ADMM.q1: Subgroup detection in setting of regression with ADMM...

In PengWu12245/RegSubDetect: Regression and Subgroup Detection for Heterogeneous Samples

Description

The model is

Y_i = X_i β + Z_i θ_i.

This ADMM algorithm can detect the subgroup effects of θ_i and estimate the regression coefficient β simultaneously.

Usage

ADMM.q1(Y, X, Z0, penalty, lam_vec, ga = 3.7, nu = 1, maxiter = 1000,
  ep = 5e-04)

Arguments

Y	a n*1 vector, response.
X	a n*p matrix, p-dimensional covariate.
Z0	a n*1 matrix, treatment indicator.
lam_vec	a series of candidate tuning parameter lambda for penalty function, which is a vector.
ga	a parameter for penalty function, default 3.7.
nu	a tuning parameter for augmented Largranian objection function, the default value is 1.
maxiter	The maximum number of iterations. Defaults to 1000.
ep	the absolute convergence tolerance.
peanlty	"SCAD" or "MCP".

Value

• BIC the values of BIC for each lam_vec.

• lam_opt the optimal lambda that have. the mimimal BIC.

• beta_Est_lam the regression coefficients matrix of covariates for different value of lam_vec, each column denotes a value of lam_vec.

• theta_Est_lam the regression coefficients matrix of treatment indicator for each individuals, each column denotes a different value of lam_vec.

• theta_est_opt the regression coefficients of treatment indicator for optimal lambda.

• beta_est_opt the regression coefficients of covariates for optimal lambda.

See Also

ADMM

Examples

set.seed(1)
n = 200; p = 2
x = matrix(rnorm(n*p, mean = 2), nrow = n, ncol = p) # covariates
z = sample(c(0,1), n, T)    # treatment indicator
beta = c(-2, -3)            # regression coefficients of covariates
mu = c(-2, 2)               # regression coefficients of treatment indicator

y = x %*% beta + z * mu[1] + rnorm(n, sd = 0.5)
index = sample(c(0,1), n, T)
y[index == 1] = y[index == 1] + z[index == 1] * (mu[2] - mu[1])
lam_vec = seq(0,2,0.2)
result = ADMM.q1(y, x, z, penalty = 'SCAD', lam_vec = lam_vec)
result$beta_est_opt
unique( round(result$theta_est_opt, 1) )

# solution paths
py_mu = result$theta_Est_lam
plot(x=lam_vec, y=py_mu[1,], xlab=expression(lambda),
   ylab=expression(paste("Estimated value of  ", vartheta, sep=" ")),
   xlim=c(0,2), ylim=c(min(py_mu),max(py_mu)),
   main="Solution path for domain I", type='l')
for(j in 1:nrow(py_mu) ){
   lines(lam_vec, py_mu[j,], lty=j, col=j+1,lwd=2 )
}
abline(v=result$lam_opt, lty=3, col="lightblue",lwd =3)

PengWu12245/RegSubDetect documentation built on Dec. 30, 2019, 6:01 p.m.