rq.group.fit: Quantile Regresion with Group Penalty

Description Usage Arguments Value Author(s) References Examples

Description

Similar to cv.rq.pen function, but uses group penalty. Group penalties use the L1 norm instead of L2 for computational convenience. As a result of this the group lasso penalty is the same as the typical lasso penalty and thus you should only use a SCAD or MCP penalty. Only the SCAD and MCP penalties incorporate the group structure into the penalty. The group lasso penalty is implemented because it is needed for the SCAD and MCP algorithm. We use a group penalty extension of the QICD algorithm presented by Peng and Wang (2015).

Usage

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rq.group.fit(x, y, groups, tau = 0.5, lambda, intercept = TRUE, 
                penalty = "SCAD", alg = "QICD", a=3.7, penGroups=NULL, ...)

Arguments

x

Matrix of predictors.

y

Vector of response values.

groups

Vector assigning columns of x to groups.

tau

Conditional quantile being modelled.

lambda

Vector of lambdas. Default is for lambdas to be automatically generated.

intercept

Whether model should include an intercept. Constant does not need to be included in "x".

penalty

Type of penalty: "SCAD" or "MCP".

alg

If set to QICD algorithm will use coordinate descent algorithm. Otherwise, will use a linear programming algorithm, which is an extension of algorithm used in rq.lasso.fit.

a

The additional tuning parameter for SCAD and MCP.

penGroups

Specify which groups will be penalized. Default is to penalize all groups.

...

Additional arguments to be sent to rq.lasso.fit or groupQICD.

Value

Returns the following:

coefficients

Coefficients of the model.

residuals

Residuals from the fitted model.

rho

Unpenalized portion of the objective function.

tau

Quantile being modeled.

n

Sample size.

intercept

Whether intercept was included in model.

Author(s)

Ben Sherwood; Adam Maidman

References

[1] Yuan, M. and Lin, Y. (2006). Model selection and estimation in regression with grouped variables. J. R. Statist. Soc. B, 68, 49-67.

[2] Peng, B. and Wang, L. (2015). An Iterative Coordinate Descent Algorithm for High-Dimensional Nonconvex Penalized Quantile Regression. Journal of Computational and Graphical Statistics, 24, 676-694.

Examples

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x <- matrix(rnorm(800),nrow=100)
y <- 1 + x[,1] - 3*x[,5] + rnorm(100)
cv_model <- rq.group.fit(x,y,groups=c(rep(1,4),rep(2,4)),lambda=1,penalty="SCAD")

Example output

Loading required package: quantreg
Loading required package: SparseM

Attaching package: 'SparseM'

The following object is masked from 'package:base':

    backsolve

Loading required package: regpro
Loading required package: denpro

rqPen documentation built on April 14, 2020, 7:14 p.m.