# cv.glmnet

##### Cross-validation for glmnet

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

(and `gamma`

if `relax=TRUE`

)

- Keywords
- models, regression

##### Usage

```
cv.glmnet(x, y, weights = NULL, offset = NULL, lambda = NULL,
type.measure = c("default", "mse", "deviance", "class", "auc", "mae",
"C"), nfolds = 10, foldid = NULL, alignment = c("lambda",
"fraction"), grouped = TRUE, keep = FALSE, parallel = FALSE,
gamma = c(0, 0.25, 0.5, 0.75, 1), relax = FALSE, trace.it = 0, ...)
```

##### 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- 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.`type.measure="C"`

is Harrel's concordance measure, only available for`cox`

models.- 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.- alignment
This is an experimental argument, designed to fix the problems users were having with CV, with possible values

`"lambda"`

(the default) else`"fraction"`

. With`"lambda"`

the`lambda`

values from the master fit (on all the data) are used to line up the predictions from each of the folds. In some cases this can give strange values, since the effective`lambda`

values in each fold could be quite different. With`"fraction"`

we line up the predictions in each fold according to the fraction of progress along the regularization. If in the call a`lambda`

argument is also provided,`alignment="fraction"`

is ignored (with a warning).- 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. If`relax=TRUE`

, then a list of such arrays is returned, one for each value of 'gamma'. Note: if the value 'gamma=1' is omitted, this case is included in the list since it corresponds to the original 'glmnet' fit.- parallel
If

`TRUE`

, use parallel`foreach`

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

or others. See the example below.- gamma
The values of the parameter for mixing the relaxed fit with the regularized fit, between 0 and 1; default is

`gamma = c(0, 0.25, 0.5, 0.75, 1)`

- relax
If

`TRUE`

, then CV is done with respect to the mixing parameter`gamma`

as well as`lambda`

. Default is`relax=FALSE`

- trace.it
If

`trace.it=1`

, then progress bars are displayed; useful for big models that take a long time to fit. Limited tracing if`parallel=TRUE`

- …
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.

If `relax=TRUE`

then the values of `gamma`

are used to mix the
fits. If \(\eta\) is the fit for lasso/elastic net, and \(\eta_R\) is
the relaxed fit (with unpenalized coefficients), then a relaxed fit mixed by
\(\gamma\) is $$\eta(\gamma)=(1-\gamma)\eta_R+\gamma\eta$$. There is
practically no extra cost for having a lot of values for `gamma`

.
However, 5 seems sufficient for most purposes. CV then selects both
`gamma`

and `lambda`

.

##### Value

an object of class `"cv.glmnet"`

is returned, which is a list
with the ingredients of the cross-validation fit. If the object was created
with `relax=TRUE`

then this class has a prefix class of
`"cv.relaxed"`

.

the values of `lambda`

used in the
fits.

The mean cross-validated error - a vector of length
`length(lambda)`

.

estimate of standard error of
`cvm`

.

upper curve = `cvm+cvsd`

.

lower
curve = `cvm-cvsd`

.

number of non-zero coefficients at
each `lambda`

.

a text string indicating type of measure (for plotting purposes).

a fitted glmnet object for the full data.

value of `lambda`

that gives minimum
`cvm`

.

largest value of `lambda`

such that
error is within 1 standard error of the minimum.

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

if `keep=TRUE`

, the fold assignments used

if `relax=TRUE`

, this additional item has the CV info
for each of the mixed fits. In particular it also selects ```
lambda,
gamma
```

pairs corresponding to the 1SE rule, as well as the minimum error.

##### References

Friedman, J., Hastie, T. and Tibshirani, R. (2008)
*Regularization Paths for Generalized Linear Models via Coordinate
Descent*, https://web.stanford.edu/~hastie/Papers/glmnet.pdf
*Journal of Statistical Software, Vol. 33(1), 1-22 Feb 2010*
https://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* https://www.jstatsoft.org/v39/i05/

##### See Also

`glmnet`

and `plot`

, `predict`

, and `coef`

methods for `"cv.glmnet"`

and `"cv.relaxed"`

objects.

##### Examples

```
# NOT RUN {
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)
# }
# NOT RUN {
cvob1r = cv.glmnet(x, y, relax = TRUE)
plot(cvob1r)
predict(cvob1r, newx = x[, 1:5])
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 = glmnet:::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 = 0.3, 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)
# Parallel
require(doMC)
registerDoMC(cores = 4)
x = matrix(rnorm(1e+05 * 100), 1e+05, 100)
y = rnorm(1e+05)
system.time(cv.glmnet(x, y))
system.time(cv.glmnet(x, y, parallel = TRUE))
# }
# NOT RUN {
# }
```

*Documentation reproduced from package glmnet, version 4.0-2, License: GPL-2*