R: control.ncpen: do preliminary works for 'ncpen'.

control.ncpen {ncpen}

R Documentation

control.ncpen: do preliminary works for `ncpen`.

Description

The function returns controlled samples and tuning parameters for ncpen by eliminating unnecessary errors.

Usage

control.ncpen(y.vec, x.mat, family = c("gaussian", "binomial", "poisson",
  "multinomial", "cox"), penalty = c("scad", "mcp", "tlp", "lasso",
  "classo", "ridge", "sridge", "mbridge", "mlog"), x.standardize = TRUE,
  intercept = TRUE, lambda = NULL, n.lambda = NULL,
  r.lambda = NULL, w.lambda = NULL, gamma = NULL, tau = NULL,
  alpha = NULL, aiter.max = 100, b.eps = 1e-07)

Arguments

`y.vec`	(numeric vector) response vector. Must be 0,1 for `binomial` and 1,2,..., for `multinomial`.
`x.mat`	(numeric matrix) design matrix without intercept. The censoring indicator must be included at the last column of the design matrix for `cox`.
`family`	(character) regression model. Supported models are `gaussian`, `binomial`, `poisson`, `multinomial`, and `cox`. Default is `gaussian`.
`penalty`	(character) penalty function. Supported penalties are `scad` (smoothly clipped absolute deviation), `mcp` (minimax concave penalty), `tlp` (truncated LASSO penalty), `lasso` (least absolute shrinkage and selection operator), `classo` (clipped lasso = mcp + lasso), `ridge` (ridge), `sridge` (sparse ridge = mcp + ridge), `mbridge` (modified bridge) and `mlog` (modified log). Default is `scad`.
`x.standardize`	(logical) whether to standardize `x.mat` prior to fitting the model (see details). The estimated coefficients are always restored to the original scale.
`intercept`	(logical) whether to include an intercept in the model.
`lambda`	(numeric vector) user-specified sequence of `lambda` values. Default is supplied automatically from samples.
`n.lambda`	(numeric) the number of `lambda` values. Default is 100.
`r.lambda`	(numeric) ratio of the smallest `lambda` value to largest. Default is 0.001 when n>p, and 0.01 for other cases.
`w.lambda`	(numeric vector) penalty weights for each coefficient (see references). If a penalty weight is set to 0, the corresponding coefficient is always nonzero.
`gamma`	(numeric) additional tuning parameter for controlling shrinkage effect of `classo` and `sridge` (see references). Default is half of the smallest `lambda`.
`tau`	(numeric) concavity parameter of the penalties (see reference). Default is 3.7 for `scad`, 2.1 for `mcp`, `classo` and `sridge`, 0.001 for `tlp`, `mbridge` and `mlog`.
`alpha`	(numeric) ridge effect (weight between the penalty and ridge penalty) (see details). Default value is 1. If penalty is `ridge` and `sridge` then `alpha` is set to 0.
`aiter.max`	(numeric) maximum number of iterations in CD algorithm.
`b.eps`	(numeric) convergence threshold for coefficients vector.

Details

The function is used internal purpose but useful when users want to extract proper tuning parameters for ncpen. Do not supply the samples from control.ncpen into ncpen or cv.ncpen directly to avoid unexpected errors.

Value

An object with S3 class ncpen.

`y.vec`	response vector.
`x.mat`	design matrix adjusted to supplied options such as family and intercept.
`family`	regression model.
`penalty`	penalty.
`x.standardize`	whether to standardize `x.mat`.
`intercept`	whether to include the intercept.
`std`	scale factor for `x.standardize`.
`lambda`	lambda values for the analysis.
`n.lambda`	the number of `lambda` values.
`r.lambda`	ratio of the smallest `lambda` value to largest.
`w.lambda`	penalty weights for each coefficient.
`gamma`	additional tuning parameter for controlling shrinkage effect of `classo` and `sridge` (see references).
`tau`	concavity parameter of the penalties (see references).
`alpha`	ridge effect (amount of ridge penalty). see details.

Author(s)

Dongshin Kim, Sunghoon Kwon, Sangin Lee

References

Fan, J. and Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American statistical Association, 96, 1348-60. Zhang, C.H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of statistics, 38(2), 894-942. Shen, X., Pan, W., Zhu, Y. and Zhou, H. (2013). On constrained and regularized high-dimensional regression. Annals of the Institute of Statistical Mathematics, 65(5), 807-832. Kwon, S., Lee, S. and Kim, Y. (2016). Moderately clipped LASSO. Computational Statistics and Data Analysis, 92C, 53-67. Kwon, S. Kim, Y. and Choi, H.(2013). Sparse bridge estimation with a diverging number of parameters. Statistics and Its Interface, 6, 231-242. Huang, J., Horowitz, J.L. and Ma, S. (2008). Asymptotic properties of bridge estimators in sparse high-dimensional regression models. The Annals of Statistics, 36(2), 587-613. Zou, H. and Li, R. (2008). One-step sparse estimates in nonconcave penalized likelihood models. Annals of statistics, 36(4), 1509. Lee, S., Kwon, S. and Kim, Y. (2016). A modified local quadratic approximation algorithm for penalized optimization problems. Computational Statistics and Data Analysis, 94, 275-286.

Examples

### linear regression with scad penalty
sam =  sam.gen.ncpen(n=200,p=10,q=5,cf.min=0.5,cf.max=1,corr=0.5)
x.mat = sam$x.mat; y.vec = sam$y.vec
tun = control.ncpen(y.vec=y.vec,x.mat=x.mat,n.lambda=10,tau=1)
tun$tau
### multinomial regression with sridge penalty
sam =  sam.gen.ncpen(n=200,p=10,q=5,k=3,cf.min=0.5,cf.max=1,corr=0.5,family="multinomial")
x.mat = sam$x.mat; y.vec = sam$y.vec
tun = control.ncpen(y.vec=y.vec,x.mat=x.mat,n.lambda=10,
                    family="multinomial",penalty="sridge",gamma=10)
### cox regression with mcp penalty
sam =  sam.gen.ncpen(n=200,p=10,q=5,r=0.2,cf.min=0.5,cf.max=1,corr=0.5,family="cox")
x.mat = sam$x.mat; y.vec = sam$y.vec
tun = control.ncpen(y.vec=y.vec,x.mat=x.mat,n.lambda=10,family="cox",penalty="scad")

[Package ncpen version 1.0.0 Index]

control.ncpen: do preliminary works for ncpen.