crankshaft/doc/21_gwr.md

Regression

Predictive geographically weighted regression (GWR)

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Arguments

Name	Type	Description
subquery	text	SQL query that expose the data to be analyzed (e.g., SELECT * FROM regression_inputs). This query must have the geometry column name (see the optional geom_col for default), the id column name (see id_col), dependent and independent column names.
dep_var	text	name of the dependent variable in the regression model
ind_vars	text[]	Text array of independent used in the model to describe the dependent variable
bw (optional)	numeric	bandwidth value consisting of either a distance or N nearest neighbors. Defaults to calculate an optimal bandwidth.
fixed (optional)	boolean	True for distance based kernel function and False for adaptive (nearest neighbor) kernel function (default). Defaults to false.
kernel	text	Type of kernel function used to weight observations. One of gaussian, bisquare (default), or exponential.

Returns

Column Name	Type	Description
coeffs	JSON	JSON object with parameter estimates for each of the dependent variables. The keys of the JSON object are the dependent variables, with values corresponding to the parameter estimate.
stand_errs	JSON	Standard errors for each of the dependent variables. The keys of the JSON object are the dependent variables, with values corresponding to the respective standard errors.
t_vals	JSON	T-values for each of the dependent variables. The keys of the JSON object are the dependent variable names, with values corresponding to the respective t-value.
predicted	numeric	predicted value of y
residuals	numeric	residuals of the response
r_squared	numeric	R-squared for the parameter fit
bandwidth	numeric	bandwidth value consisting of either a distance or N nearest neighbors
rowid	int	row id of the original row

Example Usage

SELECT
  g.cartodb_id,
  g.the_geom,
  g.the_geom_webmercator,
  (gwr.coeffs->>'pctblack')::numeric as coeff_pctblack,
  (gwr.coeffs->>'pctrural')::numeric as coeff_pctrural,
  (gwr.coeffs->>'pcteld')::numeric as coeff_pcteld,
  (gwr.coeffs->>'pctpov')::numeric as coeff_pctpov,
  gwr.residuals
FROM cdb_crankshaft.CDB_GWR('select * from g_utm'::text, 'pctbach'::text, Array['pctblack', 'pctrural', 'pcteld', 'pctpov']) As gwr
JOIN g_utm as g
on g.cartodb_id = gwr.rowid

Note: See PostgreSQL syntax for parsing JSON objects.

Descriptive geographically weighted regression

-- add description here

Arguments

Name	Type	Description
subquery	text	SQL query that expose the data to be analyzed (e.g., SELECT * FROM regression_inputs). This query must have the geometry column name (see the optional geom_col for default), the id column name (see id_col), dependent and independent column names.
dep_var	text	name of the dependent variable in the regression model
ind_vars	text[]	Text array of independent used in the model to describe the dependent variable
bw (optional)	numeric	bandwidth value consisting of either a distance or N nearest neighbors. Defaults to calculate an optimal bandwidth.
fixed (optional)	boolean	True for distance based kernel function and False for adaptive (nearest neighbor) kernel function (default). Defaults to false.
kernel	text	Type of kernel function used to weight observations. One of gaussian, bisquare (default), or exponential.

Returns

Column Name	Type	Description
coeffs	JSON	JSON object with parameter estimates for each of the dependent variables. The keys of the JSON object are the dependent variables, with values corresponding to the parameter estimate.
stand_errs	JSON	Standard errors for each of the dependent variables. The keys of the JSON object are the dependent variables, with values corresponding to the respective standard errors.
t_vals	JSON	T-values for each of the dependent variables. The keys of the JSON object are the dependent variable names, with values corresponding to the respective t-value.
predicted	numeric	predicted value of y
residuals	numeric	residuals of the response
r_squared	numeric	R-squared for the parameter fit
bandwidth	numeric	bandwidth value consisting of either a distance or N nearest neighbors
rowid	int	row id of the original row

Example Usage

SELECT
  g.cartodb_id,
  g.the_geom,
  g.the_geom_webmercator,
  (gwr.coeffs->>'pctblack')::numeric as coeff_pctblack,
  (gwr.coeffs->>'pctrural')::numeric as coeff_pctrural,
  (gwr.coeffs->>'pcteld')::numeric as coeff_pcteld,
  (gwr.coeffs->>'pctpov')::numeric as coeff_pctpov,
  gwr.residuals
FROM cdb_crankshaft.CDB_GWR('select * from g_utm'::text, 'pctbach'::text, Array['pctblack', 'pctrural', 'pcteld', 'pctpov']) As gwr
JOIN g_utm as g
on g.cartodb_id = gwr.rowid

Note: See PostgreSQL syntax for parsing JSON objects.

Advanced reading

• Fotheringham, A. Stewart, Chris Brunsdon, and Martin Charlton. 2002. Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. John Wiley & Sons. http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471496162.html

• Brunsdon, Chris, A. Stewart Fotheringham, and Martin E. Charlton. 1996. "Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity." Geographical Analysis 28 (4): 281–98. http://onlinelibrary.wiley.com/doi/10.1111/j.1538-4632.1996.tb00936.x/abstract

• Brunsdon, Chris, Stewart Fotheringham, and Martin Charlton. 1998. "Geographically Weighted Regression." Journal of the Royal Statistical Society: Series D (The Statistician) 47 (3): 431–43. http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00145/abstract

• Fotheringham, A. S., M. E. Charlton, and C. Brunsdon. 1998. "Geographically Weighted Regression: A Natural Evolution of the Expansion Method for Spatial Data Analysis." Environment and Planning A 30 (11): 1905–27. doi:10.1068/a301905. https://www.researchgate.net/publication/23538637_Geographically_Weighted_Regression_A_Natural_Evolution_Of_The_Expansion_Method_for_Spatial_Data_Analysis

GWR for prediction

• Harris, P., A. S. Fotheringham, R. Crespo, and M. Charlton. 2010. "The Use of Geographically Weighted Regression for Spatial Prediction: An Evaluation of Models Using Simulated Data Sets." Mathematical Geosciences 42 (6): 657–80. doi:10.1007/s11004-010-9284-7. https://www.researchgate.net/publication/225757830_The_Use_of_Geographically_Weighted_Regression_for_Spatial_Prediction_An_Evaluation_of_Models_Using_Simulated_Data_Sets

GWR in application

• Cahill, Meagan, and Gordon Mulligan. 2007. "Using Geographically Weighted Regression to Explore Local Crime Patterns." Social Science Computer Review 25 (2): 174–93. doi:10.1177/0894439307298925. http://isites.harvard.edu/fs/docs/icb.topic923297.files/174.pdf

• Gilbert, Angela, and Jayajit Chakraborty. 2011. "Using Geographically Weighted Regression for Environmental Justice Analysis: Cumulative Cancer Risks from Air Toxics in Florida." Social Science Research 40 (1): 273–86. doi:10.1016/j.ssresearch.2010.08.006. http://scholarcommons.usf.edu/cgi/viewcontent.cgi?article=2985&context=etd

• Ali, Kamar, Mark D. Partridge, and M. Rose Olfert. 2007. "Can Geographically Weighted Regressions Improve Regional Analysis and Policy Making?" International Regional Science Review 30 (3): 300–329. doi:10.1177/0160017607301609. https://www.researchgate.net/publication/249682503_Can_Geographically_Weighted_Regressions_Improve_Regional_Analysis_and_Policy_Making

• Lu, Binbin, Martin Charlton, and A. Stewart Fotheringhama. 2011. "Geographically Weighted Regression Using a Non-Euclidean Distance Metric with a Study on London House Price Data." Procedia Environmental Sciences, Spatial Statistics 2011: Mapping Global Change, 7: 92–97. doi:10.1016/j.proenv.2011.07.017. https://www.researchgate.net/publication/261960122_Geographically_weighted_regression_with_a_non-Euclidean_distance_metric_A_case_study_using_hedonic_house_price_data