krige.cv: (co)kriging cross validation, n-fold or leave-one-out

In gstat: Spatial and Spatio-Temporal Geostatistical Modelling, Prediction and Simulation

(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)

gstat documentation built on Sept. 11, 2024, 7:46 p.m.