cv.ncvreg {ncvreg}

Cross-validation for ncvreg/ncvsurv

Description

Performs k-fold cross validation for MCP- or SCAD-penalized regression models over a grid of values for the regularization parameter lambda.

Usage

cv.ncvreg(
  X,
  y,
  ...,
  cluster,
  nfolds = 10,
  seed,
  fold,
  returnY = FALSE,
  trace = FALSE
)

cv.ncvsurv(
  X,
  y,
  ...,
  cluster,
  nfolds = 10,
  seed,
  fold,
  se = c("quick", "bootstrap"),
  returnY = FALSE,
  trace = FALSE
)

Arguments

X

The design matrix, without an intercept, as in ncvreg() or ncvsurv().

y

The response, as in ncvreg() or ncvsurv().

...

Additional arguments to ncvreg() or ncvsurv().

cluster

cv.ncvreg() and cv.ncvsurv() can be run in parallel across a cluster using the parallel package. The cluster must be set up in advance using the parallel::makeCluster() function from that package. The cluster must then be passed to cv.ncvreg() or cv.ncvsurv() (see example).

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.ncvreg()/cv.ncvsurv() return the linear predictors 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.ncvsurv(), the rows of Y are ordered by time on study, and therefore will not correspond to the original order of observations pased to cv.ncvsurv().

trace

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

se

For cv.ncvsurv(), 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 ncvreg/ncvsurv 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 family="binomial" models, the cross-validation fold assignments are balanced across the 0/1 outcomes, so that each fold has the same proportion of 0/1 outcomes (or as close to the same proportion as it is possible to achieve if cases do not divide evenly).

For Cox models, cv.ncvsurv() 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.

Value

An object with S3 class cv.ncvreg or cv.ncvsurv 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.

fold

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

lambda

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

fit

The fitted ncvreg() or ncvsurv() object for the whole data.

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. If you have supplied your own lambda sequence, this quantity may not be meaningful.

Bias

The estimated bias of the minimum cross-validation error, as in Tibshirani and Tibshirani (2009) doi:10.1214/08-AOAS224

pe

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

Y

If returnY=TRUE, the matrix of cross-validated fitted values (see above).

Author(s)

Patrick Breheny; Grant Brown helped with the parallelization support

References

Breheny P and Huang J. (2011) Coordinate descent algorithms for nonconvex penalized regression, with applications to biological feature selection. Annals of Applied Statistics, 5: 232-253. doi:10.1214/10-AOAS388

See Also

ncvreg(), plot.cv.ncvreg(), summary.cv.ncvreg()

Examples

data(Prostate)

cvfit <- cv.ncvreg(Prostate$X, Prostate$y)
plot(cvfit)
summary(cvfit)

fit <- cvfit$fit
plot(fit)
beta <- fit$beta[,cvfit$min]

## requires loading the parallel package
## Not run: 
library(parallel)
X <- Prostate$X
y <- Prostate$y
cl <- makeCluster(4)
cvfit <- cv.ncvreg(X, y, cluster=cl, nfolds=length(y))
## End(Not run)

# Survival
data(Lung)
X <- Lung$X
y <- Lung$y

cvfit <- cv.ncvsurv(X, y)
summary(cvfit)
plot(cvfit)
plot(cvfit, type="rsq")