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

Description Usage Arguments Value References See Also Examples

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

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,
  ...
)

`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.

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.

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

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)