Multiscale Geographically Weighted Regression (MGWR)¶

mgwr is a Python implementation of multiscale geographically weighted regression for investigating process spatial heterogeneity and scale. It incorporates the widely used approach to modeling process spatial heterogeneity - Geographically Weighted Regression (GWR) as well as the newly proposed approach - Multiscale GWR (MGWR) which relaxes the assumption that all of the processes being modeled operate at the same spatial scale. Inferences are available for both approaches.

GWR-MGWR Estimated Parameter Surface (Georgia Dataset)

Installation¶

mgwr supports python 3.5 and 3.6 only. Please make sure that you are operating in a python 3 environment.

Installing released version¶

mgwr is available on the Python Package Index. Therefore, you can either install directly with pip from the command line:

pip install -U mgwr

or download the source distribution (.tar.gz) and decompress it to your selected destination. Open a command shell and navigate to the decompressed folder. Type:

pip install .

Installing development version¶

Potentially, you might want to use the newest features in the development version of mgwr on github - pysal/mgwr while have not been incorporated in the Pypi released version. You can achieve that by installing pysal/mgwr by running the following from a command shell:

pip install https://github.com/pysal/mgwr/archive/master.zip

You can also fork the pysal/mgwr repo and create a local clone of your fork. By making changes to your local clone and submitting a pull request to pysal/mgwr, you can contribute to the mgwr development.

API reference¶

GWR Model Estimation and Inference¶

`mgwr.gwr.GWR`(coords, y, X, bw[, family, …])	Geographically weighted regression.
`mgwr.gwr.GWRResults`(model, params, predy, S, …)	Basic class including common properties for all GWR regression models
`mgwr.gwr.GWRResultsLite`(model, resid, influ, …)	Lightweight GWR that computes the minimum diagnostics needed for bandwidth selection

MGWR Estimation and Inference¶

`mgwr.gwr.MGWR`(coords, y, X, selector[, …])	Multiscale GWR estimation and inference.
`mgwr.gwr.MGWRResults`(model, params, predy, …)	Class including common properties for a MGWR model.

Utility Functions¶

Kernel Specification¶

`mgwr.kernels.Kernel`(i, data[, bw, fixed, …])	GWR kernel function specifications.
`mgwr.kernels.local_cdist`(coords_i, coords, …)	Compute Haversine (spherical=True) or Euclidean (spherical=False) distance for a local kernel.

Bandwidth Selection¶

mgwr.sel_bw.Sel_BW(coords, y, X_loc[, …])

Select bandwidth for kernel

Visualization¶

`utils.shift_colormap`(cmap[, start, …])	Function to offset the “center” of a colormap.
`utils.truncate_colormap`(cmap[, minval, …])	Function to truncate a colormap by selecting a subset of the original colormap’s values
`utils.compare_surfaces`(\args, \\*kwargs)

References¶

BKW80: D. A. Belsey, E. Kuh, and R. E. Welsch. Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. Wiley, New York, 1980.
BFC99: Chris Brunsdon, A Stewart Fotheringham, and Martin Charlton. Some notes on parametric significance tests for geographically weighted regression. Journal of Regional Science, 39(3):497–524, 1999.
BFC08: Chris Brunsdon, A Stewart Fotheringham, and Martin Charlton. Geographically weighted regression: a method for exploring spatial nonstationarity. Encyclopedia of Geographic Information Science, pages 558, 2008.
dSF16: Alan Ricardo da Silva and A. Stewart Fotheringham. The multiple testing issue in geographically weighted regression. Geographical Analysis, 48(3):233–247, 2016. URL: https://onlinelibrary.wiley.com/doi/abs/10.1111/gean.12084, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/gean.12084, doi:10.1111/gean.12084.
FB99: A Stewart Fotheringham and Chris Brunsdon. Local forms of spatial analysis. Geographical Analysis, 31(4):340–358, 1999.
FBC02: A. Stewart Fotheringham, Chris Brunsdon, and Martin Charlton. Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. John Wiley & Sons, February 2002. ISBN 978-0-470-85525-6.
FO16: A. Stewart Fotheringham and Taylor M. Oshan. Geographically weighted regression and multicollinearity: dispelling the myth. Journal of Geographical Systems, 18(4):303–329, 2016. URL: http://dx.doi.org/10.1007/s10109-016-0239-5, doi:10.1007/s10109-016-0239-5.
FYK17: A. Stewart Fotheringham, Wenbai Yang, and Wei Kang. Multiscale geographically weighted regression (mgwr). Annals of the American Association of Geographers, 107(6):1247–1265, 2017. URL: http://dx.doi.org/10.1080/24694452.2017.1352480, arXiv:http://dx.doi.org/10.1080/24694452.2017.1352480, doi:10.1080/24694452.2017.1352480.
HFCC10: P. Harris, A. S. Fotheringham, R. Crespo, and M. Charlton. The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets. Mathematical Geosciences, 42(6):657–680, June 2010. URL: http://link.springer.com/article/10.1007/s11004-010-9284-7, doi:10.1007/s11004-010-9284-7.
NFBC05: T Nakaya, AS Fotheringham, Chris Brunsdon, and Martin Charlton. Geographically weighted poisson regression for disease association mapping. Statistics in Medicine, 24(17):2695–2717, 2005.
OF17: Taylor M. Oshan and A. Stewart Fotheringham. A Comparison of Spatially Varying Regression Coefficient Estimates Using Geographically Weighted and Spatial-Filter-Based Techniques: A Comparison of Spatially Varying Regression. Geographical Analysis, June 2017. URL: http://doi.wiley.com/10.1111/gean.12133, doi:10.1111/gean.12133.
Whe07: David C. Wheeler. Diagnostic Tools and a Remedial Method for Collinearity in Geographically Weighted Regression. Environment and Planning A, 39(10):2464–2481, October 2007. URL: http://epn.sagepub.com/content/39/10/2464, doi:10.1068/a38325.
YFL+19: Hanchen Yu, Alexander Stewart Fotheringham, Ziqi Li, Taylor Oshan, Wei Kang, and Levi John Wolf. Inference in multiscale geographically weighted regression. Geographical Analysis, 2019. URL: https://onlinelibrary.wiley.com/doi/abs/10.1111/gean.12189, arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1111/gean.12189, doi:10.1111/gean.12189.