# gwer: Geographically Weighted Elliptical Regression In gwer: Geographically Weighted Elliptical Regression

## Description

The function fit geographically weighted elliptical regression model to explore the non-stationarity for a certain bandwidth and weighting function.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28``` ```gwer( formula, data, regression.points, bandwidth, kernel = "bisquare", p = 2, theta = 0, adapt = NULL, hatmatrix = FALSE, family = Normal, longlat = NULL, dMat, weights, dispersion = NULL, subset, na.action = "na.fail", method = "gwer.fit", control = glm.control(epsilon = 1e-04, maxit = 100, trace = F), model = FALSE, x = FALSE, y = TRUE, contrasts = NULL, offset, spdisp = TRUE, parplot = FALSE, ... ) ```

## Arguments

 `formula` regression model formula as in `glm`. `data` model data frame, or may be a SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp. `regression.points` a Spatial*DataFrame object, i.e. SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp; Note that no diagnostic information will returned if it is assigned. `bandwidth` value of the selected bandwidth used in the weighting function (see `bw.gwer` for bandwidth optimization). `kernel` function chosen as follows: gaussian: wgt = exp(-.5*(vdist/bw)^2); exponential: wgt = exp(-vdist/bw); bisquare: wgt = (1-(vdist/bw)^2)^2 if vdist < bw, wgt=0 otherwise; tricube: wgt = (1-(vdist/bw)^3)^3 if vdist < bw, wgt=0 otherwise; boxcar: wgt=1 if dist < bw, wgt=0 otherwise `p` the power of the Minkowski distance, default is 2, i.e. the Euclidean distance `theta` an angle in radians to rotate the coordinate system, default is 0 `adapt` defines the type of bandwidth used. either NULL (default) or a proportion between 0 and 1 of observations to include in weighting scheme (k-nearest neighbours). `hatmatrix` if TRUE, return the hatmatrix as a component of the result. `family` a description of the error distribution to be used in the model (see `family.elliptical` for details of family functions). `longlat` TRUE if point coordinates are longitude-latitude decimal degrees, in which case distances are measured in kilometers. If x is a SpatialPoints object, the value is taken from the object itself. `dMat` a pre-specified distance matrix, it can be calculated by the function gw.dist `weights` an optional numeric vector of weights to be used in the fitting process. `dispersion` an optional fixed value for dispersion parameter. `subset` an optional numeric vector specifying a subset of observations to be used in the fitting process. `na.action` a function which indicates what should happen when the data contain NAs (see `glm`). `method` the method to be used in fitting local models. The default method "bw.gwer" uses Fisher's scoring method. The alternative "model.frame" returns the model frame and does no fitting. `control` a list of parameters for controlling the fitting process. For `elliptical` this is passed by `glm.control`. `model` a logical value indicating whether model frame should be included as a component of the return. `x` a logical value indicating whether the response vector used in the fitting process should be returned as components of the return. `y` a logical value indicating whether model matrix used in the fitting process should be returned as components of the return. `contrasts` an optional list. See the `contrasts.arg` of `model.matrix.default`. `offset` this can be used to specify an a priori known component to be included in the linear predictor during fitting as in `glm`. `spdisp` if TRUE dispersion parameter varies geographically. `parplot` if TRUE the parameters boxplots are plotted. `...` arguments to be used to form the default control argument if it is not supplied directly.

## Value

returns an object of class “gwer”, a list with follow components:

 `SDF` a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package sp) with fit.points, weights, GWR coefficient estimates, dispersion and the residuals in its `data` slot. `coef` the matrices of coefficients, standard errors and significance values for parameters hypothesis test. `dispersion` either the supplied argument or the estimated dispersion with standard error. `hat` hat matrix of the geographically weighted elliptical model. `lm` elliptical global regression on the same model formula. `results` a list of results values for fitted geographically weighted elliptical model. `bandwidth` the bandwidth used in geographical weighting function. `fitted` the fitted mean values of the geographically weighted elliptical model. `hatmatrix` a logical value indicating if hatmatrix was considered `gweights` a matrix with the geographical weighting for all local elliptical models. `family` the `family` object used. `flm` a matrix with the fitted values for all local elliptical models. `adapt` the `adapt` object used. `kernel` the `kernel` object used. `spdisp` the `spdisp` object used. `this.call` the function call used. `longlat` the `longlat` object used.

## References

Brunsdon, C., Fotheringham, A. S. and Charlton, M. E. (1996). Geographically weighted regression: a method for exploring spatial nonstationarity. Geographical analysis, 28(4), 281-298. doi: 10.1111/j.1538-4632.1996.tb00936.x

Cysneiros, F. J. A., Paula, G. A., and Galea, M. (2007). Heteroscedastic symmetrical linear models. Statistics & probability letters, 77(11), 1084-1090. doi: 10.1016/j.spl.2007.01.012

Fang, K. T., Kotz, S. and NG, K. W. (1990, ISBN:9781315897943). Symmetric Multivariate and Related Distributions. London: Chapman and Hall.

`bw.gwer`, `elliptical`, `family.elliptical`

## Examples

 ```1 2 3 4 5 6 7``` ```data(georgia, package = "spgwr") fit.formula <- PctBach ~ TotPop90 + PctRural + PctFB + PctPov gwer.bw.t <- bw.gwer(fit.formula, data = gSRDF, family = Student(3), adapt = TRUE) gwer.fit.t <- gwer(fit.formula, data = gSRDF, family = Student(3), bandwidth = gwer.bw.t, adapt = TRUE, parplot = FALSE, hatmatrix = TRUE, spdisp = TRUE, method = "gwer.fit") print(gwer.fit.t) ```

gwer documentation built on April 28, 2021, 9:07 a.m.