Description Usage Arguments Details Value Author(s) References See Also Examples
This function assesses the goodnessoffit of a spatial linear model by
Kfold crossvalidation. In more detail, the model is refitted
K times by robust (or Gaussian) (RE)ML, excluding each time
1/Kth of the data. The refitted models are used to compute robust
(or customary) external Kriging predictions for the omitted observations.
If the response variable is logtransformed 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 crossvalidation errors are described for the function
validate.predictions
.
1 2 3 4 5 6 7 8 9 10 11 12 13  ## S3 method for class '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, ...)

object 
an object of class of 
formula 
an optional formula for the regression model passed by

subset 
an optional vector specifying a subset of observations to be used in the fitting process. 
method 
keyword, controlling whether subsets are formed by
partitioning data set into 
nset 
positive integer defining the number K of subsets into
which the data set is partitioned (default: 
seed 
optional integer seed to initialize random number generation,
see 
sets 
an optional vector of the same length as the response vector
of the fitted model and with positive integers taking values in
(1,2,…,K), defining in this way the K subsets into which
the data set is split. If 
duplicates.in.same.set 
logical controlling whether replicated
observations at a given location are assigned to the same subset when
partitioning the data (default 
re.estimate 
logical controlling whether the model is refitted to
the reduced data sets before computing the Kriging predictions
( 
param 
a named numeric vector or a matrix or data frame with
initial values of variogram parameters passed by

fit.param 
a named logical vector or a matrix or data frame
defining which variogram parameters should be adjusted by

aniso 
a named numeric vector or a matrix or data frame with
initial values of anisotropy parameters passed by

fit.aniso 
a named logical vector or a matrix or data frame
defining which anisotropy parameters should be adjusted by

variogram.object 
an optional list that gives initial values of for fitting a possibly nested variogram model for the crossvalidation sets. Each component is a list with the following components:

use.fitted.param 
logical scalar controlling whether fitted values
of 
return.fit 
logical controlling whether information about the fit
should be returned when reestimating the model with the reduced data
sets (default 
reduced.output 
logical controlling whether the complete fitted
model objects, fitted to the reduced data sets, are returned
( 
lgn 
logical controlling whether Kriging predictions of a
logtransformed response should be transformed back to the original scale
of the measurements (default 
mfl.action 
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 ( 
ncores 
positive integer controlling how many cores are used for parallelized computations, see Details. 
verbose 
positive integer controlling logging of diagnostic
messages to the console during model fitting. Passed by

... 
additional arguments passed by 
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 packages parallel, snow
and snowfall 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
reestimated the model with the reduced data sets. Therefore, any
argument accepted by georob
except data
can be
changed when refitting 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 crossvalidate a fitted model
without reestimating 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.
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
crossvalidation prediction results with the following variables:
subset 
an integer vector defining to which of the K subsets an observation was assigned. 
data 
the values of the (possibly logtransformed) response. 
pred 
the Kriging predictions. 
se 
the Kriging standard errors. 
If lgn = TRUE
then pred
has the additional variables:
lgn.data 
the untransformed response. 
lgn.pred 
the unbiased backtransformed predictions of a logtransformed response. 
lgn.se 
the Kriging standard errors of the backtransformed predictions of a logtransformed response. 
The second component fit
contains either the full outputs of
georob
, fitted for the K reduced data sets
(reduced.output = FALSE
), or K lists with the components
tuning.psi
, converged
,
convergence.code
,
gradient
, variogram.model
, param
,
aniso[["aniso"]]
, coefficients
along with the standard errors of
hatβ, see
georobObject
.
Andreas Papritz [email protected]
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning; Data Mining, Inference and Prediction. New York: SpringerVerlag.
georobIntro
for a description of the model and a brief summary of the algorithms;
georob
for (robust) fitting of spatial linear models;
georobObject
for a description of the class georob
;
profilelogLik
for computing profiles of Gaussian likelihoods;
plot.georob
for display of RE(ML) variogram estimates;
control.georob
for controlling the behaviour of georob
;
georobModelBuilding
for stepwise building models of class georob
;
georobMethods
for further methods for the class georob
;
predict.georob
for computing robust Kriging predictions;
validate.predictions
for validating Kriging predictions;
lgnpp
for unbiased backtransformation of Kriging prediction
of logtransformed data;
georobSimulation
for simulating realizations of a Gaussian process
from model fitted by georob
; and finally
sample.variogram
and fit.variogram.model
for robust estimation and modelling of sample variograms.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ## 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"))
## End(Not run)

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