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Regression

Predictive geographically weighted regression (GWR)

Predictive GWR builds a spatially-varying regression model to predict unknown values from other known values. Similar to traditional linear regression, GWR takes a linear combination of independent variables and known dependent variables to calculate the best fit of a model. The model coefficients are spatially varying (controlled by the bandwidth parameter), so the model fit varies from geometry to geometry. GWR exposes places where non-stationarity is taking places--that is, where local behavior differs from what would be seen by doing a model without spatial variation.

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), and the dependent (dep_var) and independent (ind_vars) column names.
dep_var TEXT Name of the dependent variable in the regression model
ind_vars TEXT[] Text array of independent variable column names used in the model to describe the dependent variable.
bw (optional) NUMERIC Value of bandwidth. If NULL then select optimal (default).
fixed (optional) BOOLEAN True for distance based kernel function and False (default) for adaptive (nearest neighbor) kernel function. Defaults to False.
kernel (optional) 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 INTEGER 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_Predict('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.

Geographically weighted regression model estimation

Similar to the prediction-based GWR, this analysis generates the model coefficients for a spatially-varying regression. The model coefficients, along with their respective statistics, allow one to make inferences or describe a dependent variable based on the independent variables that make up the model.

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 variables used in the model to describe the dependent variable
bw (optional) NUMERIC Value of bandwidth. If NULL then select optimal (default).
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 INTEGER 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

GWR for prediction

GWR in application

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