rqPen (version 2.3)

LASSO.fit.nonpen: LASSO Penalized Quantile Regression with some nonpenalized coefficients

Description

LASSO.fit.nonpen obtains coefficient estimates for Lasso penalized quantile regression with some nonpenalized coefficients. It is called by the QICD.nonpen function to obtain initial estimates when they are not provided.

Usage

LASSO.fit.nonpen(y, x, z, tau, lambda, intercept, coef.cutoff, weights=NULL)

Value

Returns a vector containing the intercept (if intercept=TRUE) and the estimated coefficients for each column in x and z.

Arguments

y

Vector of responses.

x

n x p matrix of covariates.

z

n x q matrix of observations with each row corresponding to one observation. Penalties (and variable selection) WILL NOT be applied to these coefficients. Do not include column of 1's; set intercept=TRUE, if intercept is desired.

tau

Conditional quantile being modelled.

lambda

Tuning parameter. Must be positive.

intercept

If TRUE, an intercept is included in the model. If FALSE, no intercept is included.

coef.cutoff

Coefficients with magnitude less than this value are set to 0.

weights

If not NULL, weights must be a vector of length n with a positive weight for each observation. This is used for the linear programming solution for the SCAD and MCP penalties.

Author

Adam Maidman

Details

This is a barebones function that only provides coefficient estimates. It will not provide any warnings or errors, so you need to check that inputs are accurate and appropriate. The rq.lasso.fit function should be used to obtain more information from the Lasso fit.

References

[1] Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B, 58, 267--288.

Examples

library(splines)
n = 50
p = 100
x <- matrix(rnorm(n*p),nrow=n)
z1 <- runif(n)
z <- bs(z1)
y <- 0 + x[,1] - 3*x[,5] + z1^3 + rnorm(n)
fit1 <- LASSO.fit.nonpen(y,x,z, tau=.5, lambda=1, intercept=TRUE, coef.cutoff=1e-08)
fit2 <- LASSO.fit.nonpen(y,x,z, tau=.5, lambda=.1, intercept=TRUE, coef.cutoff=1e-08)