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simulated_example_robust_analysis.R
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simulated_example_robust_analysis.R
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###########################################################
## R code for simulation examples ##
## in "Robust regression with Compositional Covariates" ##
###########################################################
rm(list = ls())
## Install and load the package "robregcc" from CRAN/GitHub
library(devtools)
# devtools::install_github("amishra-stats/robregcc/robregcc")
library(robregcc)
## Load required packages
library(MASS)
require(ggplot2)
require(reshape2)
library(magrittr)
library(graphics)
######################################
## R code for simulation examples ##
######################################
## -------------------Simulation setting-------------------
## n: sample size
## p: number of predictors
## o: fraction of observations as outliers
## L: {0,1} => leveraged {no, yes}, indicator variable for outlier type
## s: multiplicative factor of true standard deviation by which O, i.e., outliers fraction of observations are shifted.
## ngrp: number of subgroup in the model
## snr: noise to signal ratio for computing true standard deviation of error
## nsim: number of simulation run
## For each setting, generate 100 simulation run
n <- 200
p <- c(100, 300)
s <- c(6, 8)
L <- c(0, 1)
o <- c(0.05, 0.10, 0.15, 0.20)
nsim <- 100
# Begin simulation run setting
j = 1
sim_setting <- NULL
for (tem_p in p) {
for (i in 1:nsim) {
sim_setting <- rbind(sim_setting, c(n, tem_p, 0, 8, 0, i, j))
j <- j + 1
}
}
for (tem_p in p) {
for (tem_L in L) {
for (tem_s in s) {
for (tem_o in o) {
for (i in 1:nsim) {
sim_setting <- rbind(sim_setting, c(n, tem_p, tem_L, tem_s,
tem_o*n, i, j))
j <- j + 1
}
}
}
}
}
sim_setting <- data.frame(sim_setting)
names(sim_setting) <- c('n','p','L','s','O','index','example_seed')
# End simulation run setting
## ---------------------- single replication ------------------------
## For a chosen setting_index execute following chunk of code;
##
##
setting_index <- 1600
setting_eval <- paste(paste(names(sim_setting),
sim_setting[setting_index,] ,
sep = ' = '),collapse = ';')
# Evaluate expression to get simulation setting;
eval(parse(text = setting_eval))
# n = 200;p = 100;L = 1;s = 8;O = 0.1;index = 100;example_seed = 1600
#Additional parameter
ngrp <- 4 # number of sub-composition
snr <- 3 # Signal to noise ratio
#--------------------------------------------------------------
## Simulate true model variables, i.e., y, X, C, beta
## Follow examples from [Pixu Shi 2016]
## -----------------------Generate data--------------------
## 1. coefficient and subcomposition matrix C
# Simulate subcomposition matrix
C1 <- matrix(0,ngrp,23)
tind <- c(0,10,16,20,23)
for (ii in 1:ngrp)
C1[ii,(tind[ii] + 1):tind[ii + 1]] <- 1
C <- matrix(0,ngrp,p)
C[,1:ncol(C1)] <- C1
# model parameter beta
beta0 <- 0.5
beta <- c(1, -0.8, 0.4, 0, 0, -0.6, 0, 0, 0, 0, -1.5, 0, 1.2, 0, 0, 0.3)
beta <- c(beta,rep(0,p - length(beta)))
# Simulate response and predictor, i.e., X, y
Sigma <- 1:p %>% outer(.,.,'-') %>% abs(); Sigma <- 0.5^Sigma
data.case <- vector("list",1)
set.seed(example_seed)
data.case <- robregcc_sim(n,beta,beta0, O = O,Sigma,levg = L,
snr,shft = s,0, C,out = data.case)
#--------------------------------------------------------------
## Data preprocessing:
X <- data.case$X # predictor matrix
y <- data.case$y # model response
# Account for intercept in the model
Xt <- cbind(1,X) # accounting for intercept in predictor
C <- cbind(0,C) # accounting for intercept in constraint
bw <- c(0,rep(1,p)) # weight matrix to not penalize intercept
set.seed(example_seed) # unique seed
#--------------------------------------------------------------
# Non-robust regression, [Pixu Shi 2016]
control <- robregcc_option(maxiter = 5000, tol = 1e-8, lminfac = 1e-8)
fit.nr <- classo(Xt, y, C, we = bw, type = 1, control = control)
if (O > 0) {
fit.oracle <- classo(Xt[-(1:O),], data.case$yo[-(1:O)], C,
we = bw, type = 1, control = control)
} else {
fit.oracle <- fit.nr
}
#--------------------------------------------------------------
## Initialization
# control parameter
# Breakdown point for tukey Bisquare loss function
# b1 = 0.5; cc1 = 1.567 # 50% breakdown point
b1 = 0.25; cc1 = 2.937 # initalization for scale parameter
control <- robregcc_option(maxiter = 1000,tol = 1e-4,lminfac = 1e-7)
fit.init <- cpsc_sp(Xt, y,alp = 0.4, cfac = 2, b1 = b1,
cc1 = cc1,C,bw,1,control)
#--------------------------------------------------------------
## Robust model fitting
# control parameters
control <- robregcc_option()
beta.wt <- fit.init$betaR # Set weight for model parameter beta
beta.wt[1] <- 0
control$gamma = 1 # gamma for constructing weighted penalty
control$spb = 40/p # fraction of maximum non-zero model parameter beta
control$outMiter = 1000 # Outer loop iteration
control$inMiter = 3000 # Inner loop iteration
control$nlam = 50 # Number of tuning parameter lambda to be explored
control$lmaxfac = 1 # Parameter for constructing sequence of lambda
control$lminfac = 1e-8 # Parameter for constructing sequence of lambda
control$tol = 1e-20; # tolrence parameter for converging [inner loop]
control$out.tol = 1e-16 # tolerence parameter for convergence [outer loop]
control$kfold = 10 # number of fold of crossvalidation
control$sigmafac = 2#1.345
# Robust regression using adaptive lasso penalty
fit.ada <- robregcc_sp(Xt,y,C,
beta.init = beta.wt, cindex = 1,
gamma.init = fit.init$residuals,
control = control,
penalty.index = 1, alpha = 0.95)
# Robust regression using lasso penalty [Huber equivalent]
fit.soft <- robregcc_sp(Xt,y,C, cindex = 1,
control = control, penalty.index = 2,
alpha = 0.95)
# Robust regression using hard thresholding penalty
control$lmaxfac = 1e2 # Parameter for constructing sequence of lambda
control$lminfac = 1e-3 # Parameter for constructing sequence of lambda
control$sigmafac = 2#1.345
fit.hard <- robregcc_sp(Xt,y,C, beta.init = fit.init$betaf,
gamma.init = fit.init$residuals,
cindex = 1,
control = control, penalty.index = 3,
alpha = 0.95)
## -----------------------Figure 2 in the manuscript ------------
fdir <- getwd()
pdf(file = file.path(fdir,'cv_sim.pdf'), width = 15, height = 4)
par(mfrow = c(1,3), mar = 5*c(1,1,0.5,0.1))
plot_path(fit.ada)
plot_cv(fit.ada)
plot_resid(fit.ada, 1, s = 0)
dev.off()
#
## -----------------------Model comparisons ------------
## A function to compute the error measures for comparing different methods
## Table 2 (s = 8) in the manuscript and Table 1 (s = 6) in the supplementary material
## Figure 3 compares the misspecification measure using HM
## model_compare : provides metric to compare models
# fit : fit objects obtained using robregcc
# O: Number of outliers in the simulated data
# beta: true parameter beta
# s_index: 1/2 corresponding to minimum/1se rule cross validation error
model_compare = function(fit, O, beta,s_index){
outlier_identifier <- !fit$inlierE[,s_index]
if (O) {
# O = 0 case
FP2 <- sum(outlier_identifier[-c(1:O)])
outlier_identifier <- abs(fit$gamma0[,s_index]) > 0.001
FN <- sum(!outlier_identifier[1:O])
FP1 <- sum(outlier_identifier[-c(1:O)])
HM <- sum(!outlier_identifier[1:O]) + sum(outlier_identifier[-c(1:O)])
} else {
# O = 0 case
FP2 <- sum(outlier_identifier)
outlier_identifier <- abs(fit$gamma0[,s_index]) > 0.001
FN <- 0
FP1 <- sum(outlier_identifier)
HM <- FN + FP1
}
error_beta <- sqrt(sum((fit$betaE[,s_index] - beta)^2))/length(beta)
return(c(error_beta, FN, FP1, HM, FP2))
}
beta_oracle <- c(beta0,beta)
error_beta_nr <- sqrt(sum(((beta_oracle - fit.nr$beta))^2))/length(beta_oracle)
s_index <- 1 # 1/2 corresponding to minimum/1se rule cross validation error
compare.fit <- rbind(c(1,model_compare(fit.ada,O,beta_oracle,s_index)),
c(2,model_compare(fit.soft,O,beta_oracle,s_index)),
c(3,model_compare(fit.hard,O,beta_oracle,s_index)),
c(4,error_beta_nr,NA,NA,NA,NA))
colnames(compare.fit) <- c('Method', 'Er_beta', 'FN', 'FP_1','HM', 'FP_2')
compare.fit <- data.frame(compare.fit)
compare.fit$Method <- c('A','E','H','NR')[compare.fit$Method]
compare.fit <- cbind(n,p,L,s,O,index,s_index, compare.fit)
compare.fit