xvalid {geoR} | R Documentation

## Cross-validation using kriging

### Description

This is a function to perform model validation. Options include 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 as given model. This can be done for all or some of the locations. Alternativelly, other validation locations which are not the same as the original data locations can be used.

### 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 x 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. The second possibility is to use only a sub-set of the data for cross-validation. For this case a vector should be provided with numbers indicating at which locations the cross-validation should be performed. The third option is to perform validation on a different set of data. For this a matrix with the coordinates of the validation points should be provided and the the argument `locations.data` should also be provided.
`data.xvalid` | data values at the validation locations. Only used if the validation locations are not the same or a subset of the original data coordinates.
`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 the function `krige.conv` to predict at each location.

For models fitted by `variofit` the parameters kappa, psiA, psiR and lambda are always regarded as fixed.

See documentation of the function `likfit` for more details on the model and its 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` | difference `data - predicted`.
`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 data-frame. Each column will contain the values of the re-estimated parameters.

### Author(s)

Paulo J. Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.

### References

Further information on the package geoR can be found at:
http://www.est.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

    data(s100)
    #
    # 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)
    #

[Package geoR version 1.5-7 Index]