gwer (version 1.0)

gwer.sel: Optimization of Bandwidth for Geographically Weighted Elliptical Regression

Description

The function finds a bandwidth for a given geographically weighted elliptical regression by optimzing a selected function. For cross-validation, this scores the root mean square prediction error for the geographically weighted elliptical regressions, choosing the bandwidth minimizing this quantity.

Usage

gwer.sel(formula, data = list(), coords, adapt = FALSE,
  gweight = gwr.Gauss, method = "cv", verbose = TRUE,
  longlat = NULL, family, RMSE = FALSE, weights,
  tol = .Machine$double.eps^0.25, show.error.messages = 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.

coords

matrix of coordinates of points representing the spatial positions of the observations.

adapt

defines the type of bandwidth used. Either TRUE: find the proportion between 0 and 1 of observations to include in weighting scheme (k-nearest neighbours) or FALSE: find global bandwidth.

gweight

geographical weighting function, at present gwr.Gauss() default, or gwr.bisquare().

method

default "cv" for drop-1 cross-validation, "aic" for AIC optimisation (depends on assumptions about AIC degrees of freedom) or "sv" for spatial validation.

verbose

if TRUE (default), reports the progress of search for bandwidth.

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.

family

a description of the error distribution to be used in the model (see elliptical.family for details of family functions).

RMSE

default FALSE to correspond with CV scores in newer references (sum of squared CV errors), if TRUE the previous behaviour of scoring by LOO CV RMSE.

weights

case weights used as in weighted least squares, beware of scaling issues. Only used with the cross-validation method, probably unsafe.

tol

the desired accuracy to be passed to optimize.

show.error.messages

default FALSE. may be set to TRUE to see error messages if gwer.sel returns without a value.

...

arguments to be used to form the default control argument if it is not supplied directly.

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. https://doi.org/10.1111/j.1538-4632.1996.tb00936.x

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(columbus, package="spData")
gwer.bw <- gwer.sel(CRIME ~ INC, data=columbus, family = Normal(),
                 coords=cbind(columbus$X, columbus$Y))
# }
# NOT RUN {
data(columbus, package="spData")
gwer.bw <- gwer.sel(CRIME ~ INC, data=columbus, family = Student(df=4),
                 coords=cbind(columbus$X, columbus$Y))
# }