Estimate the prediction error of a linear model via (repeated) \(K\)-fold
cross-validation. Cross-validation functions are available for least
squares fits computed with lm as well as for the
following robust alternatives: MM-type models computed with
lmrob and least trimmed squares fits computed with
ltsReg.
repCV(object, ...)# S3 method for lm
repCV(
object,
cost = rmspe,
K = 5,
R = 1,
foldType = c("random", "consecutive", "interleaved"),
grouping = NULL,
folds = NULL,
seed = NULL,
...
)
# S3 method for lmrob
repCV(
object,
cost = rtmspe,
K = 5,
R = 1,
foldType = c("random", "consecutive", "interleaved"),
grouping = NULL,
folds = NULL,
seed = NULL,
...
)
# S3 method for lts
repCV(
object,
cost = rtmspe,
K = 5,
R = 1,
foldType = c("random", "consecutive", "interleaved"),
grouping = NULL,
folds = NULL,
fit = c("reweighted", "raw", "both"),
seed = NULL,
...
)
cvLm(
object,
cost = rmspe,
K = 5,
R = 1,
foldType = c("random", "consecutive", "interleaved"),
grouping = NULL,
folds = NULL,
seed = NULL,
...
)
cvLmrob(
object,
cost = rtmspe,
K = 5,
R = 1,
foldType = c("random", "consecutive", "interleaved"),
grouping = NULL,
folds = NULL,
seed = NULL,
...
)
cvLts(
object,
cost = rtmspe,
K = 5,
R = 1,
foldType = c("random", "consecutive", "interleaved"),
grouping = NULL,
folds = NULL,
fit = c("reweighted", "raw", "both"),
seed = NULL,
...
)
An object of class "cv" with the following components:
an integer giving the number of observations or groups.
an integer giving the number of folds.
an integer giving the number of replications.
a numeric vector containing the estimated prediction
errors. For the "lm" and "lmrob" methods, this is a single
numeric value. For the "lts" method, this contains one value for
each of the requested fits. In the case of repeated cross-validation, those
are average values over all replications.
a numeric vector containing the estimated standard
errors of the prediction loss. For the "lm" and "lmrob"
methods, this is a single numeric value. For the "lts" method, this
contains one value for each of the requested fits.
a numeric matrix containing the estimated prediction
errors from all replications. For the "lm" and "lmrob"
methods, this is a matrix with one column. For the "lts" method,
this contains one column for each of the requested fits. However, this is
only returned for repeated cross-validation.
the seed of the random number generator before cross-validation was performed.
the matched function call.
an object returned from a model fitting function. Methods
are implemented for objects of class "lm" computed with
lm, objects of class "lmrob" computed with
lmrob, and object of class "lts" computed
with ltsReg.
additional arguments to be passed to the prediction loss
function cost.
a cost function measuring prediction loss. It should expect
the observed values of the response to be passed as the first argument and
the predicted values as the second argument, and must return either a
non-negative scalar value, or a list with the first component containing
the prediction error and the second component containing the standard
error. The default is to use the root mean squared prediction error
for the "lm" method and the root trimmed mean squared prediction
error for the "lmrob" and "lts" methods (see
cost).
an integer giving the number of folds into which the data should
be split (the default is five). Keep in mind that this should be chosen
such that all folds are of approximately equal size. Setting K
equal to the number of observations or groups yields leave-one-out
cross-validation.
an integer giving the number of replications for repeated \(K\)-fold cross-validation. This is ignored for for leave-one-out cross-validation and other non-random splits of the data.
a character string specifying the type of folds to be
generated. Possible values are "random" (the default),
"consecutive" or "interleaved".
a factor specifying groups of observations. If supplied, the data are split according to the groups rather than individual observations such that all observations within a group belong to the same fold.
an object of class "cvFolds" giving the folds of the
data for cross-validation (as returned by cvFolds). If
supplied, this is preferred over the arguments for generating
cross-validation folds.
optional initial seed for the random number generator (see
.Random.seed).
a character string specifying for which fit to estimate the
prediction error. Possible values are "reweighted" (the default) for
the prediction error of the reweighted fit, "raw" for the prediction
error of the raw fit, or "both" for the prediction error of both
fits.
Andreas Alfons
(Repeated) \(K\)-fold cross-validation is performed in the following
way. The data are first split into \(K\) previously obtained blocks of
approximately equal size. Each of the \(K\) data blocks is left out once
to fit the model, and predictions are computed for the observations in the
left-out block with the predict method of the fitted
model. Thus a prediction is obtained for each observation.
The response variable and the obtained predictions for all observations are
then passed to the prediction loss function cost to estimate the
prediction error. For repeated cross-validation, this process is replicated
and the estimated prediction errors from all replications as well as their
average are included in the returned object.
cvFit, cvFolds, cost,
lm, lmrob,
ltsReg
library("robustbase")
data("coleman")
set.seed(1234) # set seed for reproducibility
# set up folds for cross-validation
folds <- cvFolds(nrow(coleman), K = 5, R = 10)
# perform cross-validation for an LS regression model
fitLm <- lm(Y ~ ., data = coleman)
repCV(fitLm, cost = rtmspe, folds = folds, trim = 0.1)
# perform cross-validation for an MM regression model
fitLmrob <- lmrob(Y ~ ., data = coleman)
repCV(fitLmrob, cost = rtmspe, folds = folds, trim = 0.1)
# perform cross-validation for an LTS regression model
fitLts <- ltsReg(Y ~ ., data = coleman)
repCV(fitLts, cost = rtmspe, folds = folds, trim = 0.1)
repCV(fitLts, cost = rtmspe, folds = folds,
fit = "both", trim = 0.1)
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