detroit Region[J]. Economic Geography, 1970, 46(2): 234-240 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.2307/143141
[13] Fotheringham A S, Brunsdon C, Charlton M. Geographically Weighted Regression: The Analysis of Spatially Varying Relationships[M]. Chichester: Wiley, 2002
[14] Cho S H, Lambert D M, Chen Z. Geographically Weighted Regression Bandwidth Selection and Spatial Autocorrelation: An Empirical Example Using Chinese Agriculture Data[J]. Applied Economics Letters, 2010, 17(8): 767 - 772 doi: 10.1080/13504850802314452
[15] Cameron A C, Trivedi P K. Microeconometrics: Methods and Applications[M]. New York: Cambridge University Press, 2005
[16] Farber S, Páez A. A Systematic Investigation of Cross-Validation in GWR Model Estimation:Empirical Analysis and Monte Carlo Simulations[J]. Journal of Geographical Systems, 2007, 9(4): 371-396 doi: 10.1007/s10109-007-0051-3
[17] Akaike H. Information Theory and an Extension of the Maximum Likelihood Principle[C]. 2nd International Symposium on Information Theory. Tsahkadsor, Armenia, 1973
[18] Mennis J. Mapping the Results of Geographically Weighted Regression[J]. The Cartographic Journal, 2006, 43(2): 171-179 doi: 10.1179/000870406X114658
[19] Leung Y, Mei C L, Zhang W X. Testing for Spatial Autocorrelation Among the Residuals of the Geographically Weighted Regression[J]. Environment and Planning A, 2000, 32(5): 871-890 doi: 10.1068/a32117
[20] Leung Y, Mei C L, Zhang W X. Statistical Tests for Spatial Nonstationarity Based on the Geographically Weighted Regression Model[J]. Environment and Planning A, 2000, 32(1): 9-32 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1068/a3162
[21] Comber A, Chi K, Huy M Q, et al. Distance Metric Choice Can Both Reduce and Induce Collinearity in Geographically Weighted Regression[J]. Environment and Planning B: Urban Analytics and City Science, 2018, DOI: 10.1177/2399808318784017
[22] Griffith D A. Spatial-Filtering-Based Contributions to a Critique of Geographically Weighted Regression (GWR)[J]. Environment and Planning A, 2008, 40(11): 2 751-2 769 doi: 10.1068/a38218
[23] 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 doi: 10.1007/s10109-005-0155-6
[24] Wheeler D C. Simultaneous Coefficient Penalization and Model Selection in Geographically Weighted Regression: The Geographically Weighted Lasso[J]. Environment and Planning A, 2009, 41(3): 722-742
[25] Wheeler D C. Diagnostic Tools and a Remedial Method for Collinearity in Geographically Weighted Regression[J]. Environment and Planning A, 2007, 39(10): 2 464-2 481 doi: 10.1068/a38325
[26] Gollini I, Lu B, Charlton M, et al. GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models[J]. Journal of Statistical Software, 2015, 63(17): 1-50 http://www.researchgate.net/publication/237000443_GWmodel_an_R_Package_for_Exploring_Spatial_Heterogeneity_using_Geographically_Weighted_Models
[27] Fotheringham A S, Oshan T M. Geographically Weighted Regression and Multicollinearity: Dispelling the Myth[J]. Journal of Geographical Systems, 2016, 18(4): 303-329 doi: 10.1007/s10109-016-0239-5
[28] Jetz W, Rahbek C, Lichstein J W. Local and Global Approaches to Spatial Data Analysis in Ecology[J]. Global Ecology and Biogeography, 2005, 14(1): 97-98 doi: 10.1111/j.1466-822X.2004.00129.x
[29] Wheeler D C, Páez A: Geographically Weighted Regression[M]. Fischer M M, Getis A. Handbook of Applied Spatial Analysis: Software Tools, Methods and Applications. Berlin, Heidelberg: Springer-Verlag, 2010: 461-486
[30] Da Silva A R, Fotheringham A S. The Multiple Testing Issue in Geographically Weighted Regression[J]. Geographical Analysis, 2016, 48(3): 233-247 doi: 10.1111/gean.12084
[31] Byrne G, Charlton M, Fotheringham S. Multiple Dependent Hypothesis Tests in Geographically Weighted Regression[C]. The 10th International Conference on Geocomputation, Sydney, Australia, 2009
[32] Kitchin R. Space Ⅱ[M]//Kitchin R, Thrift N. International Encyclopedia of Human Geography. Oxford: Elsevier, 2009: 268-275
[33] Lu B, Charlton M, Harris P, et al. Geographically Weighted Regression with a Non-Euclidean Distance Metric: A Case Study Using Hedonic House Price Data[J]. International Journal of Geographical Information Science, 2014, 28(4): 660-681 doi: 10.1080/13658816.2013.865739
[34] Lu B, Charlton M, Brunsdon C, et al. The Minkowski Approach for Choosing the Distance Metric in Geographically Weighted Regression[J]. International Journal of Geographical Information Science, 2016, 30(2): 351-368 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1080/13658816.2015.1087001
[35] Fotheringham A S, Yang W, Kang W. Multiscale Geographically Weighted Regression (MGWR)[J]. Annals of the American Association of Geographers, 2017, 107(6): 1 247-1 265 doi: 10.1080/24694452.2017.1352480
[36] Lu B, Brunsdon C, Charlton M, et al. A Response to 'A Comment on Geographically Weighted Regression with Parameter-Specific Distance Metrics'[J]. International Journal of Geographical Information Science, 2019, 33(7): 1 300-1 312 doi: 10.1080/13658816.2019.1585541
[37] Brunsdon C, Fotheringham A S, Charlton M. Some Notes on Parametric Significance Tests for Geographically Weighted Regression[J]. Journal of Regional Science, 1999, 39(3): 497-524 doi: 10.1111/0022-4146.00146
[38] 覃文忠, 王建梅, 刘妙龙.混合地理加权回归模型算法研究[J].武汉大学学报·信息科学版, 2007, 32(2): 115-119 http://ch.whu.edu.cn/article/id/1813 Qin Wenzhong, Wang Jianmei, Liu Miaolong. Algorithm for Mixed Geographically Weighted Regression Mode[J]. Geomatics and Information Science of Wuhan University, 2007, 32(2): 115-119 http://ch.whu.edu.cn/article/id/1813
[39] 玄海燕, 刘树群, 罗双华.混合地理加权回归模型的两种估计[J].兰州理工大学学报, 2007, 33(3): 142-144 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gsgydx200703038 Xuan Haiyan, Liu Shuqun, Luo Shuanghua. Two Kinds of Estimation of Mixed Geographically Weighted Regression Mode[J]. Journal of Lanzhou University of Technology, 2007, 33(3): 142-144 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=gsgydx200703038
[40] 聂磊, 舒红, 刘艳.复杂地形地区月平均气温(混合)地理加权回归克里格插值[J].武汉大学学报·信息科学版, 2018, 43(10):1 553-1 559 doi: 10.13203/j.whugis20160433 Nie Lei, Shu Hong, Liu Yan. Interpolation of Monthly Average Temperature by Using (Mixed) Geographically Weighted Regression Kriging in the Complex Terrain Region[J]. Geomatics and Information Science of Wuhan University, 2018, 43(10):1 553-1 559 doi: 10.13203/j.whugis20160433
[41] Mei C L, Xu M, Wang N. A Bootstrap Test for Constant Coefficients in Geographically Weighted Regression Models[J]. International Journal of Geographical Information Science, 2016, 30(8): 1 622-1 643 doi: 10.1080/13658816.2016.1149181
[42] Mei C L, Wang N, Zhang W X. Testing the Importance of the Explanatory Variables in a Mixed Geographically Weighted Regression Model[J]. Environment and Planning A, 2006, 38(3): 587-598 doi: 10.1068/a3768
[43] Harris P, Brunsdon C, Lu B, et al. Introducing Bootstrap Methods to Investigate Coefficient Non-stationarity in Spatial Regression Models[J]. Spatial Statistics, 2017, 21: 241-261 doi: 10.1016/j.spasta.2017.07.006
[44] Yang W, Fotheringham A S, Harris P. An Extension of Geographically Weighted Regression with Flexible Bandwidths[C]. GISRUK, Lancaster, UK, 2012
[45] Yang W. An Extension of Geographically Weighted Regression with Flexible Bandwidths[D]. UK: Centre for GeoInformatics, University of St Andrews, 2014
[46] Leong Y Y, Yue J C. A Modification to Geographically Weighted Regression[J]. International Journal of Health Geographics, 2017, 16(1): 11 doi: 10.1186/s12942-017-0085-9
[47] Lu B, Brunsdon C, Charlton M, et al. Geographically Weighted Regression with Parameter-Specific Distance Metrics[J]. International Journal of Geographical Information Science, 2017, 31(5): 982-998 doi: 10.1080/13658816.2016.1263731
[48] Lu B, Yang W, Ge Y, et al. Improvements to the Calibration of a Geographically Weighted Regression with Parameter-Specific Distance Metrics and Bandwidths[J]. Computers, Environment and Urban Systems, 2018, 71: 41-57 doi: 10.1016/j.compenvurbsys.2018.03.012
[49] Ge Y, Jin Y, Stein A, et al. Principles and Methods of Scaling Geospatial Earth Science Data[J]. Earth-Science Reviews, 2019, 197: 102 897 doi: 10.1016/j.earscirev.2019.102897
[50] Wolf L, Oshan T, Fotheringham A. Single and Multiscale Models of Process Spatial Heterogeneity[J]. Geographical Analysis, 2018, 50(3): 223-246 doi: 10.1111/gean.12147
[51] Yu H, Fotheringham A S, Li Z, et al. Inference in Multiscale Geographically Weighted Regression[J]. Geographical Analysis, 2020, 52(1): 87-106 doi: 10.1111/gean.12189
[52] Wu C, Ren F, Hu W, et al. Multiscale Geographically and Temporally Weighted Regression: Exploring the Spatiotemporal Determinants of Housing Prices[J]. International Journal of Geographical Information Science, 2019, 33(3): 489-511 doi: 10.1080/13658816.2018.1545158
[53] Huang B, Wu B, Barry M. Geographically and Temporally Weighted Regression for Modeling Spatio-Temporal Variation in House Prices[J]. International Journal of Geographical Information Science, 2010, 24(3): 383-401 doi: 10.1080/13658810802672469
[54] Fotheringham A S, Crespo R, Yao J. Geographical and Temporal Weighted Regression (GTWR)[J]. Geographical Analysis, 2015, 47(4): 431-452 doi: 10.1111/gean.12071
[55] Wu B, Li R, Huang B. A Geographically and Temporally Weighted Autoregressive Model with Application to Housing Prices[J]. International Journal of Geographical Information Science, 2014, 28(5): 1 186-1 204 doi: 10.1080/13658816.2013.878463
[56] Du Z, Wu S, Zhang F, et al. Extending Geographically and Temporally Weighted Regression to Account for Both Spatiotemporal Heterogeneity and Seasonal Variations in Coastal Seas[J]. Ecological Informatics, 2018, 43: 185-199 doi: 10.1016/j.ecoinf.2017.12.005
[57] 赵阳阳, 张小璐, 张福浩, 等.一种局部多项式时空地理加权回归方法[J].测绘学报, 2018, 47(5): 663-671 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chxb201805013 Zhao Yangyang, Zhang Xiaolu, Zhang Fuhao, et al. A Local Polynomial Geographically and Temporally Weight Regression[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(5): 663-671 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=chxb201805013
[58] Liu Y, Lam K, Wu J, et al. Geographically Weighted Temporally Correlated Logistic Regression Model[J]. Scientific Reports, 2018, 8(1): 1 417 doi: 10.1038/s41598-018-19772-6
[59] Lesage J P. A Family of Geographically Weighted Regression Models[M]//Anselin L, Florax R J, Rey S J. Advances in Spatial Econometrics. Berlin, Heidelberg: Springer, 2002
[60] Harris P, Fotheringham A S, Juggins S. Robust Geographically Weighted Regression: A Technique for Quantifying Spatial Relationships Between Freshwater Acidification Critical Loads and Catchment Attributes[J]. Annals of the Association of American Geographers, 2010, 100(2): 286-306 doi: 10.1080/00045600903550378
[61] Wang N, Mei C L, Yan X D. Local Linear Estimation of Spatially Varying Coefficient Models: An Improvement on the Geographically Weighted Regression Technique[J]. Environment and Planning A, 2008, 40(4): 986-1 005 doi: 10.1068/a3941
[62] Harris P, Juggins S. Estimating Freshwater Acidification Critical Load Exceedance Data for Great Britain Using Space-Varying Relationship Models[J]. Mathematical Geosciences, 2011, 43(3): 265-292 doi: 10.1007/s11004-011-9331-z
[63] Nakaya T, Fotheringham A S, Brunsdon C, et al. Geographically Weighted Poisson Regression for Disease Association Mapping[J]. Statistics in Medicine, 2005, 24(17): 2 695-2 717 doi: 10.1002/sim.2129
[64] Atkinson P M, German S E, Sear D A, et al. Exploring the Relations Between Riverbank Erosion and Geomorphological Controls Using Geographically Weighted Logistic Regression[J]. Geographical Analysis, 2003, 35(1): 58-82 doi: 10.1111/j.1538-4632.2003.tb01101.x
[65] Harris R, Singleton A, Grose D, et al. Grid-Enabling Geographically Weighted Regression: A Case Study of Participation in Higher Education in England[J]. Transactions in GIS, 2010, 14(1): 43-61 doi: 10.1111/j.1467-9671.2009.01181.x
[66] Dong G, Nakaya T, Brunsdon C. Geographically Weighted Regression Models for Ordinal Categorical Response Variables:An Application to Geo-referenced Life Satisfaction Data[J]. Computers, Environment and Urban Systems, 2018, 70: 35-42 doi: 10.1016/j.compenvurbsys.2018.01.012
[67] Li Z, Fotheringham A S, Li W, et al. Fast Geographically Weighted Regression (FastGWR): A Scalable Algorithm to Investigate Spatial Process Heterogeneity in Millions of Observations[J]. International Journal of Geographical Information Science, 2019, 33(1): 155-175
[68] Murakami D, Tsutsumida N, Yoshida T, et al. Scalable GWR: A Linear-Time Algorithm for Large-Scale Geographically Weighted Regression with Polynomial Kernels[OL]. https://arxiv.org/abs/1905.00266, 2019
[69] Harris P.A Simulation Study on Specifying a Regression Model for Spatial Data: Choosing Between Autocorrelation and Heterogeneity Effects[J]. Geographical Analysis, 2019, 51(2): 151-181 doi: 10.1111/gean.12163
[70] Charlton M, Fotheringham A, Brunsdon C. GWR 3: Software for Geographically Weighted Regression[OL]. http://www.uvm.edu/rsenr/gradgis/GWR3Manual.pdf, 2003
[71] Nakaya T, Charlton M, Fotheringham S, et al. How to Use SGWRWIN (GWR4.0)[R]. Ireland: National Centre for Geocomputation, 2009
[72] Oshan M 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): 1-31 http://www.researchgate.net/publication/333694051_MGWR_A_Python_Implementation_of_Multiscale_Geographically_Weighted_Regression_for_Investigating_Process_Spatial_Heterogeneity_and_Scale
[73] Lu B, Harris P, Charlton M, et al. The GWmodel R Package: Further Topics for Exploring Spatial Heterogeneity Using Geographically Weighted Models[J]. Geo-Spatial Information Science, 2014, 17(2): 85-101 http://d.wanfangdata.com.cn/periodical/dqkjxxkxxb-e201402002
[74] Eddelbuettel D, Francois R. Rcpp: Seamless R and C++ Integration[J]. Journal of Statistical Software, 2011, 1(8): 1-19 http://www.researchgate.net/publication/227450960_Rcpp_Seamless_R_and_C_Integration
[75] Wheeler D. GWRR: Fits Geographically Weighted Regression Models with Diagnostic Tools: R Package Version 0.2-1[OL]. https://CRAN.R-project.org/package=gwrr, 2013
计量
- 文章访问数:
- HTML全文浏览量:
- PDF下载量:
