A mixed geographically weighted regression model with varying-coefficient spatial lag

doi:10.7523/j.ucas.2022.081

Journal of University of Chinese Academy of Sciences ›› 2024, Vol. 41 ›› Issue (3): 345-356.DOI: 10.7523/j.ucas.2022.081

• Research Articles • Previous Articles Next Articles

A mixed geographically weighted regression model with varying-coefficient spatial lag

TANG Zhipeng¹, WU Ying^2,3, XIONG Shifeng³, HUANG Huan⁴

1. CAS Key Laboratory of Regional Sustainable Development Modeling, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China;
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China;
4. Business School, Chengdu University of Technology, Chengdu 610059, China

Received:2022-07-22 Revised:2022-10-10 Online:2024-05-15

Abstract

Abstract: Spatial correlation and spatial heterogeneity are the theoretical basis of spatial econometrics. In order to solve the local problem of spatial lag of dependent variables, this study extended the existing mixed geographically weighted regression model with constant-coefficient spatial lag, and proposed a mixed geographically weighted regression model with varying-coefficient spatial lag. The mixed geographically weighted regression model with varying-coefficient spatial lag combines spatial correlation with spatial heterogeneity, and covers most of the model forms of geographically weighted regression. Based on the parameterization reconstruction method and likelihood ratio test, the coefficient estimation method, significance test of this model and the discriminant test of varying-coefficient are given respectively. Both in Monte Carlo simulation and practical application, the results show that the mixed geographically weighted regression model with varying-coefficient spatial lag renders itself well for the fitting and forecasting effect on dependent variable. The mixed geographically weighted regression model with varying-coefficient spatial lag provides a support for setting up a suitable model form for quantitative research on spatial effects.

Key words: spatial heterogeneity, mixed geographically weighted regression, significance test, varying-coefficient

CLC Number:

O212.7

TANG Zhipeng, WU Ying, XIONG Shifeng, HUANG Huan. A mixed geographically weighted regression model with varying-coefficient spatial lag[J]. Journal of University of Chinese Academy of Sciences, 2024, 41(3): 345-356.

References

[1] Cliff A D, Ord J K. Spatial autocorrelation [M]. London, Pion, 1973.
[2] Anselin L. Local indicators of spatial association： LISA[J]. Geographical Analysis, 1995, 27(2): 93-115. DOI:10.1111/j.1538-4632.1995.tb00338.x.
[3] Fisher W D. Econometric estimation with spatial dependence[J]. Regional and Urban Economics, 1971, 1(1): 19-40. DOI:10.1016/0034-3331(71)90016-9.
[4] Kelejian H H, Prucha I R. A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances[J]. The Journal of Real Estate Finance and Economics, 1998, 17(1): 99-121. DOI:10.1023/A:1007707430416.
[5] Kelejian H H, Prucha I R. A generalized moments estimator for the autoregressive parameter in a spatial model[J]. International Economic Review, 1999, 40(2): 509-533. DOI:10.1111/1468-2354.00027.
[6] Kelejian H H, Prucha I R. HAC estimation in a spatial framework[J]. Journal of Econometrics, 2007, 140(1): 131-154. DOI:10.1016/j.jeconom.2006.09.005.
[7] Kelejian H H, Prucha I R. Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances[J]. Journal of Econometrics, 2010, 157 (1): 53-67. DOI:10.1016/j.jeconom.2009.10.025.
[8] Lee L F. Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models[J]. Econometric Theory, 2002, 18(2): 252-277. DOI:10.1017/S0266466602182028.
[9] Lee L F. Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances[J]. Econometric Reviews, 2003, 22(4): 307-335. DOI:10.1081/ETC-120025891.
[10] Lee L F. Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models[J]. Econometrica, 2004, 72(6): 1899-1925. DOI:10.1111/j.1468-0262.2004.00558.x.
[11] Lee L F. The method of elimination and substitution in the GMM estimation of mixed regressive, spatial autoregressive models[J]. Journal of Econometrics, 2007, 140(1): 155-189. DOI: 10.1016/j.jeconom.2006.09.006.
[12] Lee L F. GMM and 2SLS estimation of mixed regressive, spatial autoregressive models[J]. Journal of Econometrics, 2007, 137(2): 489-514. DOI:10.1016/j.jeconom.2005.10.004.
[13] Brunsdon C. Estimating probability surfaces for geographical point data: an adaptive Kernel algorithm[J]. Computers & Geosciences, 1995, 21(7): 877-894. DOI:10.1016/0098-3004(95)00020-9.
[14] Brunsdon C, Fotheringham A S, Charlton M E. Geogr-aphically weighted regression: a method for exploring spatial nonstationarity[J]. Geographical Analysis, 1996, 28(4): 281-298. DOI:10.1111/j.1538-4632.1996.tb00936.x.
[15] Brunsdon C, Fotheringham A S, Charlton M. Spatial nonstationarity and autoregressive models[J]. Environment and Planning A: Economy and Space, 1998, 30(6): 957-973.DOI:10.1068/a300957.
[16] 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.
[17] Fotheringham A S, Charlton M, Brunsdon C. Two techniques for exploring non-stationarity in geographical data[J]. Geographical Systems, 1997, 4(1): 59-82.
[18] 乔宁宁. 混合地理加权回归模型中的空间相关性检验和参数估计研究[J]. 数量经济技术经济研究, 2013, 30(8): 93-108. DOI:10.13653/j.cnki.jqte.2013.08.020.
[19] Páez A, Uchida T, Miyamoto K. A general framework for estimation and inference of geographically weighted regression models: 2. Spatial association and model specification tests[J]. Environment and Planning A: Economy and Space, 2002, 34(5): 883-904. DOI:10.1068/a34133.
[20] Xiong S F. The reconstruction approach: from interpolation to regression[J]. Technometrics, 2021, 63(2): 225-235. DOI:10.1080/00401706.2020.1764869.
[21] 魏传华, 梅长林. 半参数空间变系数回归模型的两步估计方法及其数值模拟[J]. 统计与信息论坛, 2005, 20(1): 16-19,50. DOI:10.3969/j.issn.1007-3116. 2005.01.004.

A mixed geographically weighted regression model with varying-coefficient spatial lag

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