A bootstrap test for constant coefficients in geographically weighted regression models

References

• Bárcena, M.J., et al., 2014. Alleviating the effect of collinearity in geographically weighted regression. Journal of Geographical Systems, 16 (4), 441–466. doi:10.1007/s10109-014-0199-6
   Web of Science ®Google Scholar
• Brunsdon, C., Charlton, M., and Harris, P., 2012. Living with collinearity in local regression models. In: Proceedings of the 10th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences. Brasil.
   Google Scholar
• Brunsdon, C., Fotheringham, A.S., and Charlton, M., 1996. Geographically weighted regression: a method for exploring spatial non-stationarity. Geographical Analysis, 28 (4), 281–298. doi:10.1111/j.1538-4632.1996.tb00936.x
   Web of Science ®Google Scholar
• Brunsdon, C., Fotheringham, A.S., and Charlton, M., 1998. Geographically weighted regression: modelling spatial non-stationarity. The Statistician, 47 (3), 431–443.
   Google Scholar
• Brunsdon, C., Fotheringham, A.S., and Charlton, M., 1999. Some notes on parametric significance tests for geographically weighted regression. Journal of Regional Science, 39 (3), 497–524. doi:10.1111/0022-4146.00146
   Web of Science ®Google Scholar
• Cai, Z., 2007. Trending time-varying coefficient time series models with serially correlated errors. Journal of Econometrics, 136 (1), 163–188. doi:10.1016/j.jeconom.2005.08.004
   Web of Science ®Google Scholar
• Casetti, E., 1972. Generating models by the expansion method: applications to geographical research. Geographical Analysis, 4 (1), 81–91. doi:10.1111/gean.1972.4.issue-1
   Web of Science ®Google Scholar
• Casetti, E., 1997. The expansion method, mathematical modeling, and spatial econometrics. International Regional Science Review, 20 (1), 9–32.
   Web of Science ®Google Scholar
• Efron, B., 1979. Bootstrap methods: another look at the jackknife. The Annals of Statistics, 7 (1), 1–26. doi:10.1214/aos/1176344552
   Web of Science ®Google Scholar
• Fan, J. and Huang, T., 2005. Profile likelihood inference on semiparametric varying-coefficient partially linear models. Bernoulli, 11 (6), 1031–1057.
   Web of Science ®Google Scholar
• Fan, J. and Jiang, J., 2007. Nonparametric inference with generalized likelihood ratio tests. Test, 16 (3), 409–444.
   Web of Science ®Google Scholar
• Fan, J., Zhang, C., and Zhang, J., 2001. Generalized likelihood ratio statistics and Wilks phenomenon. The Annals of Statistics, 29 (1), 153–193.
   Web of Science ®Google Scholar
• Fan, J. and Zhang, W., 1999. Statistical estimation in varying coefficient models. The Annals of Statistics, 27 (5), 1491–1518.
   Web of Science ®Google Scholar
• Fan, J. and Zhang, W., 2008. Statistical methods with varying coefficient models. Statistics and Its Interface, 1 (1), 179–195.
   PubMed Web of Science ®Google Scholar
• Farber, S. and Páez, A., 2007. A systematic investigation of cross-validation in GWR model estimation: empirical analysis and Monte Carlo simulations. Journal of Geographical Systems, 9 (4), 371–396.
   Web of Science ®Google Scholar
• Fotheringham, A.S., Brunsdon, C., and Charlton, M., 2002. Geographically weighted regression: the analysis of spatially varying relationships. Chichester, UK: John Wiley and Sons.
   Google Scholar
• Fotheringham, A.S., Crespo, R., and Yao, J., 2015. Geographically and temporal weighted regression (GTWR). Geographical Analysis, 47 (4), 431–452.
   Web of Science ®Google Scholar
• Gilley, O.W. and Pace, R.K., 1996. On the Harrison and Rubinfeld data. Journal of Environmental Economics and Management, 31 (3), 403–405.
   Web of Science ®Google Scholar
• Gollini, I., et al., 2015. GW model: an R package for exploring spatial heterogeneity using geographically weighted models. Journal of Statistical Software, 63 (17), 1–50.
   Web of Science ®Google Scholar
• Harris, P., et al., 2015. Using bootstrap methods to investigate coefficient non-stationarity in regression model: an empirical case study. Procedia Environmental Sciences, 27, 112–115.
   Google Scholar
• Huang, B., Wu, B., and Barry, M., 2010. Geographically and temporally weighted regression for modeling spatio-temporal variation in house prices. International Journal of Geographical Information Science, 24 (3), 383–401.
   Web of Science ®Google Scholar
• Hurrison, D. and Rubinfeld, D.L., 1978. Hedonic housing prices and the demand for clean air. Journal of Environmental Economics and Management, 5 (1), 81–102.
   Web of Science ®Google Scholar
• Jetz, W., Rahbek, C., and Lichstein, J.W., 2005. Local and global approaches to spatial data analysis in ecology. Global Ecology and Biogeography, 14 (1), 97–98. doi:10.1111/geb.2005.14.issue-1
   Web of Science ®Google Scholar
• Jones III, J.P. and Casetti, E., 1992. Applications of the Expansion Method. London: Routledge.
   Google Scholar
• Leung, Y., Mei, C.-L., and Zhang, W.-X., 2000. Statistical tests for spatial nonstationarity based on the geographically weighted regression model. Environment and Planning A, 32 (1), 9–32. doi:10.1068/a3162
   Web of Science ®Google Scholar
• Mei, C.-L., He, S.-Y., and Fang, K.-T., 2004. A Note on the Mixed Geographically Weighted Regression Model. Journal of Regional Science, 44 (1), 143–157. doi:10.1111/j.1085-9489.2004.00331.x
   Web of Science ®Google Scholar
• Mei, C.-L., Wang, N., and Zhang, W.-X., 2006. Testing the importance of the explanatory variables in a mixed geographically weighted regression model. Environment and Planning A, 38 (3), 587–598. doi:10.1068/a3768
   Web of Science ®Google Scholar
• Páez, A., Farber, S., and Wheeler, D.C., 2011. A simulation-based study of geographically weighted regression as a method for investigating spatially varying relationships. Environment and Planning A, 43 (12), 2992–3010. doi:10.1068/a44111
   Web of Science ®Google Scholar
• Páez, A., Uchida, T., and Miyamoto, K., 2002a. A general framework for estimation and inference of geographically weighted regression models: 1. Location-specific kernel bandwidths and a test for locational heterogeneity. Environment and Planning A, 34 (4), 733–754. doi:10.1068/a34110
   Web of Science ®Google Scholar
• Páez, A., Uchida, T., and Miyamoto, K., 2002b. A general framework for estimation and inference of geographically weighted regression models: 2. spatial association and model specification tests. Environment and Planning A, 34 (5), 883–904. doi:10.1068/a34133
   Web of Science ®Google Scholar
• Wang, N., Mei, C.-L., and Yan, X.-D., 2008. Local linear estimation of spatially varying coefficient models: an improvement on the geographically weighted regression technique. Environment and Planning A, 40 (4), 986–1005. doi:10.1068/a3941
   Web of Science ®Google Scholar
• Wheeler, D.C., 2007. Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environment and Planning A, 39 (10), 2464–2481. doi:10.1068/a38325
   Web of Science ®Google Scholar
• Wheeler, D.C., 2009. Simultaneous coefficient penalization and model selection in geographically weighted regression: the geographically weighted lasso. Environment and Planning A, 41 (3), 722–742. doi:10.1068/a40256
   Web of Science ®Google Scholar
• Wheeler, D.C. and Calder, C., 2007. An assessment of coefficient accuracy in linear regression models with spatially varying coefficients. Journal of Geographical Systems, 9 (2), 145–166. doi:10.1007/s10109-006-0040-y
   Web of Science ®Google Scholar
• Wheeler, D.C. and Tiefelsdorf, M., 2005. Multicollinearity and correlation among local regression coefficients in geographically weighted regression. Journal of Geographical Systems, 7 (2), 161–187. doi:10.1007/s10109-005-0155-6
   Google Scholar
• Yang, W., Fotheringham, A.S., and Harris, P., 2011. Model selection in GWR: the development of a flexible bandwidth GWR. London: Geocomputation 2011, UK.
   Google Scholar
• Yang, W., Fotheringham, A.S., and Harris, P., 2012. An extension of geographically weighted regression with flexible bandwidths. Lancaster: GISRUK, UK.
   Google Scholar