##################################################################################
# This code replicates the Monte Carlo simulations when GX is not observed and #
# the network is estimated using latent space model with ARD (section 3.1). #
#####################################Headline#####################################
rm(list = ls())
library(doParallel) # To run the Monte Carlo in parallel
library(foreach) # To run the Monte Carlo in parallel
library(doRNG) # To run the Monte Carlo in parallel
##################################################################################
# our summary function
our.sum <- function(x) {
out <- c(mean(x, na.rm = TRUE),
sd(x, na.rm = TRUE),
quantile(x, 0.25, na.rm = TRUE),
median(x, na.rm = TRUE),
quantile(x, 0.75, na.rm = TRUE))
names(out) <- c("Mean", "Sd.", "1st Qu.", "Median", "3rd Qu.")
return(out)
}
# function to perform the simulation
# l stands for the l-th simulation
# kappa is the concentration parameter
f.mc <- function(l, kappa){
M <- 20 # Number of groups
N <- rep(250,M) # Group size
# Parameters
genzeta <- 1.5
mu <- -1.25
sigma <- 0.37
K <- 12
P <- 3
beta <- c(2,1,1.5)
gamma <- c(5,-3)
alpha <- 0.4
se <- 1
# Some useful variables
W <- Y1 <- Y2 <- X <- GY1 <- GY2 <- GX <- GY1c <- GY2c <- GX1c <- list(M)
G2X1c <- GX1c0 <- G2X1c0 <- indexall <- GX2c <- G2X2c <-GX2c0 <- G2X2c0 <- ldistr <- list(M)
#loop over group to estimate dnetwork
for (m in 1:M) {
distr <- NULL
while(is.null(distr)){try({
#1- Generate z
genz <- rvMF(N[m], kappa*rvMF(1, rep(0, P)))
#2- Genetate nu from a Normal distribution with parameters mu and sigma
gennu <- rnorm(N[m], mu, sigma)
#3- Generate a graph G
#Before, let's compute d
gend <- N[m] * exp(gennu) * exp(mu + 0.5 * sigma ^ 2) * exp(logCpvMF(P, 0) - logCpvMF(P, genzeta))
#Link probabilities
Probabilities <- sim.dnetwork(nu = gennu, d = gend, zeta = genzeta, z = genz)
#The complete graph
G <- sim.network(Probabilities)
#4a Generate vk
genv <- rvMF(K, rep(0, P))
#fix some vk distant
genv[1, ] <- c(1, 0, 0)
genv[2, ] <- c(0, 1, 0)
genv[3, ] <- c(0, 0, 1)
#4b set eta
geneta <- abs(rnorm(K, 4, 1))
#4c Build Features matrix
densityatz <- matrix(0, N[m], K)
for (k in 1:K) {
densityatz[, k] <- dvMF(genz, genv[k, ] * geneta[k])
}
trait <- matrix(0, N[m], K)
NK <- floor(runif(K, 0.8, 0.95) * colSums(densityatz) / unlist(lapply(1:K, function(w){max(densityatz[,w])})))
for (k in 1:K) {
trait[,k] <- rbinom(N[m], 1, NK[k] * densityatz[,k] / sum(densityatz[,k]))
}
#5 contruct ADR
ARD <- G %*% trait
#Estimate the network distribution
distr <- accel_nuclear_gradient(inputs = t(trait), outputs = t(ARD), lambda = 600); ldistr[[m]] <- distr
})}
#True network row normalized
W[[m]] <- norm.network(G)
#Covariates
X[[m]] <- cbind(rnorm(N[m],0,5),rpois(N[m],6))
#True GX
GX[[m]] <- W[[m]] %*% X[[m]]
#Y for section with contextual effects
Y2[[m]] <- solve(diag(N[m]) - alpha * W[[m]], cbind(rep(1, N[m]), X[[m]]) %*% beta + GX[[m]] %*% gamma + rnorm(N[m], 0, se))
GY2[[m]] <- W[[m]] %*% Y2[[m]]
}
# Concatenate M groups data
# Y
Y2all <- do.call("c", lapply(1:M, function(x) Y2[[x]]))
# GY observed
GY2all <- do.call("c", lapply(1:M, function(x) GY2[[x]]))
# X
Xall <- do.call(rbind, lapply(1:M, function(x) X[[x]]))
# Compute W
dG <- sim.network(ldistr, normalise = TRUE)
dGXall <- peer.avg(dG, Xall)
dGdGXall <- peer.avg(dG, dGXall)
W <- solve(crossprod(cbind(1, Xall, dGXall, dGdGXall))/sum(N))
# #GY is observed and GX is not observed
# #smm
# sest2.3 <- smmSAR(Y2all ~ Xall | GY2all, dnetwork = ldistr, iv.power = 2L, W = W, smm.ctr = list(R = 15, S = 15),
# fixed.effects = F, contextual = T)$estimates
# lest2.3 <- c(sest2.3[-1], sest2.3[1])
#GY is not observed and GX is not observed
#smm
sest2.4 <- smmSAR(Y2all ~ Xall, dnetwork = ldistr, iv.power = 2L, W = W, smm.ctr = list(R = 500),
fixed.effects = F, contextual = T)$estimates
out <- c(sest2.4[-1], sest2.4[1])
cat(paste0(Sys.time(), " -- Iteration :", l), "\n")
print(out)
out
}
# Number of simulation
iteration <- 500
kappa <- c(0, 15, 30, 50)
n.kappa <- length(kappa)
#######
set.seed(123)
out.mc <- list()
for (x in n.kappa:1) {
# Construct cluster
cl <- makeCluster(6L)
# After the function is run, close the cluster.
on.exit(stopCluster(cl))
# Register parallel backend
registerDoParallel(cl)
fn <- paste0("log.kappa=", kappa[x], ".txt")
if (file.exists(fn)) {file.remove(fn)}
out.mc[[x]] <- foreach(l = 1:iteration, .combine = rbind, .packages = c("nuclearARD", "AER", "PartialNetwork")) %dorng%
{sink(fn, append = TRUE); outx <- f.mc(l, kappa = kappa[x]); sink(); outx}
save(out.mc, file = "mc.gx_unobserved_Alidaee.Rda")
}
# the colnames
c10 <- paste0("Wit Con - GY notobs GX notobs - SMM ", c("Intercept", paste0("X", 1:2), paste0("GX", 1:2), "alpha"))
# summary for all simulation using ARD
results <- lapply(1:n.kappa, function(x) {
colnames(out.mc[[x]]) <- c10
t(apply(out.mc[[x]], 2, our.sum))})
print(results[[1]])
print(results[[2]])
print(results[[3]])
print(results[[4]])
for (x in 1:n.kappa) {
write.csv(results[[x]], file = paste0("~/Dropbox/Papers - In progress/Partial Network/Simulations/Monte Carlo/Results/Gx_unobserved_Alidaee_kappa=", kappa[x], ".csv"))
}
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