getfinalSCADcoef: SCAD regularized loglikelihood for generalized linear models

Description

This function gets the final regression coefficients for the SCAD regularized loglikelihood for generalized linear models after applying (I)SIS.

Usage

getfinalSCADcoef(x, y, pickind, folds=NULL, eps0=1e-5, family=binomial(),
tune.method="AIC", inittype='NoPen', detailed=FALSE)

INDEPgetfinalSCADcoef(x, y, pickind,  folds=NULL, xtune, ytune, 
family=binomial(), inittype='NoPen', eps0=1e-5, detailed=FALSE)

Arguments

an (n * p) matrix of features.

an (n) vector of response.

pickind

predictor indice selected by (I)SIS.

folds

fold information for cross validation.

family

a description of the error distribution and link function to be used in the model.

tune.method

method for tuning regularization parameter.

inittype

inittype specifies the type of initial solution for the one-step SCAD. It can be either NoPen or L1.

xtune, ytune

independent tuning dataset.

eps0

an effective zero.

detailed

indicates whether detailed information will be provided. Default is FALSE.

Value

An initial solution vector wt.initsoln and final solution (p+1) vector SCADcoef.

References

Jianqing Fan and Runze Li (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association, 96, 1348-1360. Hui Zou and Runze Li (2008) One-step Sparse Estimates in Nonconcave Penalized Likelihood Models (with discussion). The Annals of Statistics, 36, 1509-1533

Examples

Run this code

set.seed(0)
b <- c(4,4,4,-6*sqrt(2))
n=150
p=200
truerho=0.5
corrmat=diag(rep(1-truerho, p))+matrix(truerho, p, p)
corrmat[,4]=sqrt(truerho)
corrmat[4, ]=sqrt(truerho)
corrmat[4,4]=1
cholmat=chol(corrmat)
x=matrix(rnorm(n*p, mean=0, sd=1), n, p)
x=x%*%cholmat
feta=x[, 1:4]%*%b
fprob=exp(feta)/(1+exp(feta))
y=rbinom(n, 1, fprob)

nsis=floor(n/log(n)/4)
xtune=matrix(rnorm(n*p, mean=0, sd=1), n, p)
xtune=xtune%*%cholmat
feta=xtune[, 1:4]%*%b
fprob=exp(feta)/(1+exp(feta))
ytune=rbinom(n, 1, fprob)

ISIScoef = INDEPgetfinalSCADcoef(x = x, y = y, 
                pickind = 1:4, xtune = xtune, ytune = ytune, 
                family = binomial())