cv.grpreg {grpreg}

Cross-validation for grpreg/grpsurv

Description

Performs k-fold cross validation for penalized regression models with grouped covariates over a grid of values for the regularization parameter lambda.

Usage

cv.grpreg(X, y, group=1:ncol(X), ..., nfolds=10, seed, fold,
returnY=FALSE, trace=FALSE)
cv.grpsurv(X, y, group, ..., nfolds=10, seed, fold, se=c('quick',
'bootstrap'), returnY=FALSE, trace=FALSE)

Arguments

X

The design matrix, as in grpreg/grpsurv.

y

The response vector (or matrix), as in grpreggrpsurv.

group

The grouping vector, as in grpreggrpsurv.

...

Additional arguments to grpreggrpsurv.

nfolds

The number of cross-validation folds. Default is 10.

seed

You may set the seed of the random number generator in order to obtain reproducible results.

fold

Which fold each observation belongs to. By default the observations are randomly assigned.

returnY

Should cv.grpreggrpsurv return the fitted values from the cross-validation folds? Default is FALSE; if TRUE, this will return a matrix in which the element for row i, column j is the fitted value for observation i from the fold in which observation i was excluded from the fit, at the jth value of lambda. NOTE: For cv.grpsurv, the rows of Y are ordered by time on study, and therefore will not correspond to the original order of observations pased to cv.grpsurv.

trace

If set to TRUE, cv.grpreg will inform the user of its progress by announcing the beginning of each CV fold. Default is FALSE.

se

For cv.grpsurv, the method by which the cross-valiation standard error (CVSE) is calculated. The 'quick' approach is based on a rough approximation, but can be calculated more or less instantly. The 'bootstrap' approach is more accurate, but requires additional computing time.

Details

The function calls grpreg/cv.grpsurv nfolds times, each time leaving out 1/nfolds of the data. The cross-validation error is based on the deviance; see here for more details.

For Gaussian and Poisson responses, the folds are chosen according to simple random sampling. For binomial responses, the numbers for each outcome class are balanced across the folds; i.e., the number of outcomes in which y is equal to 1 is the same for each fold, or possibly off by 1 if the numbers do not divide evenly. This approach is used for Cox regression as well to balance the amount of censoring cross each fold.

For Cox models, cv.grpsurv uses the approach of calculating the full Cox partial likelihood using the cross-validated set of linear predictors. Other approaches to cross-validation for the Cox regression model have been proposed in the literature; the strengths and weaknesses of the various methods for penalized regression in the Cox model are the subject of current research. A simple approximation to the standard error is provided, although an option to bootstrap the standard error (se='bootstrap') is also available.

As in grpreg, seemingly unrelated regressions/multitask learning can be carried out by setting y to be a matrix, in which case groups are set up automatically (see grpreg for details), and cross-validation is carried out with respect to rows of y. As mentioned in the details there, it is recommended to standardize the responses prior to fitting.

Value

An object with S3 class "cv.grpreg" containing:

cve

The error for each value of lambda, averaged across the cross-validation folds.

cvse

The estimated standard error associated with each value of for cve.

lambda

The sequence of regularization parameter values along which the cross-validation error was calculated.

fit

The fitted grpreg object for the whole data.

fold

The fold assignments for cross-validation for each observation; note that for cv.grpsurv, these are in terms of the ordered observations, not the original observations.

min

The index of lambda corresponding to lambda.min.

lambda.min

The value of lambda with the minimum cross-validation error.

null.dev

The deviance for the intercept-only model.

pe

If family="binomial", the cross-validation prediction error for each value of lambda.

Author(s)

Patrick Breheny

See Also

grpreg, plot.cv.grpreg, summary.cv.grpreg, predict.cv.grpreg

Examples

data(Birthwt)
X <- Birthwt$X
y <- Birthwt$bwt
group <- Birthwt$group

cvfit <- cv.grpreg(X, y, group)
plot(cvfit)
summary(cvfit)
coef(cvfit) ## Beta at minimum CVE

cvfit <- cv.grpreg(X, y, group, penalty="gel")
plot(cvfit)
summary(cvfit)