rq.nc.fit: Non-convex penalized quantile regression

View source: R/mainFunctions.R

rq.nc.fitR Documentation

Non-convex penalized quantile regression

Description

Warning: this function is no longer exported. Produces penalized quantile regression models for a range of lambdas and penalty of choice. If lambda is unselected than an iterative algorithm is used to find a maximum lambda such that the penalty is large enough to produce an intercept only model. Then range of lambdas goes from the maximum lambda found to "eps" on the log scale. Local linear approximation approach used by Wang, Wu and Li to extend LLA as proposed by Zou and Li (2008) to the quantile regression setting.

Usage

rq.nc.fit(
  x,
  y,
  tau = 0.5,
  lambda = NULL,
  weights = NULL,
  intercept = TRUE,
  penalty = "SCAD",
  a = 3.7,
  iterations = 1,
  converge_criteria = 1e-06,
  alg = ifelse(p < 50, "LP", "QICD"),
  penVars = NULL,
  internal = FALSE,
  ...
)

Arguments

x

Matrix of predictors.

y

Vector of response values.

tau

Conditional quantile being modelled.

lambda

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

weights

Weights for the objective function.

intercept

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

penalty

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

a

Additional tuning parameter for SCAD and MCP

iterations

Number of iterations to be done for iterative LLA algorithm.

converge_criteria

Difference in betas from iteration process that would satisfy convergence.

alg

Defaults for small p to linear programming (LP), see Wang, Wu and Li (2012) for details. Otherwise a coordinate descent algorithm is used (QICD), see Peng and Wang (2015) for details. Both methods rely on the One-step sparse estimates algorithm.

penVars

Variables that should be penalized. With default value of NULL all variables are penalized.

internal

Whether call to this function has been made internally or not.

...

Additional items to be sent to rq.lasso.fit.

Value

Returns the following:

  • coefficientsCoefficients from the penalized model.

  • PenRhoPenalized objective function value.

  • residuals Residuals from the model.

  • rho Objective function evaluation without the penalty.

  • coefficients Coefficients from the penalized model.

  • tau Conditional quantile being modeled.

  • n Sample size.

  • penalty Penalty used, SCAD or MCP.

  • penaltyPenalty selected.

Author(s)

Ben Sherwood, ben.sherwood@ku.edu and Adam Maidman.

References

  • Wang, L., Wu, Y. and Li, R. (2012). Quantile regression of analyzing heterogeneity in ultra-high dimension. J. Am. Statist. Ass, 107, 214–222.

  • Wu, Y. and Liu, Y. (2009). Variable selection in quantile regression. Statistica Sinica, 19, 801–817.

  • Zou, H. and Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models. Ann. Statist., 36, 1509–1533.

  • Peng, B. and Wang, L. (2015). An iterative coordinate-descent algorithm for high-dimensional nonconvex penalized quantile regression. J. Comp. Graph., 24, 676–694.

Examples

## Not run: 
x <- matrix(rnorm(800),nrow=100)
y <- 1 + x[,1] - 3*x[,5] + rnorm(100)
scadModel <- rq.nc.fit(x,y,lambda=1)

## End(Not run)

rqPen documentation built on Aug. 25, 2023, 1:07 a.m.