repCV {cvTools}

Cross-validation for linear models

Description

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.

Usage

repCV(object, ...)

## S3 method for class 'lm'
repCV(
  object,
  cost = rmspe,
  K = 5,
  R = 1,
  foldType = c("random", "consecutive", "interleaved"),
  grouping = NULL,
  folds = NULL,
  seed = NULL,
  ...
)

## S3 method for class 'lmrob'
repCV(
  object,
  cost = rtmspe,
  K = 5,
  R = 1,
  foldType = c("random", "consecutive", "interleaved"),
  grouping = NULL,
  folds = NULL,
  seed = NULL,
  ...
)

## S3 method for class '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,
  ...
)

Arguments

object

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.

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).

K

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.

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".

grouping

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.

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 the arguments for generating cross-validation folds.

seed

optional initial seed for the random number generator (see .Random.seed).

fit

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.

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.

Value

An object of class "cv" with the following components:

n

an integer giving the number of observations or groups.

K

an integer giving the number of folds.

R

an integer giving the number of replications.

cv

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.

se

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.

reps

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.

seed

the seed of the random number generator before cross-validation was performed.

call

the matched function call.

Note

The repCV methods are simple wrapper functions that extract the data from the fitted model and call cvFit to perform cross-validation. In addition, cvLm, cvLmrob and cvLts are aliases for the respective methods.

Author(s)

Andreas Alfons

See Also

cvFit, cvFolds, cost, lm, lmrob, ltsReg

Examples

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)