R: (co)kriging cross validation, n-fold or leave-one-out

krige.cv {gstat} | R Documentation

## (co)kriging cross validation, n-fold or leave-one-out

### Description

Cross validation functions for simple, ordinary or universal point (co)kriging, kriging in a local neighbourhood.

### Usage

    gstat.cv(object, nfold, remove.all = FALSE, verbose = interactive(),
    	all.residuals = FALSE, ...)
    krige.cv(formula, locations, ...)
    krige.cv.locations(formula, locations, data, model = NULL, ..., beta = NULL,
    	nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(data),
    	verbose = interactive(), debug.level = 0)
    krige.cv.spatial(formula, locations, model = NULL, ..., beta = NULL,
    	nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(locations),
    	verbose = interactive(), debug.level = 0)

### Arguments

`object` | object of class gstat; see function gstat
`nfold` | integer; if larger than 1, then apply n-fold cross validation; if `nfold` equals `nrow(data)` (the default), apply leave-one-out cross validation; if set to e.g. 5, five-fold cross validation is done. To specify the folds, pass an integer vector of length `nrow(data)` with fold indexes.
`remove.all` | logical; if TRUE, remove observations at cross validation locations not only for the first, but for all subsequent variables as well
`verbose` | logical; if FALSE, progress bar is suppressed
`all.residuals` | logical; if TRUE, residuals for all variables are returned instead of for the first variable only
`...` | other arguments that will be passed to predict in case of `gstat.cv`, or to gstat in case of `krige.cv`
`formula` | formula that defines the dependent variable as a linear model of independent variables; suppose the dependent variable has name `z`, for ordinary and simple kriging use the formula `z~1`; for simple kriging also define `beta` (see below); for universal kriging, suppose `z` is linearly dependent on `x` and `y`, use the formula `z~x+y`
`locations` | data object deriving from class `Spatial` or `sf`
`data` | data frame (deprecated); should contain the dependent variable, independent variables, and coordinates; only to be provided if `locations` is a formula
`model` | variogram model of dependent variable (or its residuals), defined by a call to vgm or fit.variogram
`beta` | only for simple kriging (and simulation based on simple kriging); vector with the trend coefficients (including intercept); if no independent variables are defined the model only contains an intercept and this should be the simple kriging mean
`nmax` | for local kriging: the number of nearest observations that should be used for a kriging prediction or simulation, where nearest is defined in terms of the space of the spatial locations. By default, all observations are used
`nmin` | for local kriging: if the number of nearest observations within distance `maxdist` is less than `nmin`, a missing value will be generated; see maxdist
`maxdist` | for local kriging: only observations within a distance of `maxdist` from the prediction location are used for prediction or simulation; if combined with `nmax`, both criteria apply
`debug.level` | print debugging information; 0 suppresses debug information

### Details

Leave-one-out cross validation (LOOCV) visits a data point, and predicts the value at that location by leaving out the observed value, and proceeds with the next data point. (The observed value is left out because kriging would otherwise predict the value itself.) N-fold cross validation makes a partitions the data set in N parts. For all observation in a part, predictions are made based on the remaining N-1 parts; this is repeated for each of the N parts. N-fold cross validation may be faster than LOOCV.

### Value

data frame containing the coordinates of `data` or those of the first variable in `object`, and columns of prediction and prediction variance of cross validated data points, observed values, residuals, zscore (residual divided by kriging standard error), and fold.

If `all.residuals` is true, a data frame with residuals for all variables is returned, without coordinates.

### Methods

formula = "formula", locations = "formula"

  locations specifies which coordinates in `data` refer to spatial coordinates

formula = "formula", locations = "Spatial"

  Object locations knows about its own spatial locations

### Note

Leave-one-out cross validation seems to be much faster in plain (stand-alone) gstat, apparently quite a bit of the effort is spent moving data around from R to gstat.

### Author(s)

Edzer Pebesma

### References

http://www.gstat.org/

### See Also

krige, gstat, predict

### Examples

    library(sp)
    data(meuse)
    coordinates(meuse) <- ~x+y
    m <- vgm(.59, "Sph", 874, .04)
    # five-fold cross validation:
    x <- krige.cv(log(zinc)~1, meuse, m, nmax = 40, nfold=5)
    bubble(x, "residual", main = "log(zinc): 5-fold CV residuals")

    # multivariable; thanks to M. Rufino:
    meuse.g <- gstat(id = "zn", formula = log(zinc) ~ 1, data = meuse)
    meuse.g <- gstat(meuse.g, "cu", log(copper) ~ 1, meuse)
    meuse.g <- gstat(meuse.g, model = vgm(1, "Sph", 900, 1), fill.all = TRUE)
    x <- variogram(meuse.g, cutoff = 1000)
    meuse.fit = fit.lmc(x, meuse.g)
    out = gstat.cv(meuse.fit, nmax = 40, nfold = 5)
    summary(out)
    out = gstat.cv(meuse.fit, nmax = 40, nfold = c(rep(1,100), rep(2,55)))
    summary(out)
    # mean error, ideally 0:
    mean(out$residual)
    # MSPE, ideally small
    mean(out$residual^2)
    # Mean square normalized error, ideally close to 1
    mean(out$zscore^2)
    # correlation observed and predicted, ideally 1
    cor(out$observed, out$observed - out$residual)
    # correlation predicted and residual, ideally 0
    cor(out$observed - out$residual, out$residual)

[Package gstat version 2.0-3 Index]