# glmnet

##### fit an elasticnet model path

Fit a regularization path for the elasticnet at a grid of values for the regularization parameter lambda. Can deal with all shapes of data, including very large sparse data matrices. Fits linear, logistic and multinomial regression models.

- Keywords
- models, regression

##### Usage

```
glmnet(x, y, family=c("gaussian","binomial","multinomial"), weights, alpha = 1,
nlambda = 100, lambda.min = ifelse(nobs
```

##### Arguments

- x
- input matrix, of dimension nobs x nvars; each row is an observation vector. Can be in sparse column format (class
`"dgCMatrix"`

as in package`Matrix`

) - y
- response variable. Quantitative for
`family="gaussian"`

. For`family="binomial"`

should be either a factor with two levels, or a two-column matrix of counts or proportions. For`family="multinomial"`

, can be a`nc>=2<`

- family
- Response type (see above)
- weights
- observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation
- alpha
- The elasticnet mixing parameter, with
$0<\alpha\le 1$.="" the="" penalty="" is="" defined="" as="" $$(1-\alpha)="" 2||\beta||_2^2+\alpha||\beta||_1.$$=""
`alpha=1 is the lasso penalty; Currently`

`alpha<0.01< code=""> not reliable, unless you supply`

- nlambda
- The number of
`lambda`

values - default is 100. - lambda.min
- Smallest value for
`lambda`

, as a fraction of`lambda.max`

, the (data derived) entry value (i.e. the smallest value for which all coefficients are zero). The default depends on the sample size`nobs`

relative to th - lambda
- A user supplied
`lambda`

sequence. Typical usage is to have the program compute its own`lambda`

sequence based on`nlambda`

and`lambda.min`

. Supplying a value of`lambda`

overrides - standardize
- Logical flag for variable standardization, prior to
fitting the model sequence. The coefficients are always returned on
the original scale. Default is is
`standardize=TRUE`

- thresh
- Convergence threshold for coordinate descent. Each inner
coordinate-descent loop continues until the relative change in any
coefficient is less than
`thresh`

. Defaults value is`1E-4`

. - dfmax
- Limit the maximum number of variables in the
model. Useful for very large
`nvars`

, if a partial path is desired. - pmax
- Limit the maximum number of variables ever to be nonzero
- exclude
- Indices of variables to be excluded from the model. Default is none. Equivalent to an infinite penalty factor (next item).
- penalty.factor
- Separate penalty factors can be applied to each
coefficient. This is a number that multiplies
`lambda`

to allow differential shrinkage. Can be 0 for some variables, which implies no shrinkage, and that variable is always included in - maxit
- Maximum number of outer-loop iterations for
`"binomial"`

or`"multinomial"`

families. Default is 100. - HessianExact
- Only applies to
`"binomial"`

or`"multinomial"`

families. If`FALSE`

(the default), an upper-bound approximation is made to the hessian, which is not recalculated at each outer loop. - type
- Two algorithm types are supported for (only)
`family="gaussian"`

. The default`type="covariance"`

saves all inner-products ever computed, and can be much faster than`type="naive"`

. The latter can be more effic

##### Details

The sequence of models implied by `lambda`

is fit by coordinate
descent. For `family="gaussian"`

this is the lasso sequence if
`alpha=1`

, else it is the elasticnet sequence.
For `family="binomial"`

or `family="multinomial"`

, this is a lasso or elasticnet regularization path
for fitting the linear logistic or multinomial logistic regression
paths. Sometimes the sequence is truncated before `nlambda`

values of `lambda`

have been used, because of instabilities in
the logistic or multinomial models near a saturated fit. `glmnet(...,family="binomial")`

fits a traditional logistic regression model for the
log-odds. `glmnet(...,family="multinomial")`

fits a symmetric multinomial model, where
each class is represented by a linear model (on the log-scale). The
penalties take care of redundancies. A two-class `"multinomial"`

model
will produce the same fit as the corresponding `"binomial"`

model,
except the pair of coefficient matrices will be equal in magnitude and
opposite in sign, and half the `"binomial"`

values.
Note that the objective function for `"gaussian"`

is $$1/(2*nobs)RSS + \lambda*penalty$$, and for the logistic models it is $$1/nobs -loglik + \lambda*penalty$$

##### Value

- An object with S3 class
`"glmnet","*"`

, where`"*"`

is`"elnet"`

,`"lognet"`

or`"multnet"`

for the three types of models. call the call that produced this object a0 Intercept sequence of length `length(lambda)`

beta For `"elnet"`

and`"lognet"`

models, a`nvars x length(lambda)`

matrix of coefficients, stored in sparse column format (`"dgCMatrix"`

). For`"multnet"`

, a list of`nc`

such matrices, one for each class.lambda The actual sequence of `lambda`

values useddev The fraction of (null) deviance explained (for `"elnet"`

, this is the R-square).nulldev Null deviance (per observation) df The number of nonzero coefficients for each value of `lambda`

. For`"multnet"`

, this is the number of variables with a nonzero coefficient for*any*class.dfmat For `"multnet"`

only. A matrix consisting of the number of nonzero coefficients per classdim dimension of coefficient matrix (ices) npasses total passes over the data summed over all lambda values jerr error flag, for warnings and errors (largely for internal debugging).

##### References

Friedman, J., Hastie, T. and Tibshirani, R. (2008)
*Regularization Paths for Generalized Linear Models via Coordinate
Descent*

##### See Also

`print`

, `predict`

and `coef`

methods.

##### Examples

```
x=matrix(rnorm(100*20),100,20)
y=rnorm(100)
g2=sample(1:2,100,replace=TRUE)
g4=sample(1:4,100,replace=TRUE)
fit1=glmnet(x,y)
print(fit1)
coef(fit1,s=0.01) # extract coefficients at a single value of lambda
predict(fit1,newx=x[1:10,],s=c(0.01,0.005)) # make predictions
fit2=glmnet(x,g2,family="binomial")
fit3=glmnet(x,g4,family="multinomial")
```

*Documentation reproduced from package glmnet, version 1.1-5, License: GPL-2*

### Community examples

**mayweiwang**at Apr 26, 2017 glmnet v2.0-5

## first ```{r} N=500; p=20 nzc=5 x=matrix(rnorm(N*p),N,p) beta=rnorm(nzc) f = x[,seq(nzc)]%*%beta mu=exp(f) y=rpois(N,mu) fit=glmnet(x,y,family="poisson") plot(fit) pfit = predict(fit,x,s=0.001,type="response") plot(pfit,y) ```