xvalid {geoR}

Cross-validation by kriging

Description

A function to perform model validation by comparing observed and values predicted by kriging. Options include: (i) leaving-one-out cross-validation where each data location is removed from the data set and the variable at this location is predicted using the remaining locations, for a given model. This can be computed for all or a subset of the data locations; (ii) external validation can be performed by using validation locations other than data locations.

Usage

xvalid(geodata, coords = geodata$coords, data = geodata$data,
       model, reestimate = FALSE, variog.obj = NULL,
       output.reestimate = FALSE, locations.xvalid = "all",
       data.xvalid = NULL, messages, ...)

Arguments

geodata

a list containing element coords as described next. Typically an object of the class "geodata" - a geoR data-set. If not provided the arguments coords must be provided instead.

coords

an n \times 2 matrix containing coordinates of the n data locations in each row. Defaults to geodata$coords, if provided.

data

a vector or matrix with data values. If a matrix is provided, each column is regarded as one variable or realization. Defaults to geodata$data, if provided.

model

an object containing information on a fitted model. Typically an output of likfit, variofit. If an object of the class eyefit is passed it takes the first model specified in the object.

reestimate

logical. Indicates whether or not the model parameters should be re-estimated for each point removed from the data-set.

variog.obj

on object with the empirical variogram, typically an output of the function variog. Only used if reestimate = TRUE and the object passed to the argument model is the result of a variogram based estimation, i.e. if the model was fitted by variofit.

output.reestimate

logical. Only valid if reestimate = TRUE. Specifies whether the re-estimated parameters are returned.

locations.xvalid

there are three possible specifications for this argument: "all" indicates the leaving-on-out method is used at all data locations. The second possibility is to use only a sub-set of the data for cross-validation in which case the argument takes a vector with numbers (indexes) indicating at which of the data locations the cross-validation should be performed. The third option is to perform external validation, on locations other than data locations used for the model. For the latter a matrix with the coordinates of the validation points should be provided and the argument data.xvalid mandatory.

data.xvalid

data values at the validation locations. Only used if the validation locations are other than the data locations.

messages

logical. Indicates whether status messages should be printed on the screen (or output device) while the function is running.

...

further arguments to the minimization functions used by likfit, variofit.

Details

The cross-validation uses internally the function krige.conv to predict at each location.

For models fitted by variofit the parameters \kappa, \psi_A, \psi_R and \lambda are always regarded as fixed when reestimating the model.

See documentation of the function likfit for further details on the model specification and parameters.

Value

An object of the class "xvalid" which is a list with the following components:

data

the original data.

predicted

the values predicted by cross-validation.

krige.var

the cross-validation prediction variance.

error

the differences data - predicted value.

std.error

the errors divided by the square root of the prediction variances.

prob

the cumulative probability at original value under a normal distribution with parameters given by the cross-validation results.

A method for summary returns summary statistics for the errors and standard errors.

If reestimate = TRUE and output = TRUE additional columns are added to the resulting data-frame with the values of the re-estimated parameters.

Author(s)

Paulo J. Ribeiro Jr. [e-mail],
Peter J. Diggle [e-mail].

References

Further information on the package geoR can be found at:
http://www.leg.ufpr.br/geoR/.

See Also

plot.xvalid for plotting of the results, likfit, variofit for parameter estimation and krige.conv for the kriging method used for predictions.

Examples

#
# Maximum likelihood estimation
#
s100.ml <- likfit(s100, ini = c(.5, .5), fix.nug = TRUE)
#
# Weighted least squares estimation
#
s100.var <- variog(s100, max.dist = 1)
s100.wls <- variofit(s100.var, ini = c(.5, .5), fix.nug = TRUE)
#
# Now, performing cross-validation without reestimating the model
#
s100.xv.ml <- xvalid(s100, model = s100.ml)
s100.xv.wls <- xvalid(s100, model = s100.wls)
##
## Plotting results
##
par.ori <- par(no.readonly = TRUE)
##
par(mfcol=c(5,2), mar=c(2.3,2.3,.5,.5), mgp=c(1.3, .6, 0))
plot(s100.xv.ml)
par(mfcol=c(5,2))
plot(s100.xv.wls)
##
par(par.ori)
#