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Testing the Importance of the Explanatory Variables in a Mixed Geographically Weighted Regression Model

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  • Chang-Lin Mei
  • Ning Wang
  • Wen-Xiu Zhang

Abstract

A mixed geographically weighted regression (MGWR) model is a kind of regression model in which some coefficients of the explanatory variables are constant, but others vary spatially. It is a useful statistical modelling tool in a number of areas of spatial data analysis. After an MGWR model is identified and calibrated, which has been well studied recently, one of the important inference problems is to evaluate the influence of the explanatory variables in the constant-coefficient part on the response of the model. This is useful in the selection of the variables and for the purpose of explanation. In this paper, a statistical inference framework for this issue is suggested and, besides the F -approximation, which has been frequently used in the literature of the geographically weighted regression technique, a bootstrap procedure for deriving the p -value of the test is also suggested. The performance of the test is investigated by extensive simulations. It is demonstrated that both the F -approximation and the bootstrap procedure work satisfactorily.

Suggested Citation

  • Chang-Lin Mei & Ning Wang & Wen-Xiu Zhang, 2006. "Testing the Importance of the Explanatory Variables in a Mixed Geographically Weighted Regression Model," Environment and Planning A, , vol. 38(3), pages 587-598, March.
    • Handle: RePEc:sae:envira:v:38:y:2006:i:3:p:587-598
    DOI: 10.1068/a3768
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    Cited by:

    1. Chang-Lin Mei & Feng Chen & Wen-Tao Wang & Peng-Cheng Yang & Si-Lian Shen, 2021. "Efficient estimation of heteroscedastic mixed geographically weighted regression models," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 66(1), pages 185-206, February.
    2. Dongwoo Kang & Sandy Dall’erba, 2016. "Exploring the spatially varying innovation capacity of the US counties in the framework of Griliches’ knowledge production function: a mixed GWR approach," Journal of Geographical Systems, Springer, vol. 18(2), pages 125-157, April.
    3. Li, Deng-Kui & Mei, Chang-Lin & Wang, Ning, 2019. "Tests for spatial dependence and heterogeneity in spatially autoregressive varying coefficient models with application to Boston house price analysis," Regional Science and Urban Economics, Elsevier, vol. 79(C).
    4. Yaxiong Ma & Sucharita Gopal, 2018. "Geographically Weighted Regression Models in Estimating Median Home Prices in Towns of Massachusetts Based on an Urban Sustainability Framework," Sustainability, MDPI, vol. 10(4), pages 1-27, March.
    5. Marco Helbich & Wolfgang Brunauer & Eric Vaz & Peter Nijkamp, 2014. "Spatial Heterogeneity in Hedonic House Price Models: The Case of Austria," Urban Studies, Urban Studies Journal Limited, vol. 51(2), pages 390-411, February.
    6. Xijian Hu & Yaori Lu & Huiguo Zhang & Haijun Jiang & Qingdong Shi, 2021. "Selection of the Bandwidth Matrix in Spatial Varying Coefficient Models to Detect Anisotropic Regression Relationships," Mathematics, MDPI, vol. 9(18), pages 1-14, September.
    7. Cem Ertur & Julie Le Gallo, 2008. "Regional Growth and Convergence: Heterogenous reaction versus interaction in spatial econometric approaches," Working Papers hal-00463274, HAL.
    8. Wei, Chuan-Hua & Qi, Fei, 2012. "On the estimation and testing of mixed geographically weighted regression models," Economic Modelling, Elsevier, vol. 29(6), pages 2615-2620.
    9. Desalegn Markos Shifti & Catherine Chojenta & Elizabeth G Holliday & Deborah Loxton, 2020. "Application of geographically weighted regression analysis to assess predictors of short birth interval hot spots in Ethiopia," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-18, May.
    10. Bełej, Mirosław & Cellmer, Radosław & Foryś, Iwona & Głuszak, Michał, 2023. "Airports in the urban landscape: externalities, stigmatization and housing market," Land Use Policy, Elsevier, vol. 126(C).

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