TJuser / WQRADMM

R package for longitudinal quantile regression in distributed big data based on multi-block ADMM

WQRADMM for Windows users

Instructions

R package for distributed quantile regression in longitudinal big data based on ADMM.

It can be used to reproduce the simulation studies in the following paper:

Ye Fan, Nan Lin and Liqun Yu. Distributed Quantile Regression for Longitudinal Big Data.

Two main functions are included: WQRADMM( ) and paraWQRADMM( ), repectively designed for non-distributed and distributed environments.

Installation requirements

Install RTools and further put its location on the environment variable PATH before installing this package. 
In addition, please update your cpp to version 1.0.9. 

Code for installing WQRADMM

install.packages("Rcpp")
library(Rcpp)
install.packages("RcppArmadillo")
library(RcppArmadillo)
install.packages("devtools")
library(devtools)
install_github("https://github.com/nanlin999/WQRADMM", force = TRUE)
library(WQRADMM)

Code for testing WQRADMM and paraWQRADMM

###function for generating the correlation matrix (AR(1) or exchangeable)
gcov = function(p, rho, type){
  if(type == "exchangeable"){
    cov = matrix(rho, p, p)
    diag(cov) = rep(1, p)
  }
  else{
    cov = diag(p)
    for(i in 1:p){
      for(j in 1:p){
        if(i < j) cov[i,j] = rho^{j-i}
        else cov[i,j] = cov[j,i]
      }
    }
  }
  cov
}

###generate synthetic data (heteroscedastic model with d = 0.75*p under Student's t error)
N = 10000
p = 100
n = 10
rep = rep(n, N)
nsum = sum(rep)
d = 0.75*p
rho_X = 0.5
rho_e = 0.5
tau = 0.75
set.seed(999)
X = matrix(rnorm(nsum*p), nsum, p)
cov_X = gcov(p, rho_X, "ar1")
X = X%*%chol(cov_X)
for(i in 1:d){
  X[,i] = pnorm(X[,i])
}
set.seed(1000)
e = matrix(rt(N*n, 3), N, n)
cov_e = gcov(n, rho_e, "ar1")
e = as.vector(t(e%*%chol(cov_e)))
sigma = 0.5
e = sigma*e
beta0 = rnorm(1)
beta = rnorm(p)
Y = beta0+X%*%beta+apply(X[,1:d]*e/d, 1, sum)
beta_true = c(beta0, quantile(e/d, tau)+beta[1:d], beta[(d+1):p])

###calculate the WQR estimator by WQR-ADMM
WQR = WQRADMM(X, Y, rep, tau, intercept = TRUE, "WQR", warmstart = FALSE)
beta_WQR = WQR$Estimation_WQR
AE_WQR = sum(abs(beta_WQR-beta_true))
Time_WQR = WQR$Time_WQR
Time_WQRADMM = WQR$Time_total

###calculate the WQR estimator by parallel WQR-ADMM
k = 10              ###number of partitions
paraWQR = paraWQRADMM(X, Y, k, rep, tau, intercept = TRUE, "WQR", warmstart = FALSE)
beta_paraWQR = paraWQR$Estimation_WQR
AE_paraWQR = sum(abs(beta_paraWQR-beta_true))
Time_paraWQR = paraWQR$Time_WQR
Time_paraWQRADMM = paraWQR$Time_total

###output the results
AE_WQR              ###estimation error of WQR-ADMM            
Time_WQRADMM        ###computational time of WQR-ADMM
AE_paraWQR          ###estimation error of parallel WQR-ADMM
Time_paraWQRADMM    ###computational time of parallel WQR-ADMM