FA_PFP {SILFS}

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)

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.

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).

Author(s)

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)