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

krige.cvR Documentation

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


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

Usage, nfold, remove.all = FALSE, verbose = interactive(), 
	all.residuals = FALSE, ...), locations, ...), locations, data, model = NULL, ..., beta = NULL, 
	nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(data), 
	verbose = interactive(), debug.level = 0), locations, model = NULL, ..., beta = NULL, 
	nmax = Inf, nmin = 0, maxdist = Inf, nfold = nrow(locations), 
	verbose = interactive(), debug.level = 0)



object of class gstat; see function gstat


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.


logical; if TRUE, remove observations at cross validation locations not only for the first, but for all subsequent variables as well


logical; if FALSE, progress bar is suppressed


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, or to gstat in case of


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


data object deriving from class Spatial or sf


data frame (deprecated); should contain the dependent variable, independent variables, and coordinates; only to be provided if locations is a formula


variogram model of dependent variable (or its residuals), defined by a call to vgm or fit.variogram


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


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


for local kriging: if the number of nearest observations within distance maxdist is less than nmin, a missing value will be generated; see 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


print debugging information; 0 suppresses debug information


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.


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.


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


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.


Edzer Pebesma


See Also

krige, gstat, predict


coordinates(meuse) <- ~x+y
m <- vgm(.59, "Sph", 874, .04)
# five-fold cross validation:
x <-, 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) = fit.lmc(x, meuse.g)
out =, nmax = 40, nfold = 5) 
out =, nmax = 40, nfold = c(rep(1,100), rep(2,55))) 
# mean error, ideally 0:
# MSPE, ideally small
# Mean square normalized error, ideally close to 1
# 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)

gstat documentation built on Oct. 19, 2022, 5:28 p.m.