l2.reg {CDLasso} R Documentation

## Cyclic Coordinate Descent for L2 regression

### Description

Cyclic Coordinate Descent for L2 regression with p predictors and n cases

### Usage

```l2.reg(X, Y, lambda = 1)
```

### Arguments

 `X` `p` x `n` design matrix - Note that the rows of X correspond to predictors and the columns to cases. `Y` Outcome of length `n` `lambda` Penalization Parameter. For optimal `lambda`, use cv.l2.reg.

### Details

`l2.reg` performs an algorithm for estimating regression coefficients in a penalized L2 regression model. The algorithm is based on cyclic coordinate descent. For the new L1 algorithm that is faster, see (l1.reg).

### Value

 `X` The design matrix. `cases` The number of cases `predictors` The number of predictors `lambda` The value of penalization parameter `lambda` used. `residual` A vector of length `p` listing the residuals `L2` The sum of the residuals `estimate` The estimate of the coefficients `nonzeros` The number "selected" variables included in the model. `selected` The name of the "selected" variables included in the model.

### Author(s)

Edward Grant, Kenneth Lange, Tong Tong Wu

Maintainer: Edward Grant edward.m.grant@gmail.com

### References

Wu, T.T. and Lange, K. (2008). Coordinate Descent Algorithms for Lasso Penalized Regression. Annals of Applied Statistics, Volume 2, No 1, 224-244.

`print.l2.reg`

`summary.l2.reg`

`cv.l2.reg`

`plot.cv.l2.reg`

`l1.reg`

### Examples

```set.seed(100)
n=500
p=2000
nzfixed = c(1:5)
true.beta<-rep(0,p)
true.beta[nzfixed] = c(1,1,1,1,1)

x=matrix(rnorm(n*p),p,n)
y = t(x) %*% true.beta

rownames(x)<-1:nrow(x)
colnames(x)<-1:ncol(x)

#Lasso penalized L2 regression
out<-l2.reg(x,y,lambda=2)

#Re-estimate parameters without penalization
out2<-l2.reg(x[out\$selected,],y,lambda=0)
out2
```

[Package CDLasso version 1.1 Index]