This introduction has three purposes:
Describes the functions and structures included with
drcarlate.
Show how to use the functions in drcarlate for
numerical simulation to get results similar to those in Jiang et
al.(2022).
Provides an example of research using
drcarlate.
There are six families of functions in drcarlate:
Data generation: these functions provide a way to generate random data according to the three DGPs in Jiang et al.(2022).
Statistics calculation: these functions are used to calculate the statistics and the LATE used in Jiang et al.(2022).
Estimation strategy: these functions provide a method for estimating treatment effects according to the three estimation strategies including L, NL and R presented in Jiang et al.(2022).
Output function: this function integrates the functions of the above three types of functions and provides a means of output results.
JLTZ function: this function calls all of the above functions and helps the user reproduce the results of the data simulation section of Jiang et al.(2022).
ATE functions: these functions are based on some of the above functions, focusing on calculating average treatment effect(ATE) under the full compliance condition, one characteristic of these functions is that they begin with the ATE prefix.
This section contains two functions, FuncDGP and
CovAdptRnd:
FuncDGP allows users to generate the corresponding
data using the three algorithms declared in the data generation process
in Jiang et al.(2022).
CovadptRnd provides four CAR schemes proposed in
Jiang et al.(2022).
Combined with the above two functions, users can generate 3 x 4 = 12 sets of data.
# Parameter dgpflag declares three ways to generate random data.
# FuncDGP will generate random data according to the method specified in (i), (ii) or (iii) when dgpflag = 1, 2 or 3 respectively.
# Parameter rndflag declares four ways to randomly assign treatment effects.
# rndflag = 1 - SRS; rndflag = 2 - WEI; rndflag = 3 - BCD; rndflag = 4 - SBR
# Note that CovadpRnd is built into FuncDGP, so it is not necessary to use CovadpRnd alone in the actual operation of generating random data
# Let's take dgpflag=1 and rndflag=2 for example
random_dgp <- FuncDGP(dgptype = 1, rndflag = 2, n = 100, g = 4, pi = c(0.5, 0.5, 0.5, 0.5))
# We can see that the return value of FuncDGP is a list of nine matrices, We can easily extract what we need from it
Y <- random_dgp$Y
X <- random_dgp$X
S <- random_dgp$S
A <- random_dgp$A
Y1 <- random_dgp$Y1
Y0 <- random_dgp$Y0
D1 <- random_dgp$D1
D0 <- random_dgp$D0
D <- random_dgp$DThis section contains four functions including
TrueValue, pihat, tau and
stanE.
pihat, tau and stanE computes
estimated treatment assignment probabilities, LATE and standard
deviation respectively, see Jiang et al.(2022) for more details.# compute estimated LATE
tauhat <- tau(muY1 = Y1, muY0 = Y0, muD1 = D1, muD0 = D0, A = A, S = S, Y = Y, D = D)
#compute estimated treatment assignment probabilities
pihat(A = A, S = S)
#> [,1]
#> [1,] 0.4615385
#> [2,] 0.5600000
#> [3,] 0.4117647
#> [4,] 0.5600000
#> [5,] 0.5000000
#> [6,] 0.5000000
#> [7,] 0.5000000
#> [8,] 0.5000000
#> [9,] 0.5000000
#> [10,] 0.4615385
#> [11,] 0.4615385
#> [12,] 0.5600000
#> [13,] 0.4615385
#> [14,] 0.5600000
#> [15,] 0.4615385
#> [16,] 0.5000000
#> [17,] 0.5000000
#> [18,] 0.5600000
#> [19,] 0.4117647
#> [20,] 0.5600000
#> [21,] 0.4117647
#> [22,] 0.4117647
#> [23,] 0.5600000
#> [24,] 0.5000000
#> [25,] 0.5600000
#> [26,] 0.5600000
#> [27,] 0.5600000
#> [28,] 0.4615385
#> [29,] 0.5600000
#> [30,] 0.5600000
#> [31,] 0.4615385
#> [32,] 0.4117647
#> [33,] 0.5600000
#> [34,] 0.4117647
#> [35,] 0.5000000
#> [36,] 0.5600000
#> [37,] 0.4615385
#> [38,] 0.4117647
#> [39,] 0.4117647
#> [40,] 0.4615385
#> [41,] 0.5600000
#> [42,] 0.5000000
#> [43,] 0.5600000
#> [44,] 0.4117647
#> [45,] 0.4615385
#> [46,] 0.5000000
#> [47,] 0.5000000
#> [48,] 0.4615385
#> [49,] 0.4615385
#> [50,] 0.4615385
#> [51,] 0.4615385
#> [52,] 0.4615385
#> [53,] 0.5000000
#> [54,] 0.4615385
#> [55,] 0.5000000
#> [56,] 0.5000000
#> [57,] 0.5000000
#> [58,] 0.4615385
#> [59,] 0.5600000
#> [60,] 0.4615385
#> [61,] 0.4615385
#> [62,] 0.5000000
#> [63,] 0.5000000
#> [64,] 0.4615385
#> [65,] 0.4117647
#> [66,] 0.5000000
#> [67,] 0.4117647
#> [68,] 0.5000000
#> [69,] 0.4615385
#> [70,] 0.5000000
#> [71,] 0.5000000
#> [72,] 0.5600000
#> [73,] 0.4117647
#> [74,] 0.5600000
#> [75,] 0.4117647
#> [76,] 0.5000000
#> [77,] 0.5600000
#> [78,] 0.5600000
#> [79,] 0.5000000
#> [80,] 0.4615385
#> [81,] 0.5600000
#> [82,] 0.5000000
#> [83,] 0.5000000
#> [84,] 0.4117647
#> [85,] 0.5600000
#> [86,] 0.5000000
#> [87,] 0.4615385
#> [88,] 0.4117647
#> [89,] 0.5000000
#> [90,] 0.4615385
#> [91,] 0.5600000
#> [92,] 0.5000000
#> [93,] 0.5000000
#> [94,] 0.4615385
#> [95,] 0.4117647
#> [96,] 0.5000000
#> [97,] 0.5000000
#> [98,] 0.4615385
#> [99,] 0.4117647
#> [100,] 0.5600000
# compute estimated standard deviation
stanE(muY1 = Y1, muY0 = Y0, muD1 = D1, muD0 = D0, A = A, S = S, Y = Y, D = D, tauhat = tauhat)
#> [1] 4.418164TrueValue differs a little from the above three
functions，it calculates the LATE of all four kinds of CAR schemes
(rndflag = 1, 2, 3 and 4) under the specified DGP (dgpflag = 1, 2, or
3). So the user who runs Truevalue is supposed to get four
values at once.# let's take dgpflag = 1 for example.
true_value <- TrueValue(dgptype = 1, vIdx = 1:4, n = 100, g = 4, pi = c(0.5, 0.5, 0.5, 0.5))
true_tau <- true_value$tau# SRS - WEI - BCD - SBR
true_tau
#> [1] 0.9252152 0.9237937 0.9192154 0.9215521This section contains three functions including
LogisticReg, feasiblePostLassoMatTool and
LinearLogit.
LinearLogit provides users with three regression
estimation combination strategies: L (modelflag = 1), NP (modelflag =
2), and R (modelflag = 3), see Jiang et al.(2022) for more
details.
feasiblePostLassoMatTool is the computing engine for
function LinearLogit when modelflag = 3.
LogisticReg provides a simple way to use logistic
CDF.
# remember that we set dgpflag = 1 and rndflag = 2 before
LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 4, modelflag = 1, iridge = 0.001)
#> $theta_0s
#> [,1]
#> [1,] 0.4104139
#> [2,] 2.1014655
#>
#> $theta_1s
#> [,1]
#> [1,] -0.4238703
#> [2,] 0.7981997
#>
#> $beta_0s
#> [,1]
#> [1,] 0.10671410
#> [2,] 0.01534334
#>
#> $beta_1s
#> [,1]
#> [1,] -0.2452247
#> [2,] 0.2143404Output is the most important integration function,
which has the functions of generating random data, estimating LATE by
regression analysis based on different estimation strategies: (1) NA (2)
LP (3) LG (4) F (5) NP (6) R (when dgp = 3) (7) TSLS (8) R (when dgp = 1
or 2) and summarizing analysis results. This function is key to
generating the simulation results in Jiang et al.(2022). See the paper
for more details about all the estimation strategies.# set random seed
set.seed(1)# get true tau
true_tau <- TrueValue(dgptype = 1, vIdx = 1:4, n = 1000, g = 4, pi = c(0.5, 0.5, 0.5, 0.5))
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#> currently at 1000th sample for simulating true value# see the output: size, iPert = 0
Output(ii = 1, tau = tauhat[1], dgptype = 1, rndflag = 1, n = 1000, g = 4,
pi = c(0.5, 0.5, 0.5, 0.5),
iPert = 0, iq = 0.05, iridge = 0.001)
#> Currently at 1 th sample!
#> $vtauhat
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 1.236257 1.011659 1.014877 1.034401 1.070561 NaN 0.9797705 1.116384 NaN
#> [,10] [,11] [,12]
#> [1,] NaN NaN NaN
#>
#> $vsighat
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 14.71728 10.93291 10.97075 10.81983 9.691528 NaN 11.10584 9.792131 NaN
#> [,10] [,11] [,12]
#> [1,] NaN NaN NaN
#>
#> $vstat
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> [1,] 0.1822901 0.4042457 0.3935777 0.3420046 0.2638352 NaN 0.4887518 0.1131412
#> [,9] [,10] [,11] [,12]
#> [1,] NaN NaN NaN NaN
#>
#> $vdeci
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0 0 0 0 0 NaN 0 0 NaN NaN NaN NaN
# see the output: power, iPert = 1
Output(ii = 1, tau = tauhat[1], dgptype = 1, rndflag = 1, n = 1000, g = 4,
pi = c(0.5, 0.5, 0.5, 0.5),
iPert = 1, iq = 0.05, iridge = 0.001)
#> Currently at 1 th sample!
#> $vtauhat
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 1.848939 1.270918 1.271093 1.313234 1.036465 NaN 1.266284 1.060324 NaN
#> [,10] [,11] [,12]
#> [1,] NaN NaN NaN
#>
#> $vsighat
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 14.14772 10.91436 10.91949 10.57321 9.554213 NaN 10.48309 9.306626 NaN
#> [,10] [,11] [,12]
#> [1,] NaN NaN NaN
#>
#> $vstat
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9]
#> [1,] 0.6760993 2.551125 2.549418 2.506875 3.690303 NaN 2.670054 3.707407 NaN
#> [,10] [,11] [,12]
#> [1,] NaN NaN NaN
#>
#> $vdeci
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0 1 1 1 1 NaN 1 1 NaN NaN NaN NaNJLTZ provides users with a convenient way to reproduce
the simulation results in Jiang et al.(2022), The user only needs to set
parameters according to the corresponding DGP, sample size and Monte
Carlo simulation times in the paper, and the results consistent with
Jiang et al.(2022) can be obtained under the condition that the random
number seed is set as 1. It should be noted that because the results in
the original text are implemented in MATLAB, the results obtained by
using JLTZ are not numerically the same as those in the paper, but they
are very close.# For example, if we wanted to get the results shown in Panel A in Table 1, we could run the following two functions separately.
# First of all, There are four strata data (g = 4), the probability of data being treated at each strata is equal to 0.5 (pi = c(0.5, 0.5, 0.5, 0.5)), the random data generation process follows the data generation process 1 (DGP = 1), the total sample size is 200 (n = 200), run 10,000 Monte Carlo simulations (iMonte = 10000), the confidence level for hypothesis testing is 5%, and finally，get the size of the Monte Carlo simulation (iPert = 0).
# Time Consumeing. This command will take about 1.4 hours to execute, so do not run it unless necessary.
# JLTZ(iMonte = 10000, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 0, iq = 0.05, iridge = 0.001)
# Second of all, There are four strata data (g = 4), the probability of data being treated at each strata is equal to 0.5 (pi = c(0.5, 0.5, 0.5, 0.5)), the random data generation process follows the digital generation process 1 (DGP = 1), the total sample size was 200 (n = 200), run 10,000 Monte Carlo simulations (iMonte = 10000), the confidence level for hypothesis testing is 5%, and finally，get the power of the Monte Carlo simulation (iPert = 1).
# Time Consumeing. This command will take about 1.4 hours to execute, so do not run it unless necessary.
# JLTZ(iMonte = 10000, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 1, iq = 0.05, iridge = 0.001)ATEDGP is a version of FuncDGP under full
compliance condition.ATETrueValue is a version of TrueValue
under full compliance condition.ATEOutput is a version of Output under
full compliance condition.ATEJLTZ is a version of JLTZ under full
compliance condition.ATEOutput is a list containing four 1x4 vectors rather
than a list containing four 1x12 vectors, which is the result of
Output. For details, please refer to the help documentation
for related functions.In this section we will show the user how to reproduce the results of
the numerical simulation section of Jiang et al.(2022) by using the
JLTZ function. Since it may take a long time to get the
results of all three kinds of GDPS in Jiang et al. (2022), we will focus
on only one case as an example.
Let’s consider a case like this:
First, the total sample was set at 200, which means
size = 200.
And second, the number of Monte Carlo simulations was set at
10,000, which means iMonte = 10000.
Third, calculate the size of the hypothesis test instead of the
power and consider a five percent confidence interval in hypothesis
testing,, which means iPert = 0 and
iq = 0.05.
Fourth, the data generation process follows DGP-1 in Jiang et
al.(2022), which means dgptype = 1.
Fifth, the samples are divided into four strata, and the
probability of the samples being processed in each strata is 0.5, which
means g = 4 and
pi = c(0.5, 0.5, 0.5, 0.5).
Sixth, the penalization parameter in ridge regression is 0.001,
which means iridge = 0.001.
# With the above Settings in mind, we get the following JLTZ function.
# JLTZ(iMonte = 10000, dgptype = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5), iPert = 0,iq = 0.05, iridge = 0.001)
# Since it takes about 1.4 hours to run this function, we'll give you the results directly that users can check them out themselves.
# vProb_d1 vProb_d2 vProb_d3 vProb_d4
# [1,] 0.03139898 0.03548546 0.03071509 0.03139898
# [2,] 0.04356403 0.04189256 0.03951368 0.04356403
# [3,] 0.04307085 0.04238541 0.03919373 0.04307085
# [4,] 0.05622226 0.04632824 0.05327148 0.05622226
# [5,] 0.10833470 0.08854937 0.09486482 0.10833470
# [6,] NaN NaN NaN NaN
# [7,] 0.03435805 0.03334976 0.03455447 0.03435805
# [8,] 0.04586553 0.05076392 0.05087186 0.04586553In this section we further show an example of using the
drcarlate package to analyze real data. For detailed
information on this case, see Section 7 and Table 5 of Jiang et
al.(2022).
# Set up ------------------------------------------------------------------
library(drcarlate)
library(pracma)
# Load data ---------------------------------------------------------------
# data_for_final.csv add covariates b_total_income log_b_total_income b_exp_total_30days
# edu_index b_asset_index b_health_index to data_for_tab4.csv
data_table <- drcarlate::data_table
data1 <- as.matrix(data_table)
colnames(data1) <- NULL
# create S for wave 1: number of stratnum, total 41 stratnum
n <- size(data1,1)
S <- zeros(n,1)
for (i in 1:41) {
S[data1[, size(data1,2)-i+1] == 1] <- 41 - i + 1
}
data1 <- cbind(data1, S)
# create Y, X, S, D: number of outcomes considered is 9:
# save the results for NA, TSLS, L, NL, F
vtauhat <- NaN * ones(8,5)
vsighat <- NaN * ones(8,5)
n_vec <- NaN * ones(8,1)
iridge = 0.01 #tuning parameter for in ridge regression
for (i in 1:8) {
if (i <= 4) {
# data_used: 1st col- Y, 2nd col- A, 3rd col- D, 4~(end-1)th col- X,
# last col is strata number
data_used <- cbind(data1[, 4+(i-1)*3], data1[, 2:3], data1[, 5:6],
data1[, size(data1,2)-1-41], data1[, size(data1,2)])
} else {
data_used <- cbind(data1[, 4+(i-1)*3], data1[,2:3], data1[, (4+(i-1)*3+1):(4+(i-1)*3+2)],
data1[, size(data1,2)-1-41], data1[, size(data1,2)])
}
# delete the outcome variables with NaN
data_used <- data_used[!is.nan(data_used[,1]), ]
# check whether a strata has obs less than 10
for (s in 1:41) {
if (length(data_used[data_used[, size(data_used,2)] == s,1]) < 10) {
# delete strata has obs less than 10
data_used[data_used[, size(data_used,2)] ==s, ] <- matrix()
data_used <- data_used[!is.na(data_used[,1]),]
}
}
# update n
n <- size(data_used,1)
n_vec[i] <- n
# find the unique value for stratnum
stratnum <- sort(base::unique(data_used[, size(data_used,2)]))
# create A
A <- matrix(data_used[, 2])
# create D
D <- matrix(data_used[, 3])
# create Y
Y <- matrix(data_used[, 1])
# create S
S <- matrix(data_used[, size(data_used,2)])
# create X
# use baseline total income
X <- data_used[,4:6]
# make a index
print(stringr::str_c("Now i equals to ", i, " !"))
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% No adjustment (z) NA
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
muY0_z <- zeros(n,1)
muY1_z <- zeros(n,1)
muD0_z <- zeros(n,1)
muD1_z <- zeros(n,1)
vtauhat[i,1] <- tau(muY1 = muY1_z, muY0 = muY0_z, muD1 = muD1_z, muD0 = muD0_z,
A = A, S = S, Y = Y, D = D, stratnum = stratnum)
vsighat[i,1] <- stanE(muY1 = muY1_z, muY0 = muY0_z, muD1 = muD1_z, muD0 = muD0_z,
A = A, S = S, Y = Y, D = D, tauhat = vtauhat[i,1], stratnum = stratnum)/sqrt(n)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% TSLS
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
mS_iv <- zeros(n, length(stratnum))
for (j in 1:length(stratnum)) {
s <- stratnum[j]
mS_iv[S==s, j] <- 1
}
mX_iv <- cbind(D, X, mS_iv)
mZ_iv <- cbind(A, X, mS_iv)
K <- size(mX_iv,2)
vPara_iv <- inv(t(mZ_iv) %*% mX_iv) %*% t(mZ_iv) %*% Y
mE_iv2 <- diag(((Y - mX_iv %*% vPara_iv)^2)[,])
m0_iv <- inv(t(mZ_iv) %*% mX_iv/n) %*% (t(mZ_iv) %*% mE_iv2 %*% mZ_iv/n) %*% inv(t(mX_iv) %*% mZ_iv/n)
vtauhat[i,2] <- vPara_iv[1]
vsighat[i,2] <- sqrt(m0_iv[1,1])/sqrt(n)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Linear+linear model (L)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
muY0_a <- NaN*ones(n,1)
muY1_a <- NaN*ones(n,1)
muD0_a <- NaN*ones(n,1)
muD1_a <- NaN*ones(n,1)
for (j in 1:length(stratnum)) {
s = stratnum[j]
result <- LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = s, modelflag = 1, iridge = iridge)
theta_0s_a <- result[["theta_0s"]]
theta_1s_a <- result[["theta_1s"]]
beta_0s_a <- result[["beta_0s"]]
beta_1s_a <- result[["beta_1s"]]
muY0_a[S==s] <- X[S==s,] %*% theta_0s_a
muY1_a[S==s] <- X[S==s,] %*% theta_1s_a
muD0_a[S==s] <- X[S==s,] %*% beta_0s_a
muD1_a[S==s] <- X[S==s,] %*% beta_1s_a
}
vtauhat[i,3] <- tau(muY1 = muY1_a, muY0 = muY0_a, muD1 = muD1_a, muD0 = muD0_a,
A = A, S = S, Y = Y, D = D, stratnum = stratnum)
vsighat[i,3] <- stanE(muY1 = muY1_a, muY0 = muY0_a, muD1 = muD1_a, muD0 = muD0_a,
A = A, S = S, Y = Y, D = D, tauhat = vtauhat[i,3], stratnum = stratnum)/sqrt(n)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Linear+logistic model (NL)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
muY0_b <- NaN*ones(n,1)
muY1_b <- NaN*ones(n,1)
muD0_b <- NaN*ones(n,1)
muD1_b <- NaN*ones(n,1)
for (j in 1:length(stratnum)) {
s = stratnum[j]
result <- LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = s, modelflag = 2, iridge = iridge)
theta_0s_b <- result[["theta_0s"]]
theta_1s_b <- result[["theta_1s"]]
beta_0s_b <- result[["beta_0s"]]
beta_1s_b <- result[["beta_1s"]]
muY0_b[S==s] <- X[S==s,] %*% matrix(theta_0s_b[2:length(theta_0s_b)]) + theta_0s_b[1]
muY1_b[S==s] <- X[S==s,] %*% matrix(theta_1s_b[2:length(theta_0s_b)]) + theta_1s_b[1]
muD0_b[S==s] <- LogisticReg(x = (X[S==s,] %*% matrix(beta_0s_b[-1]) + beta_0s_b[1]))
muD1_b[S==s] <- LogisticReg(x = (X[S==s,] %*% matrix(beta_1s_b[-1]) + beta_1s_b[1]))
}
vtauhat[i,4] <- tau(muY1 = muY1_b, muY0 = muY0_b, muD1 = muD1_b, muD0 = muD0_b,
A = A, S = S, Y = Y, D = D, stratnum = stratnum)
vsighat[i,4] <- stanE(muY1 = muY1_b, muY0 = muY0_b, muD1 = muD1_b, muD0 = muD0_b,
A = A, S = S, Y = Y, D = D,tauhat = vtauhat[i,4], stratnum = stratnum)/sqrt(n)
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# %% Further Efficiency Improvement
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
X_c <- cbind(X, muD1_b, muD0_b)
muY0_c <- NaN*ones(n,1)
muY1_c <- NaN*ones(n,1)
muD0_c <- NaN*ones(n,1)
muD1_c <- NaN*ones(n,1)
for (j in 1:length(stratnum)) {
s = stratnum[j]
result <- LinearLogit(Y = Y, D = D, A = A, X = X_c, S = S, s = s, modelflag = 1, iridge = iridge)
theta_0s_c <- result[["theta_0s"]]
theta_1s_c <- result[["theta_1s"]]
beta_0s_c <- result[["beta_0s"]]
beta_1s_c <- result[["beta_1s"]]
muY0_c[S==s] <- X_c[S==s,] %*% theta_0s_c
muY1_c[S==s] <- X_c[S==s,] %*% theta_1s_c
muD0_c[S==s] <- X_c[S==s,] %*% beta_0s_c
muD1_c[S==s] <- X_c[S==s,] %*%beta_1s_c
}
vtauhat[i,5] <- tau(muY1 = muY1_c, muY0 = muY0_c, muD1 = muD1_c, muD0 = muD0_c,
A = A, S = S, Y = Y, D = D, stratnum = stratnum)
vsighat[i,5] <- stanE(muY1 = muY1_c, muY0 = muY0_c, muD1 = muD1_c, muD0 = muD0_c,
A = A, S = S, Y = Y, D = D, tauhat = vtauhat[i,5], stratnum = stratnum)/sqrt(n)
}
#> [1] "Now i equals to 1 !"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 2 !"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 3 !"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 4 !"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 5 !"
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 6 !"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 7 !"
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
#> [1] "Now i equals to 8 !"
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred
# show the LATE estimates and standard errors in Table 5 of Jiang et al.(2022).
# LATE Estimates
vtauhat
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 2.7866925 7.1528747 7.1694104 7.2542016 8.4805342
#> [2,] 20.5577389 21.1544145 22.1604884 22.3940102 22.7366686
#> [3,] -0.2076838 -0.1735085 -0.2912842 -0.2947078 -0.3099807
#> [4,] 20.3993940 21.0965957 21.9244498 22.1835123 22.3253690
#> [5,] -10.8261902 -7.4558010 -9.0040607 -8.9405514 -8.6914634
#> [6,] -1.9332078 -2.3327993 -1.2417154 -1.2579026 -1.5505684
#> [7,] -3.6211274 -3.3462369 -1.4278123 -1.5513955 -1.4265200
#> [8,] -17.6431819 -14.3166215 -15.6652067 -15.8118165 -15.5119289
# Standard Errors
vsighat
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 7.2902879 6.3684935 6.1971428 6.2712205 6.1394941
#> [2,] 3.0667814 3.0151296 2.9646743 3.0037782 2.9512801
#> [3,] 0.2233596 0.2241912 0.2119157 0.2144341 0.2094491
#> [4,] 3.0890583 3.0344251 2.9792857 3.0221352 2.9639732
#> [5,] 5.0034112 4.4034599 4.4007221 4.3728318 4.4028981
#> [6,] 1.9711334 1.8580997 1.7936724 1.8155761 1.8076464
#> [7,] 2.0402640 1.9989033 1.8654540 2.0344097 1.8689752
#> [8,] 6.1995757 5.3509212 5.1849623 5.2346367 5.1130911Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.