| Title: | Improving Estimation Efficiency in CAR with Imperfect Compliance |
|---|---|
| Description: | We provide a list of functions for replicating the results of the Monte Carlo simulations and empirical application of Jiang et al. (2022). In particular, we provide corresponding functions for generating the three types of random data described in this paper, as well as all the estimation strategies. Detailed information about the data generation process and estimation strategy can be found in Jiang et al. (2022) <doi:10.48550/arXiv.2201.13004>. |
| Authors: | Liang Jiang [aut, cph], Oliver B. Linton [aut, cph], Haihan Tang [aut, cph], Yichong Zhang [aut, cph], Mingxin Zhang [cre] |
| Maintainer: | Mingxin Zhang <[email protected]> |
| License: | MIT + file LICENSE |
| Version: | 1.2.0 |
| Built: | 2024-12-07 06:56:10 UTC |
| Source: | CRAN |
ATEDGP is the version of FuncDGP under full compliance.
ATEDGP(dgptype, rndflag, n, g, pi)ATEDGP(dgptype, rndflag, n, g, pi)
dgptype |
A scalar. 1, 2, 3 (Almost the same as 1-3 in the paper except that it does not have the DGP for D(1) or D(0)). |
rndflag |
A scalar. method of covariate-adaptive randomization. 1-SRS; 2-WEI; 3-BCD; 4-SBR. |
n |
Sample size. |
g |
Number of strata. The authors set g = 4 in the Jiang et al. (2022). |
pi |
A g x 1 vector. Targeted assignment probabilities across strata. |
ATEDGP returns a list containing 7 nx1 vectors named Y, X, S, A, Y1, Y0 and D. These seven vectors are the same as defined in Jiang et al. (2022). Note that vector X does not contain the constant term.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
ATEDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5))ATEDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5))
ATEJLTZ is the version of JLTZ under full compliance.
ATEJLTZ(iMonte, dgptype, n, g, pi, iPert, iq = 0.05, iridge = 0.001, seed = 1)ATEJLTZ(iMonte, dgptype, n, g, pi, iPert, iq = 0.05, iridge = 0.001, seed = 1)
iMonte |
A scalar. Monte Carlo sizes. |
dgptype |
A scalar. The value can be string 1, 2, or 3, respectively corresponding to the three DGP schemes in the paper (See Jiang et al. (2022) for DGP details). |
n |
Sample size. |
g |
Number of strata. The authors set g=4 in Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
iPert |
A scalar. iPert = 0 means size. Otherwise means power: iPert is the perturbation of false null. |
iq |
A scalar. Size of hypothesis testing. The authors set iq = 0.05 in Jiang et al. (2022). |
iridge |
A scalar. The penalization parameter in ridge regression. |
seed |
A scalar. The random seed, the authors set seed = 1 in Jiang et al. (2022). |
A table summarizing the estimated results, mProd.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
# size, iPert = 0 ATEJLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 0, iq = 0.05, iridge = 0.001) # power, iPert = 1 ATEJLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 1, iq = 0.05, iridge = 0.001)# size, iPert = 0 ATEJLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 0, iq = 0.05, iridge = 0.001) # power, iPert = 1 ATEJLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 1, iq = 0.05, iridge = 0.001)
ATEOutput is the version of Output under full compliance.
ATEOutput(ii, tau, dgptype, rndflag, n, g, pi, iPert, iq, iridge)ATEOutput(ii, tau, dgptype, rndflag, n, g, pi, iPert, iq, iridge)
ii |
Monte Carlo index. |
tau |
A scalar. The simulated true LATE effect. |
dgptype |
A Scalar. 1, 2, 3 (See Jiang et al. (2022) for DGP details). |
rndflag |
Method of CAR (covariate-adaptive randomizations). Its value can be 1, 2, 3 or4. 1-SRS; 2-WEI; 3-BCD; 4-SBR. See Jiang et al. (2022) for more details about CAR. |
n |
Sample size. |
g |
Number of strata. The authors set g=4 in Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
iPert |
A scalar. iPert =0 means size. Otherwise means power: iPert is the perturbation of false null. |
iq |
Size of hypothesis testing. We set iq = 0.05. |
iridge |
A scalar. The penalization parameter in ridge regression. |
A list containing four matrices named vtauhat, vsighat, vstat and vdeci respectively. vtauhat is a 1x4 vector: (1) L (2) NL (3) R(dgp = 1 or 2) (4) R(dgp = 3). vsighat is a 1x4 vector: unscaled standard errors for vtauhat. vstat is a 1x4 vector: test statistic. vdeci is a 1x4 logical vector: if applicable, 1 means rejecting the null. 0 means not rejecting the null.
ATEOutput(ii = 1, tau = 0.9122762, dgptype = 1, rndflag = 4, n = 2000, g = 4, pi = c(0.5,0.5,0.5,0.5), iPert = 1, iq = 0.05, iridge = 0.001)ATEOutput(ii = 1, tau = 0.9122762, dgptype = 1, rndflag = 4, n = 2000, g = 4, pi = c(0.5,0.5,0.5,0.5), iPert = 1, iq = 0.05, iridge = 0.001)
ATETrueValue is the version of TrueValue under full compliance.
ATETrueValue(dgptype, vIdx, n, g, pi)ATETrueValue(dgptype, vIdx, n, g, pi)
dgptype |
A scalar. The value can be string 1, 2, or 3, respectively corresponding to the three DGP schemes in the paper (See Jiang et al. (2022) for DGP details). |
vIdx |
A 1xR vector. The authors set vIdx=[1 2 3 4] in Jiang et al. (2022). Every number declares the method of covariate-adaptive randomization. 1-SRS; 2-WEI; 3-BCD; 4-SBR. |
n |
Sample size. |
g |
Number of strata. The authors set g=4 in Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
A 1xR vector. Simulated true ATE effect.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
ATETrueValue(dgptype = 1, vIdx = c(1,2,3,4), n = 100, g = 4, pi = c(0.5,0.5,0.5,0.5)) ATETrueValue(dgptype = 2, vIdx = c(1,2,3,4), n = 100, g = 4, pi = c(0.5,0.5,0.5,0.5)) ATETrueValue(dgptype = 3, vIdx = c(1,2,3,4), n = 100, g = 4, pi = c(0.5,0.5,0.5,0.5))ATETrueValue(dgptype = 1, vIdx = c(1,2,3,4), n = 100, g = 4, pi = c(0.5,0.5,0.5,0.5)) ATETrueValue(dgptype = 2, vIdx = c(1,2,3,4), n = 100, g = 4, pi = c(0.5,0.5,0.5,0.5)) ATETrueValue(dgptype = 3, vIdx = c(1,2,3,4), n = 100, g = 4, pi = c(0.5,0.5,0.5,0.5))
Generate treatment assignment under various CARs.
CovAdptRnd(rndflag, S, pi)CovAdptRnd(rndflag, S, pi)
rndflag |
Index of the assignment rule. 1 for SRS; 2 for WEI; 3 for BCD; 4 for SBR |
S |
A nx1 vector. |
pi |
Targeted assignment probability across strata. It should be a vector with the length of max(S), It should be noted that the treatment assignment process is independent of pi when rndflag == 2 or 3. |
A nx1 treatment assignment vector generated according to the specified method.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
CovAdptRnd(rndflag = 1, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5)) CovAdptRnd(rndflag = 2, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5)) CovAdptRnd(rndflag = 3, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5)) CovAdptRnd(rndflag = 4, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5))CovAdptRnd(rndflag = 1, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5)) CovAdptRnd(rndflag = 2, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5)) CovAdptRnd(rndflag = 3, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5)) CovAdptRnd(rndflag = 4, S = matrix(sample(1:4,100,TRUE)), pi = c(0.5, 0.5, 0.5, 0.5))
Data used to reproduce Table 5 results in Jiang et. al. (2022).
data("data_table")data("data_table")
A data frame with 2159 observations on the following 69 variables.
X1a numeric vector
X2a numeric vector
X3a numeric vector
X4a numeric vector
X5a numeric vector
X6a numeric vector
X7a numeric vector
X8a numeric vector
X9a numeric vector
X10a numeric vector
X11a numeric vector
X12a numeric vector
X13a numeric vector
X14a numeric vector
X15a numeric vector
X16a numeric vector
X17a numeric vector
X18a numeric vector
X19a numeric vector
X20a numeric vector
X21a numeric vector
X22a numeric vector
X23a numeric vector
X24a numeric vector
X25a numeric vector
X26a numeric vector
X27a numeric vector
X28a numeric vector
X29a numeric vector
X30a numeric vector
X31a numeric vector
X32a numeric vector
X33a numeric vector
X34a numeric vector
X35a numeric vector
X36a numeric vector
X37a numeric vector
X38a numeric vector
X39a numeric vector
X40a numeric vector
X41a numeric vector
X42a numeric vector
X43a numeric vector
X44a numeric vector
X45a numeric vector
X46a numeric vector
X47a numeric vector
X48a numeric vector
X49a numeric vector
X50a numeric vector
X51a numeric vector
X52a numeric vector
X53a numeric vector
X54a numeric vector
X55a numeric vector
X56a numeric vector
X57a numeric vector
X58a numeric vector
X59a numeric vector
X60a numeric vector
X61a numeric vector
X62a numeric vector
X63a numeric vector
X64a numeric vector
X65a numeric vector
X66a numeric vector
X67a numeric vector
X68a numeric vector
X69a numeric vector
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
Under the condition of high dimensional data, the function first selects covariables through lasso regression, then performs logit regression or linear regression according to the caller's requirements, and finally returns the adjusted Lasso regression coefficient vector. This function has been slightly adapted for this package.
feasiblePostLassoMatTool( x, y, MaxIter = 30, UpsTol = 1e-06, beta0 = c(), clusterVar = c(), Dist = "normal", link = "identity", glmTol = 1e-08, initScale = 0.5 )feasiblePostLassoMatTool( x, y, MaxIter = 30, UpsTol = 1e-06, beta0 = c(), clusterVar = c(), Dist = "normal", link = "identity", glmTol = 1e-08, initScale = 0.5 )
x |
A nxk Matrix. |
y |
A nx1 vector. |
MaxIter |
Maximum iteration. The default value is 30. |
UpsTol |
Upper limit of tolerance. The default value is 1e-6. |
beta0 |
NULL. |
clusterVar |
NULL. |
Dist |
The default value is normal. |
link |
Link can be identity or logit. This determines the method used for regression with the selected write variable after lasso. See Jiang et al. (2022) for more details. |
glmTol |
Maximum tolerance in GLM. The default value is 1e-8. |
initScale |
Initial scale, the default value is 0.5. |
A kx1 cector, the coefficients b.
Belloni, A., Chernozhukov, V., Fernández-Val, I. and Hansen, C. (2017), Program Evaluation and Causal Inference With High-Dimensional Data. Econometrica, 85: 233-298. https://doi.org/10.3982/ECTA12723
set.seed(1) # Notice that when we set dgptype = 3, FuncDGP will generate a high dimensional data for us. DGP <- FuncDGP(dgptype = 3, rndflag = 1, n = 10000, g = 4, pi = c(0.5, 0.5, 0.5, 0.5)) X <- DGP$X Y <- DGP$Y A <- DGP$A S <- DGP$S D <- DGP$D feasiblePostLassoMatTool(x = X[S==1 & A==0,], y = Y[S==1 & A==0,]) feasiblePostLassoMatTool(x = X[S==1 & A==0,], y = D[S==1 & A==0,], link = "logit")set.seed(1) # Notice that when we set dgptype = 3, FuncDGP will generate a high dimensional data for us. DGP <- FuncDGP(dgptype = 3, rndflag = 1, n = 10000, g = 4, pi = c(0.5, 0.5, 0.5, 0.5)) X <- DGP$X Y <- DGP$Y A <- DGP$A S <- DGP$S D <- DGP$D feasiblePostLassoMatTool(x = X[S==1 & A==0,], y = Y[S==1 & A==0,]) feasiblePostLassoMatTool(x = X[S==1 & A==0,], y = D[S==1 & A==0,], link = "logit")
Generate data according to one of the three DGPs in Jiang et al. (2022).
FuncDGP(dgptype, rndflag, n, g, pi)FuncDGP(dgptype, rndflag, n, g, pi)
dgptype |
A Scalar. 1, 2, 3 (See Jiang et al. (2022) for DGP details) |
rndflag |
A Scalar. Declare the method of covariate-adaptive randomization. 1-SRS; 2-WEI; 3-BCD; 4-SBR. |
n |
Sample size |
g |
Number of strata. The authors set g=4 in the Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
FuncDGP returns a list containing 9 nx1 vectors named Y, X, S, A, Y1, Y0, D1, D0 and D. These nine vectors are the same as defined in Jiang et al. (2022). Note that vector X does not contain the constant term.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
FuncDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 1, rndflag = 2, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 1, rndflag = 3, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 1, rndflag = 4, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 2, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 3, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 4, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 2, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 3, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 4, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5))FuncDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 1, rndflag = 2, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 1, rndflag = 3, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 1, rndflag = 4, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 2, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 3, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 2, rndflag = 4, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 2, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 3, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) FuncDGP(dgptype = 3, rndflag = 4, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5))
Helps the user reproduce the results of the data simulation section of Jiang et al. (2022).
JLTZ(iMonte, dgptype, n, g, pi, iPert, iq = 0.05, iridge = 0.001, seed = 1)JLTZ(iMonte, dgptype, n, g, pi, iPert, iq = 0.05, iridge = 0.001, seed = 1)
iMonte |
A scalar. Monte Carlo sizes. |
dgptype |
A scalar. The value can be string 1, 2, or 3, respectively corresponding to the three random data generation methods in the paper (See Jiang et al. (2022) for DGP details). |
n |
Sample size. |
g |
Number of strata. We set g=4 in Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
iPert |
A scalar. iPert = 0 means size. Otherwise means power: iPert is the perturbation of false null. |
iq |
A scalar. Size of hypothesis testing. The authors set iq = 0.05. |
iridge |
A scalar. The penalization parameter in ridge regression. |
seed |
A scalar. The random seed, the authors set seed = 1 in Jiang et al. (2022). |
A table summarizing the estimated results, mProd.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
# size, iPert = 0 JLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 0, iq = 0.05, iridge = 0.001, seed = 1) # power, iPert = 1 JLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 1, iq = 0.05, iridge = 0.001, seed = 1)# size, iPert = 0 JLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 0, iq = 0.05, iridge = 0.001, seed = 1) # power, iPert = 1 JLTZ(iMonte = 10, dgptype = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5), iPert = 1, iq = 0.05, iridge = 0.001, seed = 1)
LinearLogit generates estimated pseudo true values for parametric models. Different estimation strategies are adopted according to different values of modelflag. See Jiang et al. (2022) for more details about different strategies.
LinearLogit(Y, D, A, X, S, s, modelflag, iridge)LinearLogit(Y, D, A, X, S, s, modelflag, iridge)
Y |
The outcome vector. A nx1 vector. |
D |
A nx1 vector. |
A |
The treatment assignment. A nx1 vector. |
X |
Extra covariate matrix, A nxK matrix without constant. |
S |
The strata variable. |
s |
A particular stratum. |
modelflag |
Its value ranges from characters 1, 2, and 3, respectively declaring different estimation strategies. 1-L; 2-NL; 3-R. |
iridge |
A scalar. The penalization parameter in ridge regression. |
theta_0s, theta_1s, beta_0s, beta_1s are estimated coefficients vectors. The dimension is Kx1 if modelflag = 1; (K+1)x1 if modelflag = 2 or 3.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
#' set.seed(1) DGP <- FuncDGP(dgptype = 3, rndflag = 1, n = 10000, g = 4, pi = c(0.5, 0.5, 0.5, 0.5)) X <- DGP$X Y <- DGP$Y A <- DGP$A S <- DGP$S D <- DGP$D LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 1, modelflag = 1, iridge = 0.001) LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 2, modelflag = 2, iridge = 0.001) LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 3, modelflag = 3, iridge = 0.001) LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 4, modelflag = 3, iridge = 0.001)#' set.seed(1) DGP <- FuncDGP(dgptype = 3, rndflag = 1, n = 10000, g = 4, pi = c(0.5, 0.5, 0.5, 0.5)) X <- DGP$X Y <- DGP$Y A <- DGP$A S <- DGP$S D <- DGP$D LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 1, modelflag = 1, iridge = 0.001) LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 2, modelflag = 2, iridge = 0.001) LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 3, modelflag = 3, iridge = 0.001) LinearLogit(Y = Y, D = D, A = A, X = X, S = S, s = 4, modelflag = 3, iridge = 0.001)
Logestic CDF(cumulative distribution function).
LogisticReg(x)LogisticReg(x)
x |
A nx1 matrix. |
y A nx1 matrix. y equals to exp(x)/(1+exp(x)) if y is not NA and 0 else.
x <- pracma::rand(5,1) y <- LogisticReg(x = x)x <- pracma::rand(5,1) y <- LogisticReg(x = x)
Returns the inverse cdf for the normal distribution with mean MU and standard deviation SIGMA at P value Reference: https://rdrr.io/github/maxto/qapi/src/R/stats.R
norminv(p, mu = 0, sigma = 1)norminv(p, mu = 0, sigma = 1)
p |
probability value in range 0-1 |
mu |
mean value |
sigma |
standard deviation |
numeric
xx <- c(0.003,0.026,0.015,-0.009,-0.014,-0.024,0.015,0.066,-0.014,0.039) norminv(0.01,mean(xx),sd(xx))xx <- c(0.003,0.026,0.015,-0.009,-0.014,-0.024,0.015,0.066,-0.014,0.039) norminv(0.01,mean(xx),sd(xx))
Output is an integrated function that computes all the estimates (including NA, TSLS, L, NL, F, NP, R) used in Jiang et al. (2022). See the paper for more details.
Output(ii, tau, dgptype, rndflag, n, g, pi, iPert, iq, iridge)Output(ii, tau, dgptype, rndflag, n, g, pi, iPert, iq, iridge)
ii |
Monte Carlo index. |
tau |
A scalar. The simulated true LATE effect. |
dgptype |
A Scalar. 1, 2, 3 (See Jiang et al. (2022) for DGP details). |
rndflag |
Method of CAR (covariate-adaptive randomizations). Its value can be 1, 2, 3 or4. 1-SRS; 2-WEI; 3-BCD; 4-SBR. See Jiang et al. (2022) for more details about CAR. |
n |
Sample size. |
g |
Number of strata. The authors set g=4 in Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
iPert |
A scalar. iPert =0 means size. Otherwise means power: iPert is the perturbation of false null. |
iq |
Size of hypothesis testing. The authors set iq = 0.05 in Jiang et al. (2022). |
iridge |
A scalar. The penalization parameter in ridge regression. |
A list containing four matrices named vtauhat, vsighat, vstat and vdeci respectively. vtauhat is a 1x8 vector: (1) NA (2) LP (3) LG (4) F (5) NP (6) R (when dgp = 3) (7) 2SLS (8) R (when dgp = 1 or 2). vsighat is a 1x8 vector: unscaled standard errors for vtauhat. vstat is a 1x8 vector: test statistic. vdeci is a 1x8 logical vector: if applicable, 1 means rejecting the null. 0 means not rejecting the null.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
Output(ii = 1, tau = 0.9122762, dgptype = 1, rndflag = 4, n = 2000, g = 4, pi = c(0.5,0.5,0.5,0.5), iPert = 1, iq = 0.05, iridge = 0.001)Output(ii = 1, tau = 0.9122762, dgptype = 1, rndflag = 4, n = 2000, g = 4, pi = c(0.5,0.5,0.5,0.5), iPert = 1, iq = 0.05, iridge = 0.001)
Pihat computes the targeted treatment assignment probabilities across all strata in Jiang et al. (2022) and stacks them in an nx1 vector.
pihat(A, S, stratnum = NULL)pihat(A, S, stratnum = NULL)
A |
A nx1 vector. |
S |
A nx1 vector. |
stratnum |
A nx1 vector about the unique strara numbers, the default value is NULL. |
A nx1 cector, each element corresponds to the targeted treatment assignment probabilities across all strata in Jiang et al. (2022).
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
DGP <-FuncDGP(dgptype = 1,rndflag = 2,n = 100,g = 4,pi = c(0.5, 0.5, 0.5, 0.5)) A <- DGP[["A"]] S <- DGP[["S"]] pihat(A = A, S = S)DGP <-FuncDGP(dgptype = 1,rndflag = 2,n = 100,g = 4,pi = c(0.5, 0.5, 0.5, 0.5)) A <- DGP[["A"]] S <- DGP[["S"]] pihat(A = A, S = S)
For each column of an input matrix, elements which are less than the median of that column are set to 0, leaving the rest of the elements unchanged.
splinebasis(X)splinebasis(X)
X |
The extra covariates, a n x K matrix. No constant included. |
H A n x K matrix. All elements of the X that are less than the median of their corresponding columns are set to 0, leaving the rest unchanged.
library(pracma) X <- rand(4,4) H <- splinebasis(X = X)library(pracma) X <- rand(4,4) H <- splinebasis(X = X)
stanE Computes the estimated standard error of the input estimator.
stanE(muY1, muY0, muD1, muD0, A, S, Y, D, tauhat, stratnum = NULL)stanE(muY1, muY0, muD1, muD0, A, S, Y, D, tauhat, stratnum = NULL)
muY1 |
A nx1 vector of hat{mu}^Y(A=1)s. |
muY0 |
A nx1 vector of hat{mu}^Y(A=0)s. |
muD1 |
A nx1 vector of hat{mu}^D(A=1)s. |
muD0 |
A nx1 vector of hat{mu}^D(A=0)s. |
A |
A nx1 vector. Each of its elements is the treatment assignment of the corresponding observation. |
S |
A nx1 vector. Each of its elements is the stratum of corresponding observation. |
Y |
A nx1 vector. Each of its elements is the observed outcome of interest of corresponding observation. |
D |
A nx1 vector. Each of its elements is is a binary random variable indicating whether the individual i received treatment (Di = 1) or not (Di = 0) in the actual study. |
tauhat |
A scalar. LATE estimate. |
stratnum |
A scalar. Number of stratum. |
A scalar. The estimated standard deviation in Jiang et al. (2022).
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
DGP <- FuncDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) muY1 <- DGP[["Y1"]] muY0 <- DGP[["Y0"]] muD1 <- DGP[["D1"]] muD0 <- DGP[["D0"]] A <- DGP[["A"]] S <- DGP[["S"]] Y <- DGP[["Y"]] D <- DGP[["D"]] tauhat <- tau(muY1, muY0, muD1, muD0, A, S, Y, D) stanE(muY1, muY0, muD1, muD0, A, S, Y, D, tauhat)DGP <- FuncDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5,0.5,0.5,0.5)) muY1 <- DGP[["Y1"]] muY0 <- DGP[["Y0"]] muD1 <- DGP[["D1"]] muD0 <- DGP[["D0"]] A <- DGP[["A"]] S <- DGP[["S"]] Y <- DGP[["Y"]] D <- DGP[["D"]] tauhat <- tau(muY1, muY0, muD1, muD0, A, S, Y, D) stanE(muY1, muY0, muD1, muD0, A, S, Y, D, tauhat)
Computes the estimated LATE in Jiang et al. (2022).
tau(muY1, muY0, muD1, muD0, A, S, Y, D, stratnum = NULL)tau(muY1, muY0, muD1, muD0, A, S, Y, D, stratnum = NULL)
muY1 |
A nx1 vector of hat{mu}^Y(A=1)s. |
muY0 |
A nx1 vector of hat{mu}^Y(A=0)s. |
muD1 |
A nx1 vector of hat{mu}^D(A=1)s. |
muD0 |
A nx1 vector of hat{mu}^D(A=0)s. |
A |
A nx1 vector. Each of its elements is the treatment assignment of the corresponding observation. |
S |
A nx1 vector. Each of its elements is the stratum of corresponding observation. |
Y |
A nx1 vector. Each of its elements is the observed outcome of interest of corresponding observation. |
D |
A nx1 vector. Each of its elements is is a binary random variable indicating whether the individual i received treatment (Di = 1) or not (Di = 0) in the actual study. |
stratnum |
A nx1 vector about the unique strata numbers, the default value is NULL. |
A scalar. LATE estimate.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
DGP <- FuncDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5)) muY1 <- DGP[["Y1"]] muY0 <- DGP[["Y0"]] muD1 <- DGP[["D1"]] muD0 <- DGP[["D0"]] A <- DGP[["A"]] S <- DGP[["S"]] Y <- DGP[["Y"]] D <- DGP[["D"]] tau(muY1, muY0, muD1, muD0, A, S, Y, D)DGP <- FuncDGP(dgptype = 1, rndflag = 1, n = 200, g = 4, pi = c(0.5, 0.5, 0.5, 0.5)) muY1 <- DGP[["Y1"]] muY0 <- DGP[["Y0"]] muD1 <- DGP[["D1"]] muD0 <- DGP[["D0"]] A <- DGP[["A"]] S <- DGP[["S"]] Y <- DGP[["Y"]] D <- DGP[["D"]] tau(muY1, muY0, muD1, muD0, A, S, Y, D)
Calculate the true LATE tau in Jiang et al. (2022).
TrueValue(dgptype, vIdx, n, g, pi)TrueValue(dgptype, vIdx, n, g, pi)
dgptype |
A scalar. The value can be string 1, 2, or 3, respectively corresponding to the three random data generation methods in the paper (See Jiang et al. (2022)for DGP details) |
vIdx |
A 1xR vector. The authors set vIdx=[1 2 3 4]. Every number declares the method of covariate-adaptive randomization which simulates the LATE across different CAR schemes: 1-SRS; 2-WEI; 3-BCD; 4-SBR. |
n |
Sample size. |
g |
Number of strata. The authors set g=4 in Jiang et al. (2022). |
pi |
Targeted assignment probability across strata. |
A list containing two vectors named tau and mPort. tau is a 1xR vector which Simulated true LATE effect, mPort is a 3xR vector. The 1st row of mPort: the LATE of never takers across varies CAR schemes, the 2nd row of mPort: the LATE of compilers across varies CAR schemes, the 3rd row of mPort: the LATE of always takers across varies CAR schemes.
Jiang L, Linton O B, Tang H, Zhang Y. Improving estimation efficiency via regression-adjustment in covariate-adaptive randomizations with imperfect compliance [J]. 2022.
TrueValue(dgptype = 1, vIdx = c(1,2,3,4), n=100, g = 4, pi = c(0.5,0.5,0.5,0.5)) TrueValue(dgptype = 2, vIdx = c(1,2,3,4), n=100, g = 4, pi = c(0.5,0.5,0.5,0.5)) TrueValue(dgptype = 3, vIdx = c(1,2,3,4), n=100, g = 4, pi = c(0.5,0.5,0.5,0.5))TrueValue(dgptype = 1, vIdx = c(1,2,3,4), n=100, g = 4, pi = c(0.5,0.5,0.5,0.5)) TrueValue(dgptype = 2, vIdx = c(1,2,3,4), n=100, g = 4, pi = c(0.5,0.5,0.5,0.5)) TrueValue(dgptype = 3, vIdx = c(1,2,3,4), n=100, g = 4, pi = c(0.5,0.5,0.5,0.5))