SILFS (version 0.1.0)

FA_PFP: Factor Adjusted-Pairwise Fusion Penalty (FA-PFP) Method for Subgroup Identification and Variable Selection

Description

This function utilizes the FA-PFP method implemented via the Alternating Direction Method of Multipliers (ADMM) algorithm to identify subgroup structures and conduct variable selection.

Usage

FA_PFP(Y, Fhat, Uhat, vartheta, lam, gam, alpha_init, lam_lasso, epsilon)

Value

A list with the following components:

alpha_m

The estimated intercept parameter vector of length \(n\).

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 \(p\).

eta_m

A numeric matrix storing the pairwise differences of the estimated intercepts, with size of \(n \times (n\times(n-1)/2)\).

Arguments

Y

The response vector of length \(n\).

Fhat

The estimated common factors matrix of size \(n \times r\).

Uhat

The estimated idiosyncratic factors matrix of size \(n \times p\).

vartheta

The Lagrangian augmentation parameter for intercepts.

lam

The tuning parameter for Pairwise Fusion Penalty.

gam

The user-supplied parameter for Alternating Direction Method of Multipliers (ADMM) algorithm.

alpha_init

The initialization of intercept parameter.

lam_lasso

The tuning parameter for LASSO.

epsilon

The user-supplied stopping tolerance.

Author

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

References

Ma, S., Huang, J., 2017. A concave pairwise fusion approach to subgroup analysis.

Examples

n <- 50
p <- 50
r <- 3
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)
FA_PFP(Y,F_1,U,1,0.67,3,alpha_init,0.05,0.3)