Estimate the prediction error of a model via (repeated)
K-fold cross-validation. It is thereby possible to
supply an object returned by a model fitting function, a
model fitting function itself, or an unevaluated function
call to a model fitting function.
Usage
cvFit(object, ...)
## Default S3 method:
cvFit(object, data = NULL, x = NULL,
y, cost = rmspe, K = 5, R = 1,
foldType = c("random", "consecutive", "interleaved"),
folds = NULL, names = NULL, predictArgs = list(),
costArgs = list(), envir = parent.frame(), seed = NULL,
...)
## S3 method for class 'function'
cvFit(object, formula, data = NULL,
x = NULL, y, args = list(), cost = rmspe, K = 5, R = 1,
foldType = c("random", "consecutive", "interleaved"),
folds = NULL, names = NULL, predictArgs = list(),
costArgs = list(), envir = parent.frame(), seed = NULL,
...)
## S3 method for class 'call'
cvFit(object, data = NULL, x = NULL, y,
cost = rmspe, K = 5, R = 1,
foldType = c("random", "consecutive", "interleaved"),
folds = NULL, names = NULL, predictArgs = list(),
costArgs = list(), envir = parent.frame(), seed = NULL,
...)
Arguments
object
the fitted model for which to estimate the
prediction error, a function for fitting a model, or an
unevaluated function call for fitting a model (see
call for the latter). In the case of a
fitted model, the object is required to contain a
component call that stores the function call used
to fit the model, which is typically the case for objects
returned by model fitting functions.
formula
a formula describing
the model.
data
a data frame containing the variables
required for fitting the models. This is typically used
if the model in the function call is described by a
formula.
x
a numeric matrix containing the predictor
variables. This is typically used if the function call
for fitting the models requires the predictor matrix and
the response to be supplied as separate arguments.
y
a numeric vector or matrix containing the
response.
args
a list of additional arguments to be passed
to the model fitting 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 (see
cost).
K
an integer giving the number of groups into
which the data should be split (the default is five).
Keep in mind that this should be chosen such that all
groups are of approximately equal size. Setting K
equal to n yields leave-one-out cross-validation.
R
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.
foldType
a character string specifying the type of
folds to be generated. Possible values are
"random" (the default), "consecutive" or
"interleaved".
folds
an object of class "cvFolds" giving
the folds of the data for cross-validation (as returned
by cvFolds). If supplied, this is
preferred over K and R.
names
an optional character vector giving names
for the arguments containing the data to be used in the
function call (see “Details”).
predictArgs
a list of additional arguments to be
passed to the predict method of the
fitted models.
costArgs
a list of additional arguments to be
passed to the prediction loss function cost.
envir
the environment in which to
evaluate the function call for fitting the models (see
eval).
seed
optional initial seed for the random number
generator (see .Random.seed).
...
additional arguments to be passed down.
Details
(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.
Furthermore, if the response is a vector but the
predict method of the fitted models
returns a matrix, the prediction error is computed for
each column. A typical use case for this behavior would
be if the predict method returns
predictions from an initial model fit and stepwise
improvements thereof.
If formula or data are supplied, all
variables required for fitting the models are added as
one argument to the function call, which is the typical
behavior of model fitting functions with a
formula interface. In this case,
the accepted values for names depend on the
method. For the function method, a character
vector of length two should supplied, with the first
element specifying the argument name for the formula and
the second element specifying the argument name for the
data (the default is to use c("formula", "data")).
Note that names for both arguments should be supplied
even if only one is actually used. For the other
methods, which do not have a formula argument, a
character string specifying the argument name for the
data should be supplied (the default is to use
"data").
If x is supplied, on the other hand, the predictor
matrix and the response are added as separate arguments
to the function call. In this case, names should
be a character vector of length two, with the first
element specifying the argument name for the predictor
matrix and the second element specifying the argument
name for the response (the default is to use c("x",
"y")). It should be noted that the formula or
data arguments take precedence over x.
Value
An object of class "cv" with the following
components:
n
an integer giving the number of observations.
K
an integer giving the number of folds.
R
an integer giving the number of replications.
cv
a numeric vector containing the respective
estimated prediction errors. For repeated
cross-validation, those are average values over all
replications.
se
a numeric vector containing the respective
estimated standard errors of the prediction loss.
reps
a numeric matrix in which each column
contains the respective estimated prediction errors from
all replications. This is only returned for repeated
cross-validation.
seed
the seed of the random number generator
before cross-validation was performed.
call
the matched function call.
Author(s)
Andreas Alfons
See Also
cvTool, cvSelect,
cvTuning, cvFolds,
cost
Examples
library("robustbase")
data("coleman")
## via model fit
# fit an MM regression model
fit <- lmrob(Y ~ ., data=coleman)
# perform cross-validation
cvFit(fit, data = coleman, y = coleman$Y, cost = rtmspe,
K = 5, R = 10, costArgs = list(trim = 0.1), seed = 1234)
## via model fitting function
# perform cross-validation
# note that the response is extracted from 'data' in
# this example and does not have to be supplied
cvFit(lmrob, formula = Y ~ ., data = coleman, cost = rtmspe,
K = 5, R = 10, costArgs = list(trim = 0.1), seed = 1234)
## via function call
# set up function call
call <- call("lmrob", formula = Y ~ .)
# perform cross-validation
cvFit(call, data = coleman, y = coleman$Y, cost = rtmspe,
K = 5, R = 10, costArgs = list(trim = 0.1), seed = 1234)