Penalized Quantile Regression

Performs penalized quantile regression with LASSO, elastic net, SCAD and MCP penalty functions including group penalties. In addition, offers a group penalty that provides consistent variable selection across quantiles. Provides a function that automatically generates lambdas and evaluates different models with cross validation or BIC, including a large p version of BIC. Below URL provides a link to article in the R Journal.

rqPen: Penalized quantile regression

Overview

This R package provides tools for estimating a quantile regression model with a penalized objective function. Implements a variety of penalties, including group penalties.

Installation

For most up to date versions use the following code. However, be warned the github package is often in a state of testing and debugging.

devtools::install_github("bssherwood/rqpen")

The following code will install the more stable CRAN version.

install.packages("rqPen")

Example

library(rqPen)
n<- 200
p<- 30
x0<- matrix(rnorm(n*p),n,p)
x<- cbind(x0, x0^2, x0^3)[,order(rep(1:p,3))]
y<- -2+x[,1]+0.5*x[,2]-x[,3]-0.5*x[,7]+x[,8]-0.2*x[,9]+rt(n,2)
group<- rep(1:p, each=3)

# lasso estimation
# one tau
fit1 <- rq.pen(x,y)
# several values of tau
fit2 <- rq.pen(x,y,tau=c(.2,.5,.8))

# Group SCAD estimation
fit3 <- rq.group.pen(x,y,groups=group,penalty="gSCAD")

# cross validation
cv1 <- rq.pen.cv(x,y)
plot(cv1)

cv2 <- rq.pen.cv(x,y,tau=c(.2,.5,.8))
plot(cv2)

cv3 <- rq.group.pen(x,y,groups=group,penalty="gSCAD")
plot(cv3)

# BIC selection of tuning parameters
qs1 <- qic.select(fit1)
qs2 <- qic.select(fit2)
qs3 <- qic.select(fit3)