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pps-synrep.R
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pps-synrep.R
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## Simulation from PPS
library(rstan)
library(Matrix)
library(survival)
library(polyapost)
library(StanHeaders)
library(doParallel)
library(foreach)
library(tidyverse)
library(polyapost)
library(kableExtra)
library(LaplacesDemon)
library(sampling)
library(pps)
library(survey)
library(PracTools)
library(haven)
library(gridExtra)
rstan_options(auto_write = TRUE)
options(mc.cores = parallel::detectCores())
wlm_posterior <- stan_model('wgtlikelihood.stan')
acs_w = readRDS("ACS2021_w.RDS")
syn_boot = function(M, R){
n=500
L = 1
c <- 50
run_num <- 1000
runs <- list(qboot = matrix(NA, run_num, 3), #naive estimate from sample not accounting for weights
qbootvar = matrix(NA, run_num, 3), #variance estimate for naive estimate from sample not accounting for weights
htboot = matrix(NA, run_num, 3), #design-based estimate from sample
htbootvar = matrix(NA, run_num, 3), #design-based estimate from sample
qsyn = matrix(NA, run_num, 3), #estimate from synthetic data generated from original sample
qsynvar = matrix(NA, run_num, 3), #variance estimate for qsyn
wtreg = matrix(NA, run_num, 3), #estimate from weighted likelihood
wtregvar = matrix(NA, run_num, 3), #variance estimate for weighted lkl estimate
Qbar = matrix(NA, run_num, 3), #pop level Q est
qbar = matrix(NA, run_num, 3), #synth level Q est
qbar_rep = matrix(NA, run_num, 3), #rep level Q est
qbar_rep_1 = matrix(NA, run_num, 3), # R=1 rep
Bm = matrix(NA, run_num, 3), #pop level Bm est
bm = matrix(NA, run_num, 3), #synth level bm est
Bm_rep = matrix(NA, run_num, 3), #rep level Bm est
Bm_rep_1 = matrix(NA, run_num, 3), #R=1 rep level Bm est
vbar = matrix(NA, run_num, 3), #synth level vbar
vbar_rep = matrix(NA, run_num, 3), #rep level vbar
vbar_rep_1 = matrix(NA, run_num, 3), #R=1 rep vbar
bm_rep = matrix(NA, run_num, 3), #rep level bm (var between qlbar's and qbar)
bm_rep_1 = matrix(NA, run_num, 3), #R=1 rep level bm (var between qlbar's and qbar)
wbar = matrix(NA, run_num, 3), #mean of wl's
Qvar = matrix(NA, run_num, 3), #pop level Qvar est
Tm = matrix(NA, run_num, 3), #synth level Qvar est
Tm_rep = matrix(NA, run_num, 3), #rep level Qvar est
Tm_rep_1 = matrix(NA, run_num, 3), #R=1 rep level Qvar est
Tm_0 = matrix(NA, run_num, 3), #possible negative var synthe level Qvar est
Tm_rep_0 = matrix(NA, run_num, 3), #rep level Qvar est
Tm_rep_1_0 = matrix(NA, run_num, 3), #R=1 rep level Qvar est
Tm_wtreg_rep = matrix(NA, run_num, 3), #rep weighted Qvar est
result_pop = matrix(NA, run_num, 3),
result_synth = matrix(NA, run_num, 3),
result_rep = matrix(NA, run_num, 3),
result_rep_1 = matrix(NA, run_num, 3),
results_srs = matrix(NA, run_num, 3),
result_ht = matrix(NA, run_num, 3),
result_srssyn = matrix(NA, run_num, 3),
result_wtreg = matrix(NA, run_num, 3),
result_wtreg_rep = matrix(NA, run_num, 3),
wtreg_rep = matrix(NA, run_num, 3),
wtregvar_rep = matrix(NA, run_num, 3)
)
N = length(acs_w)
population <- data.frame(index = c(1:N),
W = acs_w,
X = rep(NA, N),
Y = rep(NA, N),
p = rep(NA, N))
beta1 = 20; beta2=50; sigma=50 #
population$X <- rbinom(N, 1, exp(-7+2*log(population$W))/(1+exp(-7+2*log(population$W)))) #depend on W
population$Y <- rnorm(N, beta1 + beta2*population$X, sigma)
population$p <- sampling::inclusionprobabilities(population$W, n)
population$wts <- 1/sampling::inclusionprobabilities(population$W, n)
true_val <- c(mean(population$X), mean(population$Y), beta2)
for (j in seq(1:run_num)) {
#take sample pps
orig_sample <- population[pps::ppss(population$W, n),]
orig_sample$wts <- N*orig_sample$wts/sum(orig_sample$wts)
#record sample non-design-based estimate
lm_ori_reg = summary(lm(Y ~ X, data = orig_sample))
runs$qboot[j,] = c(mean(orig_sample$X), mean(orig_sample$Y), lm_ori_reg$coef[2,1])
runs$qbootvar[j,] = c(mean(orig_sample$X)*(1-mean(orig_sample$X))/n, var(orig_sample$Y)/n, (lm_ori_reg$coef[2,2])^2)
#record design-based estimate
dsgn <- svydesign(ids=~1, data = orig_sample, weights =~wts)
htmean_y <- svymean(~Y, dsgn)
htmean_x <- svymean(~X, dsgn)
wt_svyglm = summary(svyglm(Y ~ X, dsgn))
runs$htboot[j,] = c(coef(htmean_x), coef(htmean_y), wt_svyglm$coef[2,1])
runs$htbootvar[j,] = c(SE(htmean_x)^2, SE(htmean_y)^2, (wt_svyglm$coef[2,2])^2)
#simulate from original sample and take mean
simple_synth_x <- rbinom(n, 1, mean(orig_sample$X))
simple_synth_y <- rnorm(n) * lm_ori_reg$sigma + lm_ori_reg$coef[1,1] + lm_ori_reg$coef[2,1] * simple_synth_x
runs$qsyn[j,] = c(mean(simple_synth_x), mean(simple_synth_y), lm_ori_reg$coef[2,1])
runs$qsynvar[j,] = c(mean(simple_synth_x) *(1-mean(simple_synth_x))/n, var(simple_synth_y)/n, (lm_ori_reg$coef[2,2])^2)
### pseudo-likelihood
stan_data_LW <- list(
n = n,
n_pred = n,
y = as.vector(orig_sample$Y),
x = as.vector(orig_sample$X),
weights = as.vector(orig_sample$wts)
)
sim_est_LW <- sampling(
object = wlm_posterior,
data = stan_data_LW,
chains = 4,
iter = 4000, warmup = 2000, thin = 5,
verbose = FALSE, refresh=0
)
posterior_samples <- rstan::extract(sim_est_LW, permuted = TRUE)
runs$wtreg[j,] = c(mean(posterior_samples$q_x)/n, mean(posterior_samples$q_y),mean(posterior_samples$beta2))
runs$wtregvar[j,] = c(var(posterior_samples$q_x)/n/n, var(posterior_samples$q_y), var(posterior_samples$beta2))
### Bootstrap
####
synth_samples <- list(Q_y = rep(NA, M),
synth_q_y = rep(NA, M),
synth_v_y = rep(NA,M),
Q_x = rep(NA, M),
synth_q_x = rep(NA, M),
synth_v_x = rep(NA,M),
Q_beta = rep(NA, M),
synth_q_beta = rep(NA, M),
synth_v_beta = rep(NA,M),
wtreg_boot = matrix(NA, nrow = M, ncol=3),
wtregvar_boot = matrix(NA, nrow = M, ncol=3),
rep_y = matrix(data = NA, nrow = M, ncol = R),
rep_v_y = matrix(data = NA, nrow = M, ncol = R),
rep_x = matrix(data = NA, nrow = M, ncol = R),
rep_v_x = matrix(data = NA, nrow = M, ncol = R),
rep_beta = matrix(data = NA, nrow = M, ncol = R),
rep_v_beta = matrix(data = NA, nrow = M, ncol = R)
)
####
dsgn.rw <- as.svrepdesign(design=dsgn, type="subbootstrap",replicates=M)
repwt <- as.matrix(dsgn.rw$repweights)
########
for (i in seq(1:M)) {
#create bootstrap sample for obtaining weights and then create population
n_synth <- n
wts <- repwt[,i]*orig_sample$wts
wtind <- wts!=0
wts <- wts[wtind]
polya_ind <- (1:n)[wtind]
wts <- (c*n)*(wts/sum(wts))
bootsamp_size <- length(wts)
### pseudo-likelihood
stan_data_boot <- list(
n = bootsamp_size,
n_pred = n,
y = unlist(subset(orig_sample[polya_ind,], select = "Y")),
x = unlist(subset(orig_sample[polya_ind,], select = "X")),
weights = wts
)
sim_est_boot <- sampling(
object = wlm_posterior,
data = stan_data_boot,
chains = 4,
iter = 4000, warmup = 2000, thin = 5,
#control = list(adapt_delta = 0.8, max_treedepth = 10),
verbose = FALSE, refresh=0
)
posterior_samples_boot <- rstan::extract(sim_est_boot, permuted = TRUE)
# plot(posterior_samples$beta2)
synth_samples$wtreg_boot[i,] = c(mean(posterior_samples_boot$q_x)/n, mean(posterior_samples_boot$q_y),mean(posterior_samples_boot$beta2))
synth_samples$wtregvar_boot[i,] = c(var(posterior_samples_boot$q_x)/n/n, var(posterior_samples_boot$q_y), var(posterior_samples_boot$beta2))
###
synpop <- integer()
for (l in seq(1:L)) {
pop_synth <- c(polyapost::wtpolyap(polya_ind, wts, c*n - bootsamp_size))
synpop <- c(synpop, pop_synth)
}
sample_synth <- sample(synpop, n_synth) #srs from psedo-pop
#calculate relevant quantities
synth_samples$Q_y[[i]] <- apply(orig_sample[synpop,] %>% select(Y), 2, mean)
synth_samples$synth_q_y[[i]] <- q_l <- apply(orig_sample[sample_synth,] %>% select(Y), 2, mean)
synth_samples$synth_v_y[[i]] <- v_l <- (1-n_synth/(c*n*L))*apply(orig_sample[sample_synth,] %>% select(Y), 2, var)/n_synth
synth_samples$Q_x[[i]] <- apply(orig_sample[synpop,] %>% select(X), 2, mean)
synth_samples$synth_q_x[[i]] <- q_l_x<- apply(orig_sample[sample_synth,] %>% select(X), 2, mean)
synth_samples$synth_v_x[[i]] <- v_l_x <- (1-n_synth/(c*n*L))*q_l_x * (1 - q_l_x)/n_synth
synth_samples$Q_beta[[i]] <- summary(lm(Y ~ X, orig_sample[synpop,]))$coef[2,1]
synth_samples$V_beta[[i]] <- (summary(lm(Y ~ X, orig_sample[synpop,]))$coef[2,2]) ^ 2
lm_srs_reg = summary(lm(Y ~ X, orig_sample[sample_synth,]))
synth_samples$synth_q_beta[[i]] <- lm_srs_reg$coef[2,1]
synth_samples$synth_v_beta[[i]] <- (lm_srs_reg$coef[2,2]) ^ 2
#model synthetic dataset
for (k in seq(1:R)) {
rep_x = rbinom(n_synth, 1, q_l_x)
rep_y = rnorm(n_synth) * lm_srs_reg$sigma + lm_srs_reg$coef[1,1] + lm_srs_reg$coef[2,1] * rep_x
synth_samples$rep_y[i, k] <- mean(rep_y)
synth_samples$rep_v_y[i, k] <- (1-n_synth/(c*n*L))*var(rep_y)/n_synth #(mean(apply(PPD_samples$syn_y,1, var)))/n_synth
synth_samples$rep_x[i, k] <- mean(rep_x)
synth_samples$rep_v_x[i, k] <- (1-n_synth/(c*n*L))*mean(rep_x)*(1-mean(rep_x))/n_synth
synth_samples$rep_beta[i, k] = summary(lm(rep_y~rep_x))$coef[2,1]
synth_samples$rep_v_beta[i, k] = (summary(lm(rep_y~rep_x))$coef[2,2]) ^ 2
}
}
#store information
Q <- cbind(synth_samples$Q_x,synth_samples$Q_y,synth_samples$Q_beta)
q <- cbind(synth_samples$synth_q_x, synth_samples$synth_q_y, synth_samples$synth_q_beta)
v <- cbind(synth_samples$synth_v_x, synth_samples$synth_v_y,synth_samples$synth_v_beta)
##
runs$wtreg_rep[j,] = apply(synth_samples$wtreg_boot, 2, mean)
runs$wtregvar_rep[j,] = apply(synth_samples$wtregvar_boot, 2, mean)
runs$Qbar[j,] <- Qbar <- apply(Q,2,mean)
runs$qbar[j,] <- qbar <- apply(q, 2, mean)
runs$vbar[j,] <- vbar <- apply(v, 2, mean)
runs$qbar_rep[j,] <- qbar_rep <- c(mean(synth_samples$rep_x), mean(synth_samples$rep_y), mean(synth_samples$rep_beta))
runs$vbar_rep[j,] <- vbar_rep <- c(mean(synth_samples$rep_v_x), mean(synth_samples$rep_v_y), mean(synth_samples$rep_v_beta))
ql_bar <- cbind(apply(synth_samples$rep_x,1,mean), apply(synth_samples$rep_y,1,mean), apply(synth_samples$rep_beta,1,mean))
wbar <- cbind(mean(apply(synth_samples$rep_x,1,var)), mean(apply(synth_samples$rep_y,1,var)), mean(apply(synth_samples$rep_beta,1,var)))
#R=1
q_rep_1 <- cbind(synth_samples$rep_x[,R], synth_samples$rep_y[,R], synth_samples$rep_beta[,R])
v_rep_1 <- cbind(synth_samples$rep_v_x[,R], synth_samples$rep_v_y[,R], synth_samples$rep_v_beta[,R])
runs$qbar_rep_1[j,] <- qbar_rep_1 <- c(mean(synth_samples$rep_x[,R]), mean(synth_samples$rep_y[,R]), mean(synth_samples$rep_beta[,R]))
runs$vbar_rep_1[j,] <- vbar_rep_1 <- c(mean(synth_samples$rep_v_x[,R]), mean(synth_samples$rep_v_y[,R]), mean(synth_samples$rep_v_beta[,R]))
#compute parameters for posterior from pop level estimates
for (tt in 1:3){
runs$Bm[j,tt] <- Bm <- (1/(M-1))*sum((Qbar[tt] - Q[,tt])^2)
runs$Qvar[j, tt] <- (1 + (1/M))*Bm
#compute parameters for approx posterior from sample level estimates
runs$bm[j,tt] <- bm <- sum((q[, tt]-qbar[tt])^2)/(M-1)
runs$Tm[j,tt] <- tm <- if_else((1 + (1/M))*bm - vbar[tt] <= 0,
(1 + (2/M))*vbar[tt],
(1 + (1/M))*bm - vbar[tt])
runs$Tm_0[j,tt] = (1 + (1/M))*bm - vbar[tt]
runs$Tm_wtreg_rep[j,tt] = if_else((1 + (1/M))*var(runs$wtreg_rep[j,tt] - synth_samples$wtreg_boot[,tt]) - runs$wtregvar_rep[j,tt] <=0,
(1 + (2/M))*runs$wtregvar_rep[j,tt],
(1 + (1/M))*var(runs$wtreg_rep[j,tt] - synth_samples$wtreg_boot[,tt]) - runs$wtregvar_rep[j,tt])
#compute parameters for approx posterior from replicate sample estimates
runs$bm_rep[j,tt] <- bm_rep <- sum((ql_bar[,tt] - qbar_rep[tt])^2)/(M-1)
runs$wbar[j,tt] <- wbar[tt]
runs$Bm_rep[j,tt] <- Bm_rep <- bm_rep - vbar_rep[tt] - wbar[tt]/R
runs$Tm_rep[j,tt] <- tm_rep <- if_else(((1/M) + 1)*bm_rep - vbar_rep[tt] - wbar[tt]/R <= 0,
(1 + (2/M))*vbar_rep[tt] + (1/(R*M))*wbar[tt],
((1/M) + 1)*bm_rep - vbar_rep[tt] - wbar[tt]/R)
runs$Tm_rep_0[j,tt] <- ((1/M) + 1)*bm_rep - vbar_rep[tt] - wbar[tt]/R
#R=1
runs$bm_rep_1[j,tt] <- bm_rep_1 <- var(q_rep_1[,tt])
runs$Bm_rep_1[j,tt] <- Bm_rep_1 <- bm_rep_1 - 2*vbar_rep_1[tt]
runs$Tm_rep_1_0[j,tt] <- ((1/M) + 1)*bm_rep_1 - 2*vbar_rep_1[tt]
runs$Tm_rep_1[j,tt] <- tm_rep_1 <- if_else(((1/M) + 1)*bm_rep_1 - 2*vbar_rep_1[tt] <= 0,
(1 + (3/M))*vbar_rep_1[tt],
((1/M) + 1)*bm_rep_1 - 2*vbar_rep_1[tt])
}
ci_pop <- cbind(qt(0.025, M-1) *sqrt(runs$Qvar[j,]) + runs$Qbar[j,], qt(0.975, M-1) *sqrt(runs$Qvar[j,]) + runs$Qbar[j,])
ci_synth <- cbind(qt(0.025, M-1) *sqrt(runs$Tm[j,]) + runs$qbar[j,], qt(0.975, M-1) *sqrt(runs$Tm[j,]) + runs$qbar[j,])
ci_rep <- cbind(qt(0.025, M-1) *sqrt(runs$Tm_rep[j,]) + runs$qbar_rep[j,], qt(0.975, M-1) *sqrt(runs$Tm_rep[j,]) + runs$qbar_rep[j,])
ci_rep_1 <- cbind(qt(0.025, M-1) *sqrt(runs$Tm_rep_1[j,]) + runs$qbar_rep_1[j,], qt(0.975, M-1) *sqrt(runs$Tm_rep_1[j,]) + runs$qbar_rep_1[j,])
ci_srs <- cbind(qt(0.025, M-1) *sqrt(runs$qbootvar[j,]) + runs$qboot[j,], qt(0.975, M-1) *sqrt(runs$qbootvar[j,]) + runs$qboot[j,])
ci_ht <- cbind(qt(0.025, M-1) *sqrt(runs$htbootvar[j,]) + runs$htboot[j,], qt(0.975, M-1) *sqrt(runs$htbootvar[j,]) + runs$htboot[j,])
# ci_ht <- confint(htmean)
ci_srssyn <- cbind(qt(0.025, M-1) *sqrt(runs$qsynvar[j,]) + runs$qsyn[j,], qt(0.975, M-1) *sqrt(runs$qsynvar[j,]) + runs$qsyn[j,])
ci_wtreg <- cbind(qt(0.025, M-1) *sqrt(runs$wtregvar[j,]) + runs$wtreg[j,], qt(0.975, M-1) *sqrt(runs$wtregvar[j,]) + runs$wtreg[j,])
ci_wtreg_rep <- cbind(qt(0.025, M-1) *sqrt(runs$Tm_wtreg_rep[j,]) + runs$wtreg_rep[j,], qt(0.975, M-1) *sqrt(runs$Tm_wtreg_rep[j,]) + runs$wtreg_rep[j,])
for (tt in 1:3){
runs$result_pop[j, tt] <- if_else(ci_pop[tt,1] <= true_val[tt] & true_val[tt] <= ci_pop[tt,2], "T", "F")
runs$result_synth[j, tt] <- if_else(ci_synth[tt,1] <= true_val[tt] & true_val[tt] <= ci_synth[tt,2], "T", "F")
runs$result_rep[j, tt] <- if_else(ci_rep[tt,1] <= true_val[tt] & true_val[tt] <= ci_rep[tt,2], "T", "F")
runs$result_rep_1[j, tt] <- if_else(ci_rep_1[tt,1] <= true_val[tt] & true_val[tt] <= ci_rep_1[tt,2], "T", "F")
runs$result_srs[j, tt] <- if_else(ci_srs[tt,1] <= true_val[tt] & true_val[tt] <= ci_srs[tt,2], "T", "F")
runs$result_ht[j, tt] <- if_else(ci_ht[tt,1] <= true_val[tt] & true_val[tt] <= ci_ht[tt,2], "T", "F")
runs$result_srssyn[j, tt] <- if_else(ci_srssyn[tt,1] <= true_val[tt] & true_val[tt] <= ci_srssyn[tt,2], "T", "F")
runs$result_wtreg[j, tt] <- if_else(ci_wtreg[tt,1] <= true_val[tt] & true_val[tt] <= ci_wtreg[tt,2], "T", "F")
runs$result_wtreg_rep[j, tt] <- if_else(ci_wtreg_rep[tt,1] <= true_val[tt] & true_val[tt] <= ci_wtreg_rep[tt,2], "T", "F")
}
print(j)
}
output = NULL
for (tt in 1:3){
results <- data.frame(Method = c("Direct","HT", "SRSsyn", "Pseudo-Pop", "Pseudo-SRS", "SynRep-R", "SynRep-R-PPD", "SynRep-1","Wtreg","Wtreg-BS"),
QEst_bias = c(mean(runs$qboot[,tt]), mean(runs$htboot[,tt]), mean(runs$qsyn[,tt]), mean(runs$Qbar[,tt]), mean(runs$qbar[,tt]), mean(runs$qbar_rep[,tt]),mean(runs$qbar_rep_1[,tt]), mean(runs$wtreg[,tt]),mean(runs$wtreg_rep[,tt])) - true_val[tt],
QEst_bias_relpct = (c(mean(runs$qboot[,tt]), mean(runs$htboot[,tt]), mean(runs$qsyn[,tt]), mean(runs$Qbar[,tt]), mean(runs$qbar[,tt]), mean(runs$qbar_rep[,tt]), mean(runs$qbar_rep_1[,tt]), mean(runs$wtreg[,tt]),mean(runs$wtreg_rep[,tt])) - true_val[tt])/true_val[tt] * 100,
VarEst = c(mean(runs$qbootvar[,tt]), mean(runs$htbootvar[,tt]), mean(runs$qsynvar[,tt]), mean(runs$Qvar[,tt]), mean(runs$Tm[,tt]), mean(runs$Tm_rep[,tt]), mean(runs$Tm_rep_1[,tt]), mean(runs$wtregvar[,tt]), mean(runs$Tm_wtreg_rep[,tt])),
VarComp = c(var(runs$qboot[,tt]), var(runs$htboot[,tt]), var(runs$qsyn[,tt]), var(runs$Qbar[,tt]), var(runs$qbar[,tt]), var(runs$qbar_rep[,tt]), var(runs$qbar_rep_1[,tt]), var(runs$wtreg[,tt]),var(runs$wtreg_rep[,tt])),
Var_sd = c(sd(runs$qbootvar[,tt]), sd(runs$htbootvar[,tt]), sd(runs$qsynvar[,tt]), sd(runs$Qvar[,tt]), sd(runs$Tm[,tt]), sd(runs$Tm_rep[,tt]), sd(runs$Tm_rep_1[,tt]), sd(runs$wtregvar[,tt]), sd(runs$Tm_wtreg_rep[,tt]))
)
results = results %>% mutate(Var_r = VarEst/VarComp,
Var_r_dir = VarComp /var(runs$qboot[,tt]),
Var_r_ht = VarComp /var(runs$htboot[,tt]),
Var_r_srs = VarComp /var(runs$qsyn[,tt]),
VarEst_raw = c(mean(runs$qbootvar[,tt]), mean(runs$htbootvar[,tt]), mean(runs$qsynvar[,tt]), mean(runs$Qvar[,tt]), mean(runs$Tm_0[,tt]), mean(runs$Tm_rep_0[,tt]), mean(runs$Tm_rep_1_0[,tt]), mean(runs$wtregvar[,tt]), mean(runs$Tm_wtreg_rep[,tt])),
Var_r_raw = VarEst_raw/VarComp)
ci_results <- data.frame(Method = c("Direct","HT", "SRSsyn", "Pseudo-Pop", "Pseudo-SRS", "SynRep-R", "SynRep-R-PPD", "SynRep-1","Wtreg","Wtreg-BS"),
Contained = c(mean(runs$result_srs[, tt] == "T"),
mean(runs$result_ht[, tt] == "T"),
mean(runs$result_srssyn[, tt] == "T"),
mean(runs$result_pop[, tt] == "T"),
mean(runs$result_synth[, tt] == "T"),
mean(runs$result_rep[, tt] == "T"),
mean(runs$result_rep_1[, tt] == "T"),
mean(runs$result_wtreg[, tt] == "T"),
mean(runs$result_wtreg_rep[, tt] == "T")),
Contained_raw = c(mean(runs$result_srs[runs$qbootvar[, tt] > 0, tt]== "T"),
mean(runs$result_ht[runs$htbootvar[, tt] > 0, tt]== "T"),
mean(runs$result_srssyn[runs$qsynvar[, tt] > 0, tt]== "T"),
mean(runs$result_pop[runs$Qvar[, tt] > 0, tt]== "T"),
mean(runs$result_synth[runs$Tm_0[, tt] > 0, tt]== "T"),
mean(runs$result_rep[runs$Tm_rep_0[, tt] > 0, tt]== "T"),
mean(runs$result_rep_1[runs$Tm_rep_1_0[, tt] > 0, tt]== "T"),
mean(runs$result_wtreg[runs$wtregvar[, tt] > 0, tt] == "T"),
mean(runs$result_wtreg_rep[runs$Tm_wtreg_rep[, tt] >0, tt] == "T")),
prop_neg =c(mean(runs$qbootvar[, tt]<0), mean(runs$htbootvar[, tt]<0), mean(runs$qsynvar[, tt]<0), mean(runs$Qvar[, tt]<0), mean(runs$Tm_0[, tt]<0), mean(runs$Tm_rep_0[, tt]<0), mean(runs$Tm_rep_1_0[, tt]<0), mean(runs$wtregvar[,tt]<0),mean(runs$Tm_wtreg_rep[,tt]<0))
)
output[[tt]] = list(tt, results,ci_results)
}
return(output)
}