Modeling Spatial Anisotropic Relationships Using Gradient-Based Geographically Weighted Regression

References

• Comber, A., K. Chi, M. Q. Huy, Q. Nguyen, B. B. Lu, H. H. Phe, and P. Harris. 2020. Distance metric choice can both reduce and induce collinearity in geographically weighted regression. Environment and Planning B: Urban Analytics and City Science 47 (3):489–507. doi: 10.1177/2399808318784017.
   Google Scholar
• Fotheringham, A. S., and C. Brunsdon. 1999. Local forms of spatial analysis. Geographical Analysis 31 (4):340–58. 1999.tb00989.x. doi: 10.1111/j.1538-4632.
   Web of Science ®Google Scholar
• Fotheringham, A. S., C. Brunsdon, and M. Charlton. 2002. Geographically weighted regression: The analysis of spatially varying relationships. Chichester, UK: Wiley.
   Google Scholar
• Fotheringham, A. S., Z. Q. Li, and L. J. Wolf. 2021. Scale, context, and heterogeneity: A spatial analytical perspective on the 2016 U.S. presidential election. Annals of the American Association of Geographers 116 (6):1–20. doi: 10.1080/24694452.2020.1835459.
   Google Scholar
• Fotheringham, A. S., W. B. Yang, and W. Kang. 2017. Multiscale geographically weighted regression. Annals of the American Association of Geographers 107 (6):1247–65. doi: 10.1080/24694452.2017.1352480.
   Web of Science ®Google Scholar
• He, Q. Q., and B. Huang. 2018. Satellite-based mapping of daily high-resolution ground PM2.5 in China via space-time regression modeling. Remote Sensing of Environment 206:72–83. doi: 10.1016/j.rse.2017.12.018.
   Web of Science ®Google Scholar
• Huang, J. X., X. C. Mao, H. Deng, Z. K. Liu, J. Chen, and K. Y. Xiao. 2021. An improved GWR approach for exploring the anisotropic influence of ore-controlling factors on mineralization in 3D space. Natural Resources Research 31 (4):2181–96. doi: 10.1007/s11053-021-09954-x.
   Web of Science ®Google Scholar
• Jeff, B. B., and V. D. Clayton. 2011. Programs for Kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances. Computers &Geosciences 37:495–510.
   Web of Science ®Google Scholar
• Kuila, U., Dewhurst D. N., Siggins A. F., and Raven, M. D. 2011. Stress anisotropy and velocity anisotropy in low porosity shale. Tectonophsics 503 (1):34–44. doi: 10.1016/j.tecto.2010.09.023
   Web of Science ®Google Scholar
• Leong, Y. Y., and J. C. Yue. 2017. A modification to geographically weighted regression. International Journal of Health Geographics 16 (1):11. doi: 10.1186/s12942-017-0085-9.
   PubMed Web of Science ®Google Scholar
• Lu, B. B., M. Charlton, C. Brunsdon, and P. Harris. 2016. The Minkowski approach for choosing the distance metric in geographically weighted regression. International Journal of Geographical Information Science 30 (2):351–68. doi: 10.1080/13658816.2015.1087001.
   Web of Science ®Google Scholar
• Mainali, J., H. Chang, and R. Parajuli. 2022. Stream distance-based geographically weighted regression for exploring watershed characteristics and water quality relationships. Annals of the American Association of Geographers 113 (2):390–408. doi: 10.1080/24694452.2022.2107478.
   Web of Science ®Google Scholar
• Mei, C. L., M. Xu, and N. Wang. 2016. A bootstrap test for constant coefficients in geographically weighted regression models. International Journal of Geographical Information Science 30 (8):1622–43. doi: 10.1080/13658816.2016.1149181.
   Web of Science ®Google Scholar
• Murakami, D., and D. A. Griffith. 2019. Spatially varying coefficient modeling for large datasets: Eliminating N from spatial regressions. Spatial Statistics 30:39–64. doi: 10.1016/j.spasta.2019.02.003.
   Web of Science ®Google Scholar
• Páez, A. 2004. Anisotropic variance functions in geographically weighted regression models. Geographical Analysis 36 (4):299–314. doi: 10.1353/geo.2004.0017.
   Web of Science ®Google Scholar
• Propastin, P. 2012. Modifying geographically weighted regression for estimating aboveground biomass in tropical rainforests by multispectral remote sensing data. International Journal of Applied Earth Observation and Geoinformation 18:82–90. doi: 10.1016/j.jag.2011.12.013.
   Web of Science ®Google Scholar
• Tobler, W. R. 1970. A computer movie simulating urban growth in the Detroit region. Economic Geography 46:234–40. doi: 10.2307/143141.
   Web of Science ®Google Scholar
• van Donkelaar, A., R. V. Martin, M. Brauer, N. C. Hsu, R. A. Kahn, R. C. Levy, A. Lyapustin, A. M. Sayer, and D. M. Winker. 2016. Global estimates of fine particulate matter using a combined geophysical-statistical method with information from satellites, models, and monitors. Environmental Science & Technology 50 (7):3762–72. doi: 10.1021/acs.est.5b05833.
   PubMed Web of Science ®Google Scholar
• Wang, N., C. L. Mei, and X. D. Yan. 2008. Local linear estimation of spatially varying coefficient models: An improvement on the geographically weighted regression technique. Environment and Planning A: Economy and Space 40 (4):986–1005. doi: 10.1068/a3941.
   Web of Science ®Google Scholar
• Wang, Y. X., Q. B. Fan, and L. Zhu. 2018. Variable selection and estimation using a continuous approximation to the L-0 penalty. Annals of the Institute of Statistical Mathematics 70 (1):191–214. doi: 10.1007/s10463-016-0588-3.
   Web of Science ®Google Scholar
• Wu, B., J. B. Yan, and K. Cao. 2023. l0-norm variable adaptive selection for geographically weighted regression model. Annals of the American Association of Geographers 113 (5):1190–1206. doi: 10.1080/24694452.2022.2161988.
   Web of Science ®Google Scholar
• Wu, B., J. B. Yan, and H. Lin. 2022. A cost-effective algorithm for calibrating multiscale geographically weighted regression models. International Journal of Geographical Information Science 36 (5):898–917. doi: 10.1080/13658816.2021.1999457.
   Web of Science ®Google Scholar
• Wu, S. S., Z. H. Du, Y. Y. Wang, T. Lin, F. Zhang, and R. Y. Liu. 2020. Modeling spatially anisotropic nonstationarity processes in costal environments based on a directional geographically neural network weighted regression. The Science of the Total Environment 709:136097. doi: 10.1016/j.scitotenv.2019.136097.
   PubMed Web of Science ®Google Scholar
• Xuan, W. H., F. Zhang, H. Y. Zhou, Z. H. Du, and R. Y. Liu. 2021. Improving geographically weighted regression considering directional nonstationary for ground-level PM2.5 estimations. ISPRS International Journal of Geo-Information 10 (6):413. doi: 10.3390/ijgi10060413.
   Web of Science ®Google Scholar
• Yu, H. C., A. S. Fotheringham, Z. Q. Li, O. Taylor, W. Kang, and L. J. Wolf. 2020. Inference in multiscale geographically weighted regression. Geographical Analysis 52 (1):87–106. doi: 10.1111/gean.12189.
   Web of Science ®Google Scholar
• Zhu, J. X., C. H. Wen, J. Zhu, H. P. Zhang, and X. Q. Wang. 2020. A polynomial algorithm for best-subset selection problem. Proceedings of the National Academy of Sciences of the United States of America 117 (52):33117–23. doi: 10.1073/pnas.2014241117.
   PubMed Web of Science ®Google Scholar