scadglm: SCAD regularized loglikelihood for generalized linear models

Description

These functions solve SCAD regularized loglikelihood for generalized linear models; scadcox does the one-step SCAD while fullscadcox solves the SCAD in a fully iterative method.

Usage

scadglm(x, y, wt.initsoln=NULL, lambda, initsoln=NULL, 
family = binomial(), weight = NULL, offset = NULL, 
function.precision=1e-8, nopenalty.subset=NULL)
       
fullscadglm(x, y, lambda, initsoln=NULL, family = binomial(),
   weight = NULL, offset = NULL, function.precision=1e-8, 
   nopenalty.subset=NULL, eps0=1e-6)

Arguments

an (n * p) matrix of features.

an (n) vector of response.

wt.initsoln

a (p+1) vector of initial solution for one-step SCAD.

lambda

regularization parameter for the SCAD.

initsoln

a (p+1) vector of initial solution.

family

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

weight

an optional (n) vector of weights to be used in the fitting process.

offset

this can be used to specify an a priori known component to be included in the linear predictor during fitting.

function.precision

function.precision parameter used in the internal solver. Default is 1e-8.

nopenalty.subset

a set of indices for the predictors that are not subject to the L1 penalty.

eps0

an effective zero.

Value

They return a (p+1) vector of estimated coefficients.

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(1,1,1,-3*sqrt(2)/2)
n=400
p=30
truerho=0.5
x=matrix(rnorm(n*p, mean=0, sd=1), n, p)
feta=x[, 1:4]%*%b
fprob=exp(feta)/(1+exp(feta))
y=rbinom(n, 1, fprob)
scadglm(x,y,lambda=0.0015)
coef(glm(y~x,family=binomial()))