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Andy Eschbacher 2017-01-06 10:44:25 -05:00
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doc/21_gwr.md
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### Predictive geographically weighted regression (GWR)
-- add description here
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`), 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. |
| 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
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| 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 |
| 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
@ -42,27 +42,29 @@ SELECT
(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
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](https://www.postgresql.org/docs/9.5/static/functions-json.html).
### Descriptive geographically weighted regression
### Geographically weighted regression model estimation
-- add description here
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 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. |
| 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
@ -72,11 +74,11 @@ Note: See [PostgreSQL syntax for parsing JSON objects](https://www.postgresql.or
| 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 |
| 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