diff --git a/doc/_static/references.bib b/doc/_static/references.bib index 2f35319..dd50095 100644 --- a/doc/_static/references.bib +++ b/doc/_static/references.bib @@ -1,13 +1,29 @@ %% This BibTeX bibliography file was created using BibDesk. -%% http://bibdesk.sourceforge.net/ +%% https://bibdesk.sourceforge.io/ -%% Created for Wei Kang at 2018-09-26 11:37:34 -0700 +%% Created for weikang at 2019-06-29 12:42:56 -0700 %% Saved with string encoding Unicode (UTF-8) +@article{yu:2019, + Abstract = {A recent paper expands the well-known geographically weighted regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model---a framework referred to as multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so-called ``hat matrix,'' which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model, extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as for adjusting multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real-world data set and provide a link to new software for MGWR (MGWR1.0) which includes the novel inferential framework for MGWR described here.}, + Author = {Yu, Hanchen and Fotheringham, Alexander Stewart and Li, Ziqi and Oshan, Taylor and Kang, Wei and Wolf, Levi John}, + Date-Added = {2019-06-29 12:32:28 -0700}, + Date-Modified = {2019-06-29 12:34:19 -0700}, + Doi = {10.1111/gean.12189}, + Eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/gean.12189}, + Journal = {Geographical Analysis}, + Number = {0}, + Title = {Inference in Multiscale Geographically Weighted Regression}, + Url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/gean.12189}, + Volume = {0}, + Year = {2019}, + Bdsk-File-1 = {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}, + Bdsk-Url-1 = {https://doi.org/10.1111/gean.12189}} + @article{harris_use_2010, Abstract = {Increasingly, the geographically weighted regression (GWR) model is being used for spatial prediction rather than for inference. Our study compares GWR as a predictor to (a) its global counterpart of multiple linear regression (MLR); (b) traditional geostatistical models such as ordinary kriging (OK) and universal kriging (UK), with MLR as a mean component; and (c) hybrids, where kriging models are specified with GWR as a mean component. For this purpose, we test the performance of each model on data simulated with differing levels of spatial heterogeneity (with respect to data relationships in the mean process) and spatial autocorrelation (in the residual process). Our results demonstrate that kriging (in a UK form) should be the preferred predictor, reflecting its optimal statistical properties. However the GWR-kriging hybrids perform with merit and, as such, a predictor of this form may provide a worthy alternative to UK for particular (non-stationary relationship) situations when UK models cannot be reliably calibrated. GWR predictors tend to perform more poorly than their more complex GWR-kriging counterparts, but both GWR-based models are useful in that they provide extra information on the spatial processes generating the data that are being predicted.}, Author = {Harris, P. and Fotheringham, A. S. and Crespo, R. and Charlton, M.}, @@ -93,19 +109,6 @@ @article{oshan_comparison_2017 Bdsk-Url-1 = {http://doi.wiley.com/10.1111/gean.12133}, Bdsk-Url-2 = {https://doi.org/10.1111/gean.12133}} -@misc{yu_fotheringham_li_oshan_kang_wolf_2018, - Author = {Yu, Hanchen and Fotheringham, Stewart and Li, Ziqi and Oshan, Taylor and Kang, Wei and Wolf, Levi J}, - Date-Added = {2018-09-26 11:36:33 -0700}, - Date-Modified = {2018-09-26 11:36:33 -0700}, - Doi = {10.31219/osf.io/4dksb}, - Month = {May}, - Publisher = {OSF Preprints}, - Title = {Inference in multiscale geographically weighted regression}, - Url = {osf.io/4dksb}, - Year = {2018}, - Bdsk-Url-1 = {osf.io/4dksb}, - Bdsk-Url-2 = {https://doi.org/10.31219/osf.io/4dksb}} - @article{nakaya2005geographically, Author = {Nakaya, T and Fotheringham, AS and Brunsdon, Chris and Charlton, Martin}, Date-Added = {2018-09-26 11:04:53 -0700}, @@ -117,7 +120,7 @@ @article{nakaya2005geographically Title = {Geographically weighted Poisson regression for disease association mapping}, Volume = {24}, Year = {2005}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{brunsdon2008geographically, Author = {Brunsdon, Chris and Fotheringham, A Stewart and Charlton, Martin}, @@ -128,7 +131,7 @@ @article{brunsdon2008geographically Publisher = {SAGE Publications}, Title = {Geographically weighted regression: a method for exploring spatial nonstationarity}, Year = {2008}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{Fotheringham2016, Abstract = {Geographically weighted regression (GWR) extends the familiar regression framework by estimating a set of parameters for any number of locations within a study area, rather than producing a single parameter estimate for each relationship specified in the model. Recent literature has suggested that GWR is highly susceptible to the effects of multicollinearity between explanatory variables and has proposed a series of local measures of multicollinearity as an indicator of potential problems. In this paper, we employ a controlled simulation to demonstrate that GWR is in fact very robust to the effects of multicollinearity. Consequently, the contention that GWR is highly susceptible to multicollinearity issues needs rethinking.}, @@ -145,7 +148,7 @@ @article{Fotheringham2016 Url = {http://dx.doi.org/10.1007/s10109-016-0239-5}, Volume = {18}, Year = {2016}, - Bdsk-File-1 = {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}, + Bdsk-File-1 = {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}, Bdsk-Url-1 = {http://dx.doi.org/10.1007/s10109-016-0239-5}} @article{fotheringham1999local, @@ -159,7 +162,7 @@ @article{fotheringham1999local Title = {Local forms of spatial analysis}, Volume = {31}, Year = {1999}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{Fotheringham:2017, Author = {A. Stewart Fotheringham and Wenbai Yang and Wei Kang}, @@ -175,7 +178,7 @@ @article{Fotheringham:2017 Url = {http://dx.doi.org/10.1080/24694452.2017.1352480}, Volume = {107}, Year = {2017}, - Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGJCVYJHZlcnNpb25YJG9iamVjdHNZJGFyY2hpdmVyVCR0b3ASAAGGoKgHCBMUFRYaIVUkbnVsbNMJCgsMDxJXTlMua2V5c1pOUy5vYmplY3RzViRjbGFzc6INDoACgAOiEBGABIAFgAdccmVsYXRpdmVQYXRoWWFsaWFzRGF0YV8QWy4uLy4uLy4uLy4uLy4uL3BhcGVycy9Gb3RoZXJpbmdoYW0vTXVsdGlzY2FsZSBHZW9ncmFwaGljYWxseSBXZWlnaHRlZCBSZWdyZXNzaW9uIChNR1dSKS5wZGbSFwsYGVdOUy5kYXRhTxECSAAAAAACSAACAAAMTWFjaW50b3NoIEhEAAAAAAAAAAAAAAAAAAAAAAAAAEJEAAH/////H011bHRpc2NhbGUgR2VvZ3JhcCNGRkZGRkZGRi5wZGYAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAP////8AAAAAAAAAAAAAAAAABQADAAAKIGN1AAAAAAAAAAAAAAAAAAxGb3RoZXJpbmdoYW0AAgB7LzpVc2Vyczp3ZWlrYW5nOkdvb2dsZSBEcml2ZSAod2Vpa2FuZ0B1Y3IuZWR1KTpwYXBlcnM6Rm90aGVyaW5naGFtOk11bHRpc2NhbGUgR2VvZ3JhcGhpY2FsbHkgV2VpZ2h0ZWQgUmVncmVzc2lvbiAoTUdXUikucGRmAAAOAHIAOABNAHUAbAB0AGkAcwBjAGEAbABlACAARwBlAG8AZwByAGEAcABoAGkAYwBhAGwAbAB5ACAAVwBlAGkAZwBoAHQAZQBkACAAUgBlAGcAcgBlAHMAcwBpAG8AbgAgACgATQBHAFcAUgApAC4AcABkAGYADwAaAAwATQBhAGMAaQBuAHQAbwBzAGgAIABIAEQAEgB5VXNlcnMvd2Vpa2FuZy9Hb29nbGUgRHJpdmUgKHdlaWthbmdAdWNyLmVkdSkvcGFwZXJzL0ZvdGhlcmluZ2hhbS9NdWx0aXNjYWxlIEdlb2dyYXBoaWNhbGx5IFdlaWdodGVkIFJlZ3Jlc3Npb24gKE1HV1IpLnBkZgAAEwABLwAAFQACAA7//wAAgAbSGxwdHlokY2xhc3NuYW1lWCRjbGFzc2VzXU5TTXV0YWJsZURhdGGjHR8gVk5TRGF0YVhOU09iamVjdNIbHCIjXE5TRGljdGlvbmFyeaIiIF8QD05TS2V5ZWRBcmNoaXZlctEmJ1Ryb290gAEACAARABoAIwAtADIANwBAAEYATQBVAGAAZwBqAGwAbgBxAHMAdQB3AIQAjgDsAPEA+QNFA0cDTANXA2ADbgNyA3kDggOHA5QDlwOpA6wDsQAAAAAAAAIBAAAAAAAAACgAAAAAAAAAAAAAAAAAAAOz}} + Bdsk-File-1 = {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}} @article{brunsdon:1999, Author = {Brunsdon, Chris and Fotheringham, A Stewart and Charlton, Martin}, @@ -188,7 +191,7 @@ @article{brunsdon:1999 Title = {Some notes on parametric significance tests for geographically weighted regression}, Volume = {39}, Year = {1999}, - Bdsk-File-1 = {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}} + Bdsk-File-1 = {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}} @article{Silva:2016, Abstract = {This article describes the problem of multiple testing within a Geographically Weighted Regression framework and presents a possible solution to the problem which is based on a family-wise error rate for dependent processes. We compare the solution presented here to other solutions such as the Bonferroni correction and the Byrne, Charlton, and Fotheringham proposal which is based on the Benjamini and Hochberg False Discovery Rate. We conclude that our proposed correction is superior to others and that generally some correction in the conventional t-test is necessary to avoid false positives in GWR.}, diff --git a/mgwr/gwr.py b/mgwr/gwr.py index f771c43..a7a58c7 100755 --- a/mgwr/gwr.py +++ b/mgwr/gwr.py @@ -664,8 +664,7 @@ def ENP(self): """ effective number of parameters - Defualts to tr(s) as defined in yu et. al (2018) Inference in - Multiscale GWR + Defaults to tr(s) as defined in :cite:`yu:2019` but can alternatively be based on 2tr(s) - tr(STS) @@ -761,16 +760,16 @@ def sigma2(self): if sigma2_v1 is True: only use n-tr(S) in denominator - Methods: p214, (9.6), + Methods: p214, (9.6) :cite:`fotheringham_geographically_2002` Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. - and as defined in Yu et. al. (2018) Inference in Multiscale GWR + and as defined in :cite:`yu:2019` if sigma2_v1 is False (v1v2): use n-2(tr(S)+tr(S'S)) in denominator - Methods: p55 (2.16)-(2.18) + Methods: p55 (2.16)-(2.18) :cite:`fotheringham_geographically_2002` Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. @@ -787,7 +786,7 @@ def std_res(self): """ standardized residuals - Methods: p215, (9.7) + Methods: p215, (9.7) :cite:`fotheringham_geographically_2002` Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. @@ -800,7 +799,7 @@ def bse(self): """ standard errors of Betas - Methods: p215, (2.15) and (2.21) + Methods: p215, (2.15) and (2.21) :cite:`fotheringham_geographically_2002` Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. @@ -812,7 +811,7 @@ def cooksD(self): """ Influence: leading diagonal of S Matrix - Methods: p216, (9.11), + Methods: p216, (9.11) :cite:`fotheringham_geographically_2002` Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. @@ -869,7 +868,7 @@ def adj_alpha(self): testing. Includes corrected value for 90% (.1), 95% (.05), and 99% (.01) confidence levels. Correction comes from: - da Silva, A. R., & Fotheringham, A. S. (2015). The Multiple Testing Issue in + :cite:`Silva:2016` : da Silva, A. R., & Fotheringham, A. S. (2015). The Multiple Testing Issue in Geographically Weighted Regression. Geographical Analysis. """ @@ -880,7 +879,7 @@ def adj_alpha(self): def critical_tval(self, alpha=None): """ - Utility function to derive the critial t-value based on given alpha + Utility function to derive the critical t-value based on given alpha that are needed for hypothesis testing Parameters @@ -919,7 +918,7 @@ def filter_tvals(self, critical_t=None, alpha=None): Parameters ---------- - critical : scalar + critical_t : scalar critical t-value to determine whether parameters are statistically significant @@ -1067,7 +1066,7 @@ def local_collinearity(self): Returns four arrays with the order and dimensions listed above where n is the number of locations used as calibrations points and p is the - nubmer of explanatory variables. Local correlation coefficient and local + number of explanatory variables. Local correlation coefficient and local VIF are not calculated for constant term. """ @@ -1281,6 +1280,7 @@ def resid_ss(self): class MGWR(GWR): """ Multiscale GWR estimation and inference. + See :cite:`Fotheringham:2017` :cite:`yu:2019`. Parameters ---------- @@ -1328,7 +1328,7 @@ class MGWR(GWR): intercept. spherical : boolean - True for shperical coordinates (long-lat), + True for spherical coordinates (long-lat), False for projected coordinates (defalut). hat_matrix : boolean True for computing and storing covariate-specific @@ -1768,7 +1768,7 @@ def adj_alpha_j(self): testing. Includes corrected value for 90% (.1), 95% (.05), and 99% (.01) confidence levels. Correction comes from: - da Silva, A. R., & Fotheringham, A. S. (2015). The Multiple Testing Issue in + :cite:`Silva:2016` : da Silva, A. R., & Fotheringham, A. S. (2015). The Multiple Testing Issue in Geographically Weighted Regression. Geographical Analysis. """ diff --git a/mgwr/search.py b/mgwr/search.py index fdd6662..1dc578c 100755 --- a/mgwr/search.py +++ b/mgwr/search.py @@ -10,8 +10,10 @@ def golden_section(a, c, delta, function, tol, max_iter, int_score=False, verbose=False): """ Golden section search routine + Method: p212, 9.6.4 - Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). + + :cite:`fotheringham_geographically_2002`: Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. Parameters diff --git a/mgwr/sel_bw.py b/mgwr/sel_bw.py index 34d5587..ec259a3 100755 --- a/mgwr/sel_bw.py +++ b/mgwr/sel_bw.py @@ -23,7 +23,8 @@ class Sel_BW(object): Select bandwidth for kernel Methods: p211 - p213, bandwidth selection - Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). + + :cite:`fotheringham_geographically_2002`: Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: the analysis of spatially varying relationships. Parameters