gwer (version 2.1)

gwer.sel: 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

gwer.sel(
  formula,
  data = list(),
  coords,
  adapt = FALSE,
  gweight = gwr.Gauss,
  weights,
  method = "cv",
  verbose = TRUE,
  longlat = NULL,
  family = Normal(),
  RMSE = FALSE,
  tol = .Machine$double.eps^0.25,
  show.error.messages = FALSE,
  maxit = 100
)

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.

weights

an optional numeric vector of weights to be used in the fitting process, beware of scaling issues. Only used with the cross-validation method, probably unsafe.

method

type of the method used to the compute of residuals. Is cv for drop-1 cross-validation (default), 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 family.elliptical for more 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.

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.

maxit

maximum number of iterations in model fit

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

Cysneiros, F. J. A., Paula, G. A., and Galea, M. (2007). Heteroscedastic symmetrical linear models. Statistics & probability letters, 77(11), 1084-1090. https://doi.org/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(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), method = "aic")
# }