gwer (version 3.0)

bw.gwer: Optimization of Bandwidth for Geographically Weighted Elliptical Regression Model

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. 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. 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

# NOT RUN {
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)
# }