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Postprocess_MediationEffects.R
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##---------------------------------------------------------------
## Required libraries
##---------------------------------------------------------------
#----- Parallel computing
library(doParallel)
#----- Make clusters based on the number of CPU cores
cl<-makeCluster(64) # 64 cores
registerDoParallel(cl)
getDoParWorkers()
#----- Support parallel excution
library(foreach)
##---------------------------------------------------------------
## Extract MCMC samples from Stan outputs
##---------------------------------------------------------------
#----- Load MCMC samples and Data
load("Master.RData")
load("MCMCsamples.RData")
#------ Set Treatment (TRT), Outcome (OUT), Mediators (M) and Covariates (X)
Data <- Master
OUT <- Data$PM.2.5
TRT <- Data$SO2.SC
M <- cbind(Data$SO2_Annual, Data$NOx_Annual, Data$CO2_Annual)
X <- cbind(Data$S_n_CR, Data$NumNOxControls, Data$Heat_Input/100000, Data$Barometric_Pressure, Data$Temperature, Data$PctCapacity, Data$sulfur_Content, Data$Phase2_Indicator, Data$Operating_Time/1000)
dim.cov <- dim(X)[2] #<--------- Num. of Covariates
#------ Variables by treatments
x0 <- X[which(TRT==0),]
x1 <- X[which(TRT==1),]
y0 <- OUT[which(TRT==0)]
y1 <- OUT[which(TRT==1)]
m0 <- log(M[which(TRT==0),])
m1 <- log(M[which(TRT==1),])
n0 <- dim(x0)[1]
n1 <- dim(x1)[1]
#----- Extract MCMC samples from each marginal distribution
data.y0 <- para.y0[,2:35]
data.y1 <- para.y1[,2:35]
data.m10 <- para.m10[,2:35]
data.m11 <- para.m11[,2:35]
data.m20 <- para.m20[,2:35]
data.m21 <- para.m21[,2:35]
data.m30 <- para.m30[,2:35]
data.m31 <- para.m31[,2:35]
COR <- para.C[,29:56]
#----- Parameters of the models under Z=1
gamma10 <- data.y1[,9:17]
gamma11 <- data.y1[,18:25]
w1 <- data.y1[,26:34]
beta1_10 <- data.m11[,9:17]
beta1_11 <- data.m11[,18:25]
beta2_10 <- data.m21[,9:17]
beta2_11 <- data.m21[,18:25]
beta3_10 <- data.m31[,9:17]
beta3_11 <- data.m31[,18:25]
s1_1 <- data.m11[,26:34]
s2_1 <- data.m21[,26:34]
s3_1 <- data.m31[,26:34]
psi1 <- data.y1[,1:8]
psi1_1 <- data.m11[,1:8]
psi2_1 <- data.m21[,1:8]
psi3_1 <- data.m31[,1:8]
#----- Parameters of the models under Z=0
gamma00 <- data.y0[,9:17]
gamma01 <- data.y0[,18:25]
w0 <- data.y0[,26:34]
beta1_00 <- data.m10[,9:17]
beta1_01 <- data.m10[,18:25]
beta2_00 <- data.m20[,9:17]
beta2_01 <- data.m20[,18:25]
beta3_00 <- data.m30[,9:17]
beta3_01 <- data.m30[,18:25]
s1_0 <- data.m10[,26:34]
s2_0 <- data.m20[,26:34]
s3_0 <- data.m30[,26:34]
psi0 <- data.y0[,1:8]
psi1_0 <- data.m10[,1:8]
psi2_0 <- data.m20[,1:8]
psi3_0 <- data.m30[,1:8]
#----- Setting Thinning and Burn-in's
Thin <- 5
Burn0 <- 90000 # Extra burn-in periods for Models under Z=0
Burn1 <- 90000 # Extra burn-in periods for Models under Z=1
#----- Set the number of post-processing steps, N
n.iter <- 2000
##---------------------------------------------------------------
## 'Main' function on each cluster (parallel)
##---------------------------------------------------------------
main <- function(temp){
#----- Require multivariate normal distribuion on each cluster
library(mnormt)
#----- Index of iterations (on parallel)
j <- temp
#----- The number of covariates samples (with replacement) for the empirical distribution
size <- 5000
s.covariate <- data.frame(X[sample(seq(1,dim(X)[1]), size = size, replace = TRUE),]) #----- Covariates samples
#----- Index of posterior samples
index0 <- Thin * j + Burn0; index1 <- Thin * j + Burn1
#----- Construct the correlation matrix
Cor01 <- matrix(c(1, COR[index0,c(8,9,11,12,13,8)],1,COR[index0,c(14,16,17,18,9,14)],1,COR[index0,c(20,21,22,11,16,20)],1,COR[index0,c(26,27,12,17,21,26)],1,COR[index0,c(28,13,18,22,27,28)],1),6,6,byrow=TRUE)
cor.y1m1 <- matrix(c(1,COR[index0,c(1,2,3,1)],1,COR[index0,c(8,9,2,8)],1,COR[index0,c(14,3,9,14)],1),4,4,byrow=TRUE)
cor.y0m0 <- matrix(c(1,COR[index0,c(23,24,25,23)],1,COR[index0,c(26,27,24,26)],1,COR[index0,c(28,25,27,28)],1),4,4,byrow=TRUE)
#----- mixing parameters
ppi.y0 <- pmax(psi0[index0,], 0)
ppi.y1 <- pmax(psi1[index1,], 0)
ppi.m10 <- pmax(psi1_0[index0,], 0)
ppi.m20 <- pmax(psi2_0[index0,], 0)
ppi.m30 <- pmax(psi3_0[index0,], 0)
ppi.m11 <- pmax(psi1_1[index1,], 0)
ppi.m21 <- pmax(psi2_1[index1,], 0)
ppi.m31 <- pmax(psi3_1[index1,], 0)
pi.y1 <- NULL
pi.y1[1] <- ppi.y1[1]
pi.y1[2:8] <- sapply(2:8, function(i) ppi.y1[i] * prod(1 - ppi.y1[1:(i-1)]))
pi.y1[9] <- prod(1-ppi.y1[1:8])
pi.y0 <- NULL
pi.y0[1] <- ppi.y0[1]
pi.y0[2:8] <- sapply(2:8, function(i) ppi.y0[i] * prod(1 - ppi.y0[1:(i-1)]))
pi.y0[9] <- prod(1-ppi.y0[1:8])
pi.m10 <- NULL
pi.m10[1] <- ppi.m10[1]
pi.m10[2:8] <- sapply(2:8, function(i) ppi.m10[i] * prod(1 - ppi.m10[1:(i-1)]))
pi.m10[9] <- prod(1-ppi.m10[1:8])
pi.m20 <- NULL
pi.m20[1] <- ppi.m20[1]
pi.m20[2:8] <- sapply(2:8, function(i) ppi.m20[i] * prod(1 - ppi.m20[1:(i-1)]))
pi.m20[9] <- prod(1-ppi.m20[1:8])
pi.m30 <- NULL
pi.m30[1] <- ppi.m30[1]
pi.m30[2:8] <- sapply(2:8, function(i) ppi.m30[i] * prod(1 - ppi.m30[1:(i-1)]))
pi.m30[9] <- prod(1-ppi.m30[1:8])
pi.m11 <- NULL
pi.m11[1] <- ppi.m11[1]
pi.m11[2:8] <- sapply(2:8, function(i) ppi.m11[i] * prod(1 - ppi.m11[1:(i-1)]))
pi.m11[9] <- prod(1-ppi.m11[1:8])
pi.m21 <- NULL
pi.m21[1] <- ppi.m21[1]
pi.m21[2:8] <- sapply(2:8, function(i) ppi.m21[i] * prod(1 - ppi.m21[1:(i-1)]))
pi.m21[9] <- prod(1-ppi.m21[1:8])
pi.m31 <- NULL
pi.m31[1] <- ppi.m31[1]
pi.m31[2:8] <- sapply(2:8, function(i) ppi.m31[i] * prod(1 - ppi.m31[1:(i-1)]))
pi.m31[9] <- prod(1-ppi.m31[1:8])
#---- Sampling mediators conditional on covariates
M0M1 <- function(k){
F <- pnorm(rmnorm(1, mean=rep(0,6), Cor01),0,1)
X.temp <- s.covariate[k,]
for(i in 1:3){
for(k in 0:1){
eval(parse(text=paste("clus.m",i,k," <- which(rmultinom(1, 1, pi.m",i,k,")==1)", sep="")))
}
}
s.m10<-qnorm(F[4], mean = beta1_00[index0,clus.m10] + beta1_01[index0,]%*%t(X.temp), sd = sqrt(s1_0[index0,clus.m10]))
s.m20<-qnorm(F[5], mean = beta2_00[index0,clus.m20] + beta2_01[index0,]%*%t(X.temp), sd = sqrt(s2_0[index0,clus.m20]))
s.m30<-qnorm(F[6], mean = beta3_00[index0,clus.m30] + beta3_01[index0,]%*%t(X.temp), sd = sqrt(s3_0[index0,clus.m30]))
s.m11<-qnorm(F[1], mean = beta1_10[index1,clus.m11] + beta1_11[index1,]%*%t(X.temp), sd = sqrt(s1_1[index1,clus.m11]))
s.m21<-qnorm(F[2], mean = beta2_10[index1,clus.m21] + beta2_11[index1,]%*%t(X.temp), sd = sqrt(s2_1[index1,clus.m21]))
s.m31<-qnorm(F[3], mean = beta3_10[index1,clus.m31] + beta3_11[index1,]%*%t(X.temp), sd = sqrt(s3_1[index1,clus.m31]))
return(c(s.m10,s.m20,s.m30,s.m11,s.m21,s.m31))
}
#----- Conditional distribution of Y{1;M(1,1,1)}
F.y1m1 <- function(o1, o2, o3, k){
for(i in 1:3) eval(parse(text=paste("m",i,"<- C.sample[o",i,", k]", sep="")))
X.temp <- s.covariate[k,]
Y.dist <- function(x,u){
sum(pnorm(x, mean = gamma10[index1,] + gamma11[index1,] %*% t(X.temp), sd = sqrt(w1[index1,])) * pi.y1) - u
}
M1.dist <- qnorm(max(sum(pnorm(m1, mean = beta1_10[index1,] + beta1_11[index1,] %*% t(X.temp), sd = sqrt(s1_1[index1,])) * pi.m11), 0.1^30))
M2.dist <- qnorm(max(sum(pnorm(m2, mean = beta2_10[index1,] + beta2_11[index1,] %*% t(X.temp), sd = sqrt(s2_1[index1,])) * pi.m21), 0.1^30))
M3.dist <- qnorm(max(sum(pnorm(m3, mean = beta3_10[index1,] + beta3_11[index1,] %*% t(X.temp), sd = sqrt(s3_1[index1,])) * pi.m31), 0.1^30))
con.joint <- min(1-0.1^30, max(0.1^30, pnorm(cor.y1m1[1,2:4] %*% solve(cor.y1m1[2:4,2:4]) %*% c(M1.dist,M2.dist,M3.dist))))
my.uniroot <- function(z){
e<-try(d<-uniroot(Y.dist, c(-400,600), tol = 0.01, u=z), silent=TRUE)
if(class(e) == "try-error") return(NA) else return(d$root)
}
return(vapply(con.joint, my.uniroot, numeric(1)))
}
#----- Conditional distribution of Y{0;M(0,0,0)}
F.y0m0<-function(o1, o2, o3, k){
for(i in 1:3) eval(parse(text=paste("m",i,"<- C.sample[o",i,", k]", sep="")))
X.temp <- s.covariate[k,]
Y.dist <- function(x,u){
sum(pnorm(x, mean = gamma00[index0,] + gamma01[index0,] %*% t(X.temp), sd = sqrt(w0[index0,])) * pi.y0) - u
}
M1.dist <- qnorm(max(sum(pnorm(m1, mean = beta1_00[index0,] + beta1_01[index0,] %*% t(X.temp), sd = sqrt(s1_0[index0,])) * pi.m10 ), 0.1^30))
M2.dist <- qnorm(max(sum(pnorm(m2, mean = beta2_00[index0,] + beta2_01[index0,] %*% t(X.temp), sd = sqrt(s2_0[index0,])) * pi.m20 ), 0.1^30))
M3.dist <- qnorm(max(sum(pnorm(m3, mean = beta3_00[index0,] + beta3_01[index0,] %*% t(X.temp), sd = sqrt(s3_0[index0,])) * pi.m30 ), 0.1^30))
con.joint <- min(1-0.1^30, max(0.1^30,pnorm(cor.y0m0[1,2:4] %*% solve(cor.y0m0[2:4,2:4]) %*% c(M1.dist,M2.dist,M3.dist))))
my.uniroot <- function(z){
e<-try(d<-uniroot(Y.dist, c(-400,600), tol = 0.01, u=z), silent=TRUE)
if(class(e) == "try-error") return(NA) else return(d$root)
}
return(vapply(con.joint, my.uniroot, numeric(1)))
}
#----- Sampling mediators
C.sample <- sapply(seq(1,size, by=1), function(x) M0M1(x))
#----- potential outcomes
y1000 <- sapply(seq(1,size, by=1), function(x) F.y1m1(1,2,3,x) )
y1100 <- sapply(seq(1,size, by=1), function(x) F.y1m1(4,2,3,x) )
y1010 <- sapply(seq(1,size, by=1), function(x) F.y1m1(1,5,3,x) )
y1001 <- sapply(seq(1,size, by=1), function(x) F.y1m1(1,2,6,x) )
y1110 <- sapply(seq(1,size, by=1), function(x) F.y1m1(4,5,3,x) )
y1101 <- sapply(seq(1,size, by=1), function(x) F.y1m1(4,2,6,x) )
y1011 <- sapply(seq(1,size, by=1), function(x) F.y1m1(1,5,6,x) )
y1111 <- sapply(seq(1,size, by=1), function(x) F.y1m1(4,5,6,x) )
y0000 <- sapply(seq(1,size, by=1), function(x) F.y0m0(1,2,3,x) )
#----- Causal Effects
TE <- mean(y1111, na=TRUE) - mean(y0000, na=TRUE)
JNIE123 <- mean(y1111, na=TRUE) - mean(y1000, na=TRUE)
NDE <- mean(y1000, na=TRUE) - mean(y0000, na=TRUE)
NIE1 <- mean(y1111, na=TRUE) - mean(y1011, na=TRUE)
NIE2 <- mean(y1111, na=TRUE) - mean(y1101, na=TRUE)
NIE3 <- mean(y1111, na=TRUE) - mean(y1110, na=TRUE)
JNIE12 <- mean(y1111, na=TRUE) - mean(y1001, na=TRUE)
JNIE23 <- mean(y1111, na=TRUE) - mean(y1100, na=TRUE)
JNIE13 <- mean(y1111, na=TRUE) - mean(y1010, na=TRUE)
return(c(TE, JNIE123, NDE, NIE1, NIE2, NIE3, JNIE12, JNIE23, JNIE13))
}
result<-foreach(temp = 1:n.iter, .combine = rbind) %dopar% main(temp)
save(result, file="result_MediationEffects.RData")
stopCluster(cl)