GeoCV: n-fold kriging Cross-validation

In GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis

n-fold kriging Cross-validation

Description

The procedure uses the GeoKrig or GeoKrigloc function to compute n-fold kriging cross-validation using information from a GeoFit object. The function returns prediction scores.

Usage

GeoCV(
  fit, K = 100, estimation = TRUE,
  optimizer = NULL, lower = NULL, upper = NULL,
  n.fold = 0.05, local = FALSE,
  neighb = NULL, maxdist = NULL, maxtime = NULL,
  sparse = FALSE, type_krig = "Simple", which = 1,
  parallel = TRUE, ncores = NULL, progress = TRUE,
  seed = NULL
)

Arguments

fit	An object of class GeoFit.
K	The number of iterations in cross-validation.
estimation	Logical; if TRUE, an estimation is performed at each iteration and the estimates are used in the prediction. Otherwise, the estimates in the object fit are used.
optimizer	The type of optimization algorithm if estimation is TRUE. See GeoFit for details. If NULL, then the optimization algorithm stored in fit is used.
lower	An optional named list giving the values for the lower bounds of the parameters when bounded optimization is used and estimation is TRUE.
upper	An optional named list giving the values for the upper bounds of the parameters when bounded optimization is used and estimation is TRUE.
n.fold	Numeric; the percentage of data to be deleted and predicted in each cross-validation iteration.
local	Logical; if TRUE, local kriging is performed. The default is FALSE.
neighb	Numeric; an optional positive integer indicating the order of neighborhood if local kriging is performed.
maxdist	Numeric; an optional positive value indicating the spatial neighborhood distance if local kriging is performed.
maxtime	Numeric; an optional positive value indicating the temporal neighborhood distance if local kriging is performed.
sparse	Logical; if TRUE, kriging and simulation are computed with sparse matrix algorithms using the spam package. The default is FALSE. It should be used with compactly supported covariance models.
type_krig	String; the type of kriging. If "Simple", the default, simple kriging is performed. If "Optim", optimal kriging is performed for some non-Gaussian random fields.
which	Numeric; in the case of bivariate cokriging, it indicates which variable to predict. It can be 1 or 2.
parallel	Logical; if TRUE, the cross-validation iterations are parallelized.
ncores	Numeric; number of cores involved in parallelization.
progress	Logical; if TRUE, a progress bar is shown.
seed	Optional integer seed used to make the random selection of folds and any stochastic refitting step reproducible. If NULL, the current random number generator state is left unchanged. When supplied, the previous .Random.seed is restored on exit.

Details

The function randomly removes a fraction n.fold of the observations at each iteration, predicts the removed observations using kriging, and computes a set of predictive scores.

If estimation = TRUE, the model is re-estimated at each cross-validation iteration before prediction. Otherwise, the parameter estimates contained in fit are used.

When seed is supplied, the cross-validation folds are reproducible. The function preserves and restores the user's random number generator state.

Value

Returns a list containing the following components:

rmse	The vector of root mean squared errors.
mae	The vector of mean absolute errors.
mad	The vector of median absolute errors.
brie	The vector of Brier scores.
crps	The vector of continuous ranked probability scores.
lscore	The vector of log-scores.
pit	The vector of average probability integral transform values.
intscore	The vector of interval scores.
coverage	The vector of empirical coverage values.
seed	The seed used for reproducibility, or NULL.

Author(s)

Moreno Bevilacqua, [e-mail], https://sites.google.com/view/moreno-bevilacqua/home, Víctor Morales Oñate, [e-mail], https://sites.google.com/site/moralesonatevictor/, Christian Caamaño-Carrillo, [e-mail], https://www.researchgate.net/profile/Christian-Caamano

See Also

GeoKrig, GeoKrigloc, GeoFit.

Examples

library(GeoModels)

###############################################################
### Example of spatial kriging cross-validation
###############################################################

model <- "Gaussian"
set.seed(79)
x <- runif(400, 0, 1)
y <- runif(400, 0, 1)
coords <- cbind(x, y)

corrmodel <- "GenWend"
mean <- 0
sill <- 5
nugget <- 0
scale <- 0.2
smooth <- 0
power2 <- 4

param <- list(
  mean = mean, sill = sill, nugget = nugget,
  scale = scale, smooth = smooth, power2 = power2
)

data <- GeoSim(coordx = coords, corrmodel = corrmodel,
               param = param)$data

fixed <- list(nugget = nugget, smooth = 0, power2 = power2)
start <- list(mean = 0, scale = scale, sill = 1)
I <- Inf
lower <- list(mean = -I, scale = 0, sill = 0)
upper <- list(mean = I, scale = I, sill = I)

fit <- GeoFit(
  data, coordx = coords, corrmodel = corrmodel,
  model = model, likelihood = "Marginal", type = "Pairwise",
  neighb = 3, optimizer = "nlminb", lower = lower,
  upper = upper, start = start, fixed = fixed
)

#a <- GeoCV(fit, K = 100, estimation = TRUE,
#           parallel = TRUE, seed = 123)
#mean(a$rmse)

GeoModels documentation built on July 29, 2026, 5:06 p.m.