enet: Elastic Net Penalty

In lqa: Penalized Likelihood Inference for GLMs

Description

Object of the penalty to handle the elastic net (enet) penalty (Zou \& Hastie, 2005)

Usage

enet (lambda = NULL, ...)

Arguments

lambda	two-dimensional tuning parameter. The first component corresponds to the regularization parameter λ_1 of the lasso penalty, the second one to the regularization parameter λ_2 of the ridge penalty. Both must be nonnegative.
...	further arguments.

Details

The elastic net penalty has been introduced in the linear model context by Zou \& Hastie (2005). The elastic net enables simultaneous automatic variable selection and continuous shrinkage. Furthermore, contrary to the lasso it can select groups of correlated variables. This is related to the so called grouping effect, where strongly correlated regressors tend to be in or out of the model together.

The elastic net penalty

P_{λ}^{en} (\boldsymbol{β}) = λ_1 ∑_{i=1}^p |β_i| + λ_2 ∑_{i=1}^p β_i^2, \quad λ = (λ_1, λ_2)

is a linear combination of the lasso penalty and the ridge penalty. Therefore the penalty covers these both as extreme cases.

Value

An object of the class penalty. This is a list with elements

penalty	character: the penalty name.
lambda	double: the (nonnegative) tuning parameter.
getpenmat	function: computes the diagonal penalty matrix.

Author(s)

Jan Ulbricht

References

Zou, H. \& T. Hastie (2005) Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society B 67, 301–320.

See Also

penalty, genet, lasso, ridge

lqa documentation built on May 30, 2017, 3:41 a.m.