Lasso {HDCI}

Lasso

Description

Gets Lasso estimator for a given value of lambda or for the value of lambda choosing by cross-validation (or escv).

Usage

Lasso(x, y, lambda = NULL, fix.lambda = TRUE, cv.method = "cv", nfolds = 10, foldid, 
      cv.OLS = FALSE, tau = 0, parallel = FALSE, 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.

lambda

A value of lambda - default is NULL. lambda should be given a value when fix.lambda=TRUE.

fix.lambda

If TRUE, computes Lasso+OLS (or Lasso) for a fix value of lambda given by the argument "lambda"; otherwise, computes Lasso+OLS (or Lasso) for the value of lambda choosing by cv/cv1se/escv.

cv.method

The method used to select lambda – can be cv, cv1se, and escv; the default is cv. cv.method is useful only when fix.lambda=FALSE.

nfolds, foldid, cv.OLS, tau, parallel

Arguments that can be passed to escv.glmnet (useful only when fix.lambda=FALSE).

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).

...

Other arguments that can be passed to glmnet.

Details

The function computes the Lasso estimator for a give value of lambda (if fix.lambda=TRUE) or for the value of lambda choosing by cv/cv1se/escv (if fix.lambda=FALSE).

Value

A list consisting of the following elements is returned.

beta

The Lasso estimate for the coefficients of variables/predictors.

beta0

A value of intercept term.

lambda

The value/values of lambda.

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.

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)

## Lasso estimator
# for a given value of lambda
set.seed(0)
obj.escv <- escv.glmnet(x, y)
obj <- Lasso(x, y, lambda = obj.escv$lambda.cv)
# Lasso estimate of the regression coefficients
obj$beta
# intercept term
obj$beta0
# prediction
mypredict(obj, newx = matrix(rnorm(10*p), 10, p))

# for lambda choosing by cross-validation (cv) which uses Lasso in the cv fit
set.seed(0)
obj <- Lasso(x, y, fix.lambda = FALSE)

# for lambda choosing by cross-validation (cv) which uses Lasso+OLS in the cv fit
set.seed(0)
obj <- Lasso(x, y, fix.lambda = FALSE, cv.OLS = TRUE)