bw.gwer: Optimization of Bandwidth for Geographically Weighted...

In gwer: Geographically Weighted Elliptical Regression

Description

The function compute the optimal bandwidth for a given geographically weighted elliptical regression using three differents methods: cross-validation, AIC and spatial validation. This optimal bandwidth optimzing the selected function.

Usage

bw.gwer(
  formula,
  family = Normal(),
  data,
  approach = "CV",
  kernel = "bisquare",
  adaptive = F,
  spdisp = "local",
  dispersion,
  p = 2,
  theta = 0,
  longlat = F,
  dMat
)

Arguments

formula	regression model formula of a formula object.
family	a description of the error distribution to be used in the model (see family.elliptical for more details of family functions).
data	a SpatialPointsDataFrame or SpatialPolygonsDataFrame as defined in package sp.
approach	specified by CV for cross-validation approach, by AIC for corrected Akaike information criterion approach or by MI for spatial-validation approach.
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.
adaptive	if TRUE calculate an adaptive kernel where the bandwidth (bw) corresponds to the number of nearest neighbours (i.e. adaptive distance); default is FALSE, where a fixed kernel is found (bandwidth is a fixed distance).
spdisp	if TRUE, by default, the dispersion parameter vary geographically in estimation process.
dispersion	an optional fixed value for dispersion parameter.
p	the power of the Minkowski distance, default is 2 (Euclidean distance).
theta	an angle in radians to rotate the coordinate system, default is 0
longlat	if TRUE, great circle distances will be calculated.
dMat	a pre-specified distance matrix, it can be calculated by the function gw.dist.

Value

returns the bandwidth optimization value.

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.

See Also

gwer, elliptical, family.elliptical

Examples

data(georgia, package="spgwr")
fit.formula <- PctBach ~ TotPop90 + PctRural + PctFB + PctPov
gwer.bw.n <- bw.gwer(fit.formula, data = gSRDF, family = Student(3), 
                    longlat = TRUE, adapt = TRUE)

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