SILFS {SILFS}

SILFS-Based Subgroup Identification and Variable Selection Optimized by Coordinate Descent under the L2 Distance

Description

This function employs SILFS method under L2 distance and uses the Coordinate Descent Algorithm for optimization to effectively identify subgroup structures and perform variable selection.

Usage

SILFS(Y, X_aug, r, lam_CAR, lam_lasso, alpha_init, K, epsilon)

Arguments

Y

The response vector of length n.

X_aug

The augmented design matrix created by row concatenation of common and idiosyncratic factor matrices, with a size of n \times (r+p).

r

The user supplied number of common factors.

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 user-supplied group number.

epsilon

The user-supplied stopping tolerance.

Value

A vector containing the following components:

alpha_m

The estimated intercept parameter vector of length n.

gamma

The estimated vector of subgroup centers of length K.

theta_m

The estimated regression coefficient vector, matched with common factor terms, with a dimension of r.

beta_m

The estimated regression coefficients matched with idiosyncratic factors, with a dimension of p.

Author(s)

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

References

He, Y., Liu, D., Wang, F., Zhang, M., Zhou, W., 2024. High-Dimensional Subgroup Identification under Latent Factor Structures.

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,F_1,0.1)
SILFS(Y,cbind(F_1,U),3,0.01,0.05,alpha_init,K,0.3)