georobThis function assesses the goodness-of-fit of a spatial linear model by
K-fold cross-validation. In more detail, the model is re-fitted
K times by robust (or Gaussian) (RE)ML, excluding each time
1/Kth of the data. The re-fitted models are used to compute robust
(or customary) external Kriging predictions for the omitted observations.
If the response variable is log-transformed then the Kriging predictions
can be optionally transformed back to the original scale of the
measurements. S3methods for evaluating and plotting diagnostic summaries
of the cross-validation errors are described for the function
validate.predictions.
# S3 method for georob
cv(object, formula = NULL, subset = NULL,
method = c("block", "random"), nset = 10, seed = NULL,
sets = NULL, duplicates.in.same.set = TRUE, re.estimate = TRUE,
param = object[["variogram.object"]][[1]][["param"]],
fit.param = object[["variogram.object"]][[1]][["fit.param"]],
aniso = object[["variogram.object"]][[1]][["aniso"]],
fit.aniso = object[["variogram.object"]][[1]][["fit.aniso"]],
variogram.object = NULL,
use.fitted.param = TRUE, return.fit = FALSE,
reduced.output = TRUE, lgn = FALSE,
mfl.action = c("offset", "stop"),
ncores = min(nset, detectCores()), verbose = 0, ...)an object of class of "georob", see
georobObject.
an optional vector specifying a subset of observations to be used in the fitting process.
keyword, controlling whether subsets are formed by
partitioning data set into blocks by kmeans
(default) or randomly. Ignored if sets is
non-NULL.
positive integer defining the number K of subsets into
which the data set is partitioned (default: nset = 10). Ignored
if sets is non-NULL.
optional integer seed to initialize random number generation,
see set.seed. Ignored if sets is non-NULL.
an optional vector of the same length as the response vector
of the fitted model and with positive integers taking values in
\((1,2,\ldots,K)\), defining in this way the \(K\) subsets into which
the data set is split. If sets = NULL (default) the partition is
randomly generated by kmeans or
runif (using possibly seed).
logical controlling whether replicated
observations at a given location are assigned to the same subset when
partitioning the data (default TRUE).
logical controlling whether the model is re-fitted to
the reduced data sets before computing the Kriging predictions
(TRUE, default) or whether the model passed in object is
used to compute the predictions for the omitted observations, see
Details.
a named numeric vector or a matrix or data frame with
initial values of variogram parameters passed by
update to georob. If param is
a matrix (or a data frame) then it must have nset rows and
length(object[["variogram.object"]][[1]][["param"]]) columns with
initial values of variogram parameters for the nset
cross-validation sets, and colnames(param) must match
names(object[["variogram.object"]][[1]][["param"]]).
a named logical vector or a matrix or data frame
defining which variogram parameters should be adjusted by
update. If fit.param is a matrix (or a data
frame) then it must have nset rows and
length(object[["variogram.object"]][[1]][["fit.param"]]) columns
with variogram parameter fitting flags for the nset
cross-validation sets, and colnames(param) must match
names(object[["variogram.object"]][[1]][["fit.param"]]).
a named numeric vector or a matrix or data frame with
initial values of anisotropy parameters passed by
update to georob. If aniso is
a matrix (or a data frame) then it must have nset rows and
length(object[["variogram.object"]][[1]][["aniso"]]) columns with
initial values of anisotropy parameters for the nset
cross-validation sets, and colnames(aniso) must match
names(object[["variogram.object"]][[1]][["aniso"]]).
a named logical vector or a matrix or data frame
defining which anisotropy parameters should be adjusted by
update. If fit.aniso is a matrix (or a data
frame) then it must have nset rows and
length(object[["variogram.object"]][[1]][["fit.aniso"]]) columns
with anisotropy parameter fitting flags for the nset
cross-validation sets, and colnames(param) must match
names(object[["variogram.object"]][[1]][["fit.aniso"]]).
an optional list that gives initial values of for fitting a possibly nested variogram model for the cross-validation sets. Each component is a list with the following components:
param: an optional named numeric vector or a matrix or data
frame with initial values of variogram parameters passed by
update to georob. If param
is a matrix (or a data frame) then it must have nset rows and
length(object[["variogram.object"]][[i]][["param"]]) columns
with initial values of variogram parameters for the nset
cross-validation sets (i is the ith variogram structure),
and colnames(param) must match
names(object[["variogram.object"]][[i]][["param"]]).
fit.param: an optional named logical vector or a matrix or data frame
defining which variogram parameters should be adjusted by
update. If fit.param is a matrix (or a
data frame) then it must have nset rows and
length(object[["variogram.object"]][[i]][["fit.param"]])
columns with variogram parameter fitting flags for the nset
cross-validation sets (i is the ith variogram structure),
and colnames(param) must match
names(object[["variogram.object"]][[i]][["fit.param"]]).
aniso: an optional named numeric vector or a matrix or data frame with
initial values of anisotropy parameters passed by
update to georob. If aniso
is a matrix (or a data frame) then it must have nset rows and
length(object[["variogram.object"]][[i]][["aniso"]]) columns
with initial values of anisotropy parameters for the nset
cross-validation sets (i is the ith variogram structure),
and colnames(aniso) must match
names(object[["variogram.object"]][[i]][["aniso"]]).
fit.aniso: an optional named logical vector or a matrix or
data frame defining which anisotropy parameters should be adjusted by
update. If fit.aniso is a matrix (or a
data frame) then it must have nset rows and
length(object[["variogram.object"]][[i]][["fit.aniso"]])
columns with anisotropy parameter fitting flags for the nset
cross-validation sets(i is the ith variogram structure),
and colnames(param) must match
names(object[["variogram.object"]][[i]][["fit.aniso"]]).
logical scalar controlling whether fitted values
of param (and aniso are used as initial values when
variogram parameters are fitted for the cross-validation sets (default
TRUE).
logical controlling whether information about the fit
should be returned when re-estimating the model with the reduced data
sets (default FALSE).
logical controlling whether the complete fitted
model objects, fitted to the reduced data sets, are returned
(FALSE) or only some components (TRUE, default, see
Value). Ignored if return.fit = FALSE.
logical controlling whether Kriging predictions of a
log-transformed response should be transformed back to the original scale
of the measurements (default FALSE).
character controlling what is done when some levels of
factor(s) are not present in any of the subsets used to fit the model.
The function either stops ("stop") or treats the respective
factors as model offset ("offset", default).
positive integer controlling how many cores are used for parallelized computations, see Details.
An object of class cv.georob, which is a list with the two
components pred and fit.
pred is a data frame with the coordinates and the
cross-validation prediction results with the following variables:
an integer vector defining to which of the \(K\) subsets an observation was assigned.
the values of the (possibly log-transformed) response.
the Kriging predictions.
the Kriging standard errors.
the untransformed response.
the unbiased back-transformed predictions of a log-transformed response.
the Kriging standard errors of the back-transformed predictions of a log-transformed response.
Note that the data frame passed as data
argument to georob must exist in the user workspace
when calling cv.georob.
cv.georob then uses the package parallel for parallelized
computations. By default, the function uses \(K\) CPUs but not
more than are physically available (as returned by
detectCores).
cv.georob uses the function update to
re-estimated the model with the reduced data sets. Therefore, any
argument accepted by georob except data can be
changed when re-fitting the model. Some of them (e.g. formula,
subset, etc.) are explicit arguments of cv.georob, but
also the remaining ones can be passed by … to the function.
Practitioners in geostatistics commonly cross-validate a fitted model
without re-estimating the model parameters with the reduced data sets.
This is clearly an unsound practice (see Hastie et al., 2009, sec.
7.10). Therefore, the argument re.estimate should always be set
to TRUE. The alternative is provided only for historic reasons.
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning; Data Mining, Inference and Prediction. New York: Springer-Verlag.
validate.predictions for computing statistics of the cross-validation errors;
georob for (robust) fitting of spatial linear models;
georobObject for a description of the class georob;
predict.georob for computing robust Kriging predictions.
# NOT RUN {
data(meuse)
r.logzn <- georob(log(zinc) ~ sqrt(dist), data = meuse, locations = ~ x + y,
variogram.model = "RMexp",
param = c(variance = 0.15, nugget = 0.05, scale = 200),
tuning.psi = 1)
r.logzn.cv.1 <- cv(r.logzn, seed = 1, lgn = TRUE)
r.logzn.cv.2 <- cv(r.logzn, formula = .~. + ffreq, seed = 1, lgn = TRUE)
plot(r.logzn.cv.1, type = "bs")
plot(r.logzn.cv.2, type = "bs", add = TRUE, col = "red")
legend("topright", lty = 1, col = c("black", "red"), bty = "n",
legend = c("log(Zn) ~ sqrt(dist)", "log(Zn) ~ sqrt(dist) + ffreq"))
# }
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