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

In ncpen: Unified Algorithm for Non-convex Penalized Estimation for Generalized Linear Models

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.

See Also

ncpen, cv.ncpen

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")

ncpen documentation built on May 1, 2019, 9:21 p.m.