Cross-validation for model evaluation

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Description

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

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  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

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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)