(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.
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)
object |
object of class gstat; see function gstat |
nfold |
integer; if larger than 1, then apply n-fold cross validation;
if |
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 |
formula |
formula that defines the dependent variable as a linear
model of independent variables; suppose the dependent variable has name
|
locations |
data object deriving from class |
data |
data frame (deprecated); should contain the dependent variable, independent
variables, and coordinates; only to be provided if |
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 |
for local kriging: only observations within a distance
of |
debug.level |
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.
locations specifies which coordinates in data refer to spatial coordinates
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
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)
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