Bootstrap Lasso OLS
Does residual (or paired) bootstrap Lasso+OLS and produces confidence intervals for regression coefficients.
bootLassoOLS(x, y, B = 500, type.boot = "residual", alpha = 0.05, OLS = TRUE,
cv.method = "cv", nfolds = 10, foldid, cv.OLS = TRUE, tau = 0,
parallel = FALSE, standardize = TRUE, intercept = TRUE,
parallel.boot = FALSE, ncores.boot = 1, ...)x |
Input matrix as in glmnet, of dimension nobs x nvars; each row is an observation vector. |
y |
Response variable. |
B |
Number of replications in the bootstrap – default is 500. |
type.boot |
Bootstrap method which can take one of the following two values: "residual" or "paired". The default is "residual". |
alpha |
Significance level – default is 0.05. |
OLS |
If TRUE, this function runs residual (or paired) bootstrap Lasso+OLS; if FALSE, it runs residual (or paired) bootstrap Lasso. The default value is TRUE. |
cv.method |
The method used to select lambda in the Lasso+OLS – can be cv, cv1se, and escv; the default is cv. |
nfolds, foldid, cv.OLS, tau, parallel |
Arguments that can be passed to escv.glmnet. |
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). |
parallel.boot |
If TRUE, use parallel foreach to run the bootstrap replication. Must register parallel before hand, such as doParallel or others. See the example below. |
ncores.boot |
Number of cores used in the bootstrap replication. |
... |
Other arguments that can be passed to glmnet. |
The function runs residual (type.boot="residual") or paired (type.boot="paired") bootstrap Lasso+OLS (if OLS=TRUE) procedure, and produces confidence interval for each individual regression coefficient. When the argument OLS=FALSE, it is the same as the function bootLasso, which runs residual (type.boot="residual") or paired (type.boot="paired") bootstrap Lasso procedure. Note that there are two arguments related to parallel, "parallel" and "parallel.boot": "parallel" is used for parallel foreach in the escv.glmnet; while, "paralle.boot" is used for the parallel foreach in the bootstrap replication precodure.
A list consisting of the following elements is returned.
lambda.opt |
The optimal value of lambda selected by cv/cv1se/escv. |
Beta.Lasso |
Lasso estimate of the regression coefficients. |
Beta.LassoOLS |
Lasso+OLS estimate of the regression coefficients. It gives back to Lasso estimate if the argument OLS=FALSE. |
interval.Lasso |
A 2 by p matrix containing the bootstrap Lasso confidence intervals – the first row is the lower bounds of the confidence intervals for each of the coefficients and the second row is the upper bounds of the confidence intervals. |
interval.LassoOLS |
A 2 by p matrix containing the bootstrap Lasso+OLS confidence intervals – the first row is the lower bounds of the confidence intervals for each of the coefficients and the second row is the upper bounds of the confidence intervals. It equals interval.Lasso if the argument OLS=FALSE. |
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)
## residual bootstrap Lasso+OLS
set.seed(0)
obj <- bootLassoOLS(x = x, y = y, B = 10)
# confidence interval
obj$interval
sum((obj$interval[1,]<=beta) & (obj$interval[2,]>=beta))
## using parallel in the bootstrap replication
#library("doParallel")
#registerDoParallel(2)
#set.seed(0)
#system.time(obj <- bootLassoOLS(x = x, y = y))
#system.time(obj <- bootLassoOLS(x = x, y = y, parallel.boot = TRUE, ncores.boot = 2))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.