SCAR {SILFS}

Standard Center Augmented Regularization (S-CAR) Method for Subgroup Identification and Variable Selection

Description

This function employs the S-CAR method under L2 distance and uses the Coordinate Descent Algorithm for optimization to identify subgroup structures and execute variable selection.

Usage

SCAR(Y, X, lam_CAR, lam_lasso, alpha_init, K, epsilon)

Arguments

Y

The response vector of length n.

X

The design matrix of size n \times p.

lam_CAR

The tuning parameter for Center-Augmented Regularization.

lam_lasso

The tuning parameter for lasso.

alpha_init

The initialization of intercept parameter.

K

The estimated group number.

epsilon

The user-supplied stopping tolerance.

Value

A list with the following components:

alpha_m

The estimated intercept parameter vector of length n.

gamma

The estimated vector of subgroup centers of length K.

beta_m

The estimated regression coefficient vector of dimension p.

Author(s)

Yong He, Liu Dong, Fuxin Wang, Mingjuan Zhang, Wenxin Zhou.

Examples

n <- 50
p <- 50
r <- 3
K <- 2
alpha <- sample(c(-3,3),n,replace=TRUE,prob=c(1/2,1/2))
beta <- c(rep(1,2),rep(0,48))
B <- matrix((rnorm(p*r,1,1)),p,r)
F_1 <- matrix((rnorm(n*r,0,1)),n,r)
U <- matrix(rnorm(p*n,0,0.1),n,p)
X <- F_1%*%t(B)+U
Y <- alpha + X%*%beta + rnorm(n,0,0.5)
alpha_init <- INIT(Y,X,0.1)
SCAR(Y,X,0.01,0.05,alpha_init,K,0.3)