| cv.georob {georob} | R Documentation |
Cross-Validating a Spatial Linear Model Fitted by georob
Description
This 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.
Usage
## S3 method for class 'georob'
cv(object, formula = NULL, subset = NULL,
method = c("block", "random"), nset = 10L, 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, parallel::detectCores()), verbose = 0, ...)
Arguments
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 |
a character keyword, controlling whether subsets are formed
by partitioning data set into contiguous spatial |
nset |
a positive integer defining the number K of subsets into
which the data set is partitioned (default: |
seed |
an 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
|
duplicates.in.same.set |
a logical scalar controlling whether
replicated observations at a given location are assigned to the same
subset when partitioning the data (default |
re.estimate |
a logical scalar controlling whether the model is
re-fitted 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 for fitting a possibly nested variogram model for the cross-validation sets. Each component is a list with the following components:
|
use.fitted.param |
a logical scalar controlling whether fitted values
of |
return.fit |
a logical scalar controlling whether information about the fit
should be returned when re-estimating the model with the reduced data
sets (default |
reduced.output |
a logical scalar controlling whether the complete fitted
model objects, fitted to the reduced data sets, are returned
( |
lgn |
a logical scalar controlling whether Kriging predictions of a
log-transformed response should be transformed back to the original scale
of the measurements (default |
mfl.action |
a character keyword 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 |
a positive integer controlling how many cores are used for parallelized computations, see Details. |
verbose |
a positive integer controlling logging of diagnostic
messages to the console during model fitting. Passed by
|
... |
additional arguments passed by |
Details
Note that the data frame passed as data
argument to georob must exist in the user workspace
when calling cv.georob.
cv.georob uses the packages parallel 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
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.
Value
The method cv.georob returns 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:
subset |
an integer vector defining to which of the |
data |
the values of the (possibly log-transformed) 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 back-transformed predictions of a log-transformed response. |
lgn.se |
the Kriging standard errors of the back-transformed
predictions of a |
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.object, coefficients along with
the standard errors of
\widehat{\boldsymbol{\beta}}, see
georobObject.
Author(s)
Andreas Papritz papritz@retired.ethz.ch.
References
Hastie, T., Tibshirani, R. and Friedman, J. (2009) The Elements of Statistical Learning; Data Mining, Inference and Prediction, Springer, New York, doi:10.1007/978-0-387-84858-7
See Also
georobPackage 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 back-transformation of Kriging prediction
of log-transformed 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.
Examples
## define number of cores for parallel computations
if(interactive()) ncpu <- 10L else ncpu <- 1L
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 = 1000)
if(interactive()){
## example is run only in interactive session because cpu times exceeds 5 s
r.logzn.cv.1 <- cv(r.logzn, seed = 1, lgn = TRUE, ncores = 1, verbose = 1)
r.logzn.cv.2 <- cv(r.logzn, formula = .~. + ffreq, seed = 1, lgn = TRUE,
ncores = ncpu)
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"))
}