**-g**- Print in shell script style
**-e**- Estimate optimal bandwidth
**--overwrite**- Allow output files to overwrite existing files
**--help**- Print usage summary
**--verbose**- Verbose module output
**--quiet**- Quiet module output
**--ui**- Force launching GUI dialog

**mapx**=*name[,**name*,...]**[required]**- Map(s) with X variables
**mapy**=*name***[required]**- Map with Y variable
**mask**=*name*- Raster map to use for masking
- Only cells that are not NULL and not zero are processed
**residuals**=*name*- Map to store residuals
**estimates**=*name*- Map to store estimates
**coefficients**=*string*- Prefix for maps to store coefficients
**output**=*name*- ASCII file for storing regression coefficients (output to screen if file not specified).
**kernel**=*string*- Weighing kernel function.
- Options:
*gauss, epanechnikov, bisquare, tricubic* - Default:
*gauss* **bandwidth**=*integer*- Bandwidth of the weighing kernel.
- Default:
*10* **vf**=*integer*- Variance factor for Gaussian kernel: variance = bandwith / factor.
- Options:
*1, 2, 4, 8* - Default:
*1* **npoints**=*integer*- Number of points for adaptive bandwidth
- If 0, fixed bandwidth is used
- Default:
*0* **memory**=*integer*- Memory in MB for adaptive bandwidth
- Default:
*300*

Y = b0 + sum(bi*Xi) + E

X = {X1, X2, ..., Xm} m = number of explaining variables Y = {y1, y2, ..., yn} Xi = {xi1, xi2, ..., xin} E = {e1, e2, ..., en} n = number of observations (cases)

Y ~ sum(bi*Xi) b0 is the intercept, X0 is set to 1

The β coefficients are localized, i.e. determined for each cell
individually. These β coefficients are the most important output
of *r.gwr*. Spatial patterns and localized outliers in these
coefficients can reveal details of the relation of Y to X. Outliers in
the β coefficients can also be caused by a small bandwidth and can
be removed by increasing the bandwidth.

Geographically weighted regressions should be used as a diagnostic tool and not as an interpolation method. If a geographically weighted regression provides a higher R squared than the corresponding global regression, then a crucial predictor is missing in the model. If that missing predictor can not be estimated or is supposed to behave randomly, a geographically weighted regression might be used for interpolation, but the result, in particular the variation of the β coefficients needs to be judged according to prior assumptions. See also the manual and the examples of the R package spgwr.

*r.gwr* is designed for large datasets that can not be processed
in R. A p value is therefore not provided, because even very small,
meaningless effects will become significant with a large number of
cells. Instead it is recommended to judge by the amount of variance
explained (R squared for a given variable) and the gain in AIC (AIC
without a given variable minus AIC global must be positive) whether the
inclusion of a given explaining variable in the model is justified.

The F score for each explaining variable allows to test if the inclusion
of this variable significantly increases the explaining power of the
model, relative to the global model excluding this explaining variable.
That means that the F value for a given explaining variable is only
identical to the F value of the R-function *summary.aov* if the
given explaining variable is the last variable in the R-formula. While
R successively includes one variable after another in the order
specified by the formula and at each step calculates the F value
expressing the gain by including the current variable in addition to the
previous variables, *r.gwr* calculates the F-value
expressing the gain by including the current variable in addition to all
other variables, not only the previous variables.

**Epanechnikov**- w = 1 - d / bw
**Bisquare (Quartic)**- w = (1 - (d / bw)
^{2})^{2} **Tricubic**- w = (1 - (d / bw)
^{3})^{3} **Gaussian**- w = exp(-0.5 * (d / bw)
^{2})

w = weight for current cell

d = distance to the current cell

bw = bandwidth

Fotheringham, A.S., Brunsdon, C., and Charlton, M.E., 2002, Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.

http://gwr.nuim.ie/

R package spgwr

Available at: r.gwr source code (history)

Main index | Raster index | Topics index | Keywords index | Graphical index | Full index

© 2003-2019 GRASS Development Team, GRASS GIS 7.8.2dev Reference Manual