HDCI (version 1.0-2)

PartRidge: Partial Ridge

Description

Computes the Partial Ridge estimator.

Usage

PartRidge(x, y, lambda2 = 0, varset, standardize = TRUE, intercept = TRUE)

Arguments

x

Input matrix as in glmnet, of dimension nobs x nvars; each row is an observation vector.

y

Response variable.

lambda2

Tuning parameter for the Partial Ridge. The default value is 0, which gives back to the OLS estimator.

varset

A set indicating which variable/predictors are not penalized. Partial Ridge puts l2 penalty only on the coefficients of the variables/predictors not included in the varset.

standardize

Logical flag for x variable standardization, prior to fitting the model. Default is standardize=TRUE.

intercept

Should intercept be fitted (default is TRUE) or set to zero (FALSE).

Value

A list consisting of the following elements is returned.

beta

The Lasso+Partial Ridge estimator for the coefficients of variables/predictors.

beta0

A value of intercept term.

meanx

The mean vector of variables/predictors if intercept=TRUE, otherwise is a vector of 0's.

mu

The mean of the response if intercept=TRUE, otherwise is 0.

normx

The vector of standard error of variables/predictors if standardize=TRUE, otherwise is a vector of 1's.

lambda2

The value of lambda2.

Details

This function computes the Partial Ridge estimator, which adds l2 penalty only on the coefficients of variabels/predictors not included in the set varset, to the loss function (residual sum of squares).

Examples

library("glmnet")
library("mvtnorm") 

## generate the data
set.seed(2015)
n <- 200      # number of obs
p <- 500
s <- 10
beta <- rep(0, p)
beta[1:s] <- runif(s, 1/3, 1)
x <- rmvnorm(n = n, mean = rep(0, p), method = "svd")
signal <- sqrt(mean((x %*% beta)^2))
sigma <- as.numeric(signal / sqrt(10))  # SNR=10
y <- x %*% beta + rnorm(n)

## Partial Ridge Regression
# Lasso
set.seed(0)
obj.escv <- escv.glmnet(x, y)
obj <- Lasso(x, y, lambda = obj.escv$lambda.cv)
# variable set
betalasso <- obj$beta
selectvar <- betalasso != 0
# partial ridge 
PR.obj <- PartRidge(x = x, y = y, lambda2 = 1/n, varset = selectvar)
# parial ridge estimate of the regression coefficients
beta <- PR.obj$beta
# intercept term
beta0 <- PR.obj$beta0
# prediction
mypredict(PR.obj, newx = matrix(rnorm(10*p), 10, p))