# cv.glmnet

##### Cross-validation for glmnet

Does k-fold cross-validation for glmnet, produces a plot,
and returns a value for `lambda`

- Keywords
- models, regression

##### Usage

`cv.glmnet(x, y, weights, offset, lambda, type.measure, nfolds, foldid, grouped, keep, parallel, ...)`

##### Arguments

- x
`x`

matrix as in`glmnet`

.- y
- response
`y`

as in`glmnet`

. - weights
- Observation weights; defaults to 1 per observation
- offset
- Offset vector (matrix) as in
`glmnet`

- lambda
- Optional user-supplied lambda sequence; default is
`NULL`

, and`glmnet`

chooses its own sequence - nfolds
- number of folds - default is 10. Although
`nfolds`

can be as large as the sample size (leave-one-out CV), it is not recommended for large datasets. Smallest value allowable is`nfolds=3`

- foldid
- an optional vector of values between 1 and
`nfold`

identifying what fold each observation is in. If supplied,`nfold`

can be missing. - type.measure
- loss to use for cross-validation. Currently five
options, not all available for all models. The default is
`type.measure="deviance"`

, which uses squared-error for gaussian models (a.k.a`type.measure="mse"`

there), deviance for logistic and poisson regression, and partial-likelihood for the Cox model.`type.measure="class"`

applies to binomial and multinomial logistic regression only, and gives misclassification error.`type.measure="auc"`

is for two-class logistic regression only, and gives area under the ROC curve.`type.measure="mse"`

or`type.measure="mae"`

(mean absolute error) can be used by all models except the`"cox"`

; they measure the deviation from the fitted mean to the response. - grouped
- This is an experimental argument, with default
`TRUE`

, and can be ignored by most users. For all models except the`"cox"`

, this refers to computing`nfolds`

separate statistics, and then using their mean and estimated standard error to describe the CV curve. If`grouped=FALSE`

, an error matrix is built up at the observation level from the predictions from the`nfold`

fits, and then summarized (does not apply to`type.measure="auc"`

). For the`"cox"`

family,`grouped=TRUE`

obtains the CV partial likelihood for the Kth fold by*subtraction*; by subtracting the log partial likelihood evaluated on the full dataset from that evaluated on the on the (K-1)/K dataset. This makes more efficient use of risk sets. With`grouped=FALSE`

the log partial likelihood is computed only on the Kth fold - keep
- If
`keep=TRUE`

, a*prevalidated*array is returned containing fitted values for each observation and each value of`lambda`

. This means these fits are computed with this observation and the rest of its fold omitted. The`folid`

vector is also returned. Default is keep=FALSE - parallel
- If
`TRUE`

, use parallel`foreach`

to fit each fold. Must register parallel before hand, such as`doMC`

or others. See the example below. - ...
- Other arguments that can be passed to
`glmnet`

##### Details

The function runs `glmnet`

`nfolds`

+1 times; the
first to get the `lambda`

sequence, and then the remainder to
compute the fit with each of the folds omitted. The error is
accumulated, and the average error and standard deviation over the
folds is computed.
Note that `cv.glmnet`

does NOT search for
values for `alpha`

. A specific value should be supplied, else
`alpha=1`

is assumed by default. If users would like to
cross-validate `alpha`

as well, they should call `cv.glmnet`

with a pre-computed vector `foldid`

, and then use this same fold vector
in separate calls to `cv.glmnet`

with different values of
`alpha`

. Note also that the results of `cv.glmnet`

are
random, since the folds are selected at random. Users can reduce this
randomness by running `cv.glmnet`

many times, and averaging the
error curves.

##### Value

- lambda
- the values of
`lambda`

used in the fits. - cvm
- The mean cross-validated error - a vector of length
`length(lambda)`

. - cvsd
- estimate of standard error of
`cvm`

. - cvup
- upper curve =
`cvm+cvsd`

. - cvlo
- lower curve =
`cvm-cvsd`

. - nzero
- number of non-zero coefficients at each
`lambda`

. - name
- a text string indicating type of measure (for plotting purposes).
- glmnet.fit
- a fitted glmnet object for the full data.
- lambda.min
- value of
`lambda`

that gives minimum`cvm`

. - lambda.1se
- largest value of
`lambda`

such that error is within 1 standard error of the minimum. - fit.preval
- if
`keep=TRUE`

, this is the array of prevalidated fits. Some entries can be`NA`

, if that and subsequent values of`lambda`

are not reached for that fold - foldid
- if
`keep=TRUE`

, the fold assignments used

`"cv.glmnet"`

is returned, which is a
list with the ingredients of the cross-validation fit.
##### References

Friedman, J., Hastie, T. and Tibshirani, R. (2008)
*Regularization Paths for Generalized Linear Models via Coordinate
Descent*, http://www.stanford.edu/~hastie/Papers/glmnet.pdf
*Journal of Statistical Software, Vol. 33(1), 1-22 Feb 2010*
http://www.jstatsoft.org/v33/i01/
Simon, N., Friedman, J., Hastie, T., Tibshirani, R. (2011)
*Regularization Paths for Cox's Proportional Hazards Model via
Coordinate Descent, Journal of Statistical Software, Vol. 39(5)
1-13*
http://www.jstatsoft.org/v39/i05/

##### See Also

`glmnet`

and `plot`

, `predict`

, and `coef`

methods for `"cv.glmnet"`

object.

##### Examples

`library(glmnet)`

```
set.seed(1010)
n=1000;p=100
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)
beta=rnorm(nzc)
fx= x[,seq(nzc)] %*% beta
eps=rnorm(n)*5
y=drop(fx+eps)
px=exp(fx)
px=px/(1+px)
ly=rbinom(n=length(px),prob=px,size=1)
set.seed(1011)
cvob1=cv.glmnet(x,y)
plot(cvob1)
coef(cvob1)
predict(cvob1,newx=x[1:5,], s="lambda.min")
title("Gaussian Family",line=2.5)
set.seed(1011)
cvob1a=cv.glmnet(x,y,type.measure="mae")
plot(cvob1a)
title("Gaussian Family",line=2.5)
set.seed(1011)
par(mfrow=c(2,2),mar=c(4.5,4.5,4,1))
cvob2=cv.glmnet(x,ly,family="binomial")
plot(cvob2)
title("Binomial Family",line=2.5)
frame()
set.seed(1011)
cvob3=cv.glmnet(x,ly,family="binomial",type.measure="class")
plot(cvob3)
title("Binomial Family",line=2.5)
set.seed(1011)
cvob3a=cv.glmnet(x,ly,family="binomial",type.measure="auc")
plot(cvob3a)
title("Binomial Family",line=2.5)
set.seed(1011)
mu=exp(fx/10)
y=rpois(n,mu)
cvob4=cv.glmnet(x,y,family="poisson")
plot(cvob4)
title("Poisson Family",line=2.5)
# Multinomial
n=500;p=30
nzc=trunc(p/10)
x=matrix(rnorm(n*p),n,p)
beta3=matrix(rnorm(30),10,3)
beta3=rbind(beta3,matrix(0,p-10,3))
f3=x%*% beta3
p3=exp(f3)
p3=p3/apply(p3,1,sum)
g3=rmult(p3)
set.seed(10101)
cvfit=cv.glmnet(x,g3,family="multinomial")
plot(cvfit)
title("Multinomial Family",line=2.5)
# Cox
beta=rnorm(nzc)
fx=x[,seq(nzc)]%*%beta/3
hx=exp(fx)
ty=rexp(n,hx)
tcens=rbinom(n=n,prob=.3,size=1)# censoring indicator
y=cbind(time=ty,status=1-tcens) # y=Surv(ty,1-tcens) with library(survival)
foldid=sample(rep(seq(10),length=n))
fit1_cv=cv.glmnet(x,y,family="cox",foldid=foldid)
plot(fit1_cv)
title("Cox Family",line=2.5)
## Not run:
# # Parallel
# require(doMC)
# registerDoMC(cores=4)
# x = matrix(rnorm(1e5 * 100), 1e5, 100)
# y = rnorm(1e5)
# system.time(cv.glmnet(x,y))
# system.time(cv.glmnet(x,y,parallel=TRUE))
# ## End(Not run)
```

*Documentation reproduced from package glmnet, version 2.0-5, License: GPL-2*