# groupMultLambda: Quantile Regression with Group Penalty for multiple lambdas In rqPen: Penalized Quantile Regression

## Description

Fit multiple models with L1 group penalty. QICD algorithm is using an adaptation of the algorithm presented by Peng and Wang (2015).

## Usage

 ```1 2``` ```groupMultLambda(x, y, groups, tau = 0.5, lambda, intercept = TRUE, penalty="LASSO", alg="QICD_warm",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: "LASSO", "SCAD" or "MCP". `alg` "QICD" for QICD implementation. Otherwise linear programming approach is implemented. `penGroups` Specify which groups will be penalized. Default is to penalize all groups. `...` Additional parameters to be sent to rq.group.fit.

## Value

Returns a list of rq.group.pen objects. Each element of the list is a fit for a different value of lambda.

Ben Sherwood

## 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

 ```1 2 3 4 5 6``` ```## Not run: x <- matrix(rnorm(400),nrow=100) y <- 1 + x[,1] - 3*x[,3] + rnorm(100) cv_model <- groupMultLambda(x,y,groups=c(rep(1,2),rep(2,2)),lambda=seq(.1,.5,.1)) ## End(Not run) ```

### Example output

```Loading required package: quantreg

Attaching package: 'SparseM'

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

backsolve