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The sreg package for R, offers a toolkit
for estimating average treatment effects (ATEs) in stratified randomized
experiments. The package is designed to accommodate scenarios with
multiple treatments and cluster-level treatment assignments, and
accomodates optimal linear covariate adjustment based on baseline
observable characteristics. The package computes estimators and standard
errors based on Bugni, Canay, Shaikh (2018); Bugni, Canay, Shaikh,
Tabord-Meehan (2023); and Jiang, Linton, Tang, Zhang (2023).
Dependencies: dplyr,
tidyr, extraDistr, rlang
Suggests: haven, knitr,
rmarkdown, testthat (>= 3.0.0)
R version required:
>= 2.10
Juri Trifonov jutrifonov@uchicago.edu
Yuehao Bai yuehao.bai@usc.edu
Azeem Shaikh amshaikh@uchicago.edu
Max Tabord-Meehan maxtm@uchicago.edu
PDF version of the manual: Download PDF
Sketch of the derivation of the ATE variance estimator under cluster-level treatment assignment: Download PDF
Expressions for the multiple treatment case (with and without clusters): Download PDF
The latest version can be installed using devtools. The
official CRAN release will be available soon.
library(devtools)
install_github("jutrifonov/sreg")Downloading GitHub repo jutrifonov/sreg@HEAD
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✔ checking DESCRIPTION meta-information
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* installing *source* package ‘sreg’ ...
** using staged installation
** R
** data
*** moving datasets to lazyload DB
** byte-compile and prepare package for lazy loading
** help
*** installing help indices
** building package indices
** testing if installed package can be loaded from temporary location
** testing if installed package can be loaded from final location
** testing if installed package keeps a record of temporary installation path
* DONE (sreg)library(sreg)
#> ____ ____ _____ ____ Stratified Randomized
#> / ___|| _ \| ____/ ___| Experiments
#> \___ \| |_) | _|| | _
#> ___) | _ <| |__| |_| |
#> |____/|_| \_\_____\____| version 1.0.0
#> Type 'citation("sreg")' for citing this R package in publications. sreg()Estimates the ATE(s) and the corresponding standard error(s) for a (collection of) treatment(s) relative to a control.
sreg(Y, S = NULL, D, G.id = NULL, Ng = NULL, X = NULL, HC1 = TRUE)Y - a numeric
vector/matrix/data.frame/tibble of the observed
outcomes;S - a numeric
vector/matrix/data.frame/tibble of strata indicators \(\\{0, 1, 2, \ldots\\}\); if
NULL then the estimation is performed assuming no
stratification;D - a numeric
vector/matrix/data.frame/tibble of treatments indexed by
\(\\{0, 1, 2, \ldots\\}\), where
D = 0 denotes the control;G.id - a numeric
vector/matrix/data.frame/tibble of cluster indicators; if
NULL then estimation is performed assuming treatment is
assigned at the individual level;Ng - a numeric
vector/matrix/data.frame/tibble of cluster sizes; if
NULL then Ng is assumed to be equal to the
number of available observations in every cluster;X - a
matrix/data.frame/tibble with columns representing the
covariate values for every observation; if NULL then the
estimator without linear adjustments is applied [^*];HC1 - a TRUE/FALSE
logical argument indicating whether the small sample correction should
be applied to the variance estimator. [^*]: Note: sreg cannot use
individual-level covariates for covariate adjustment in
cluster-randomized experiments. Any individual-level covariates will be
aggregated to their cluster-level averages.Here we provide an example of a data frame that can be used with
sreg.
| Y | S | D | G.id | Ng | x_1 | x_2 |
|--------------|---|---|------|----|------------|---------------|
| -0.57773576 | 2 | 0 | 1 | 10 | 1.5597899 | 0.03023334 |
| 1.69495638 | 2 | 0 | 1 | 10 | 1.5597899 | 0.03023334 |
| 2.02033740 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |
| 1.22020493 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |
| 1.64466086 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |
| -0.32365109 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |
| 2.21008191 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |
| -2.25064316 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |
| 0.37962312 | 4 | 2 | 2 | 30 | 0.8747419 | -0.77090031 |sreg prints a “Stata-style” table containing
the ATE estimates, corresponding standard errors, \(t\)-statistics, \(p\)-values, \(95\)% asymptotic confidence intervals, and
significance indicators for different levels \(\alpha\). The example of the printed output
is provided below.
Saturated Model Estimation Results under CAR with clusters and linear adjustments
Observations: 30000
Clusters: 1000
Number of treatments: 2
Number of strata: 4
Covariates used in linear adjustments: x_1, x_2
---
Coefficients:
Tau As.se T-stat P-value CI.left(95%) CI.right(95%) Significance
1 0.01614 0.04513 0.35753 0.72069 -0.07232 0.1046
2 0.78642 0.04642 16.94263 0.00000 0.69545 0.8774 ***
---
Signif. codes: 0 `***` 0.001 `**` 0.01 `*` 0.05 `.` 0.1 ` ` 1The function returns an object of class sreg that is a
list containing the following elements:
tau.hat - a \(1 \times |\mathcal A|\) vector of ATE
estimates, where \(|\mathcal A|\)
represents the number of treatments;
se.rob - a \(1 \times |\mathcal A|\) vector of standard
errors estimates, where \(|\mathcal
A|\) represents the number of treatments;
t.stat - a \(1 \times |\mathcal A|\) vector of \(t\)-statistics, where \(|\mathcal A|\) represents the number of
treatments;
p.value - a \(1 \times |\mathcal A|\) vector of
corresponding \(p\)-values, where \(|\mathcal A|\) represents the number of
treatments;
CI.left - a \(1 \times |\mathcal A|\) vector of the left
bounds of the \(95\)% as. confidence
interval;
CI.right - a \(1 \times |\mathcal A|\) vector of the right
bounds of the \(95\)% as. confidence
interval;
data - an original data of the form
data.frame(Y, S, D, G.id, Ng, X);
lin.adj - a data.frame
representing the covariates that were used in implementing linear
adjustments.
Here, we provide the empirical application example using the data
from (Chong et al., 2016), who studied the effect of iron deficiency
anemia on school-age children’s educational attainment and cognitive
ability in Peru. The example replicates the empirical illustration from
(Bugni et al., 2019). For replication purposes, the data is included in
the package and can be accessed by running data("AEJapp").
This example can be accessed directly in R via
help(sreg).
library(sreg, dplyr, haven)The description of the dataset can be accessed using
help():
help(AEJapp)We can upload the AEJapp dataset to the R
session via data():
data("AEJapp")
data <- AEJappIt is pretty straightforward to prepare the data to fit the package
syntax using dplyr:
Y <- data$gradesq34
D <- data$treatment
S <- data$class_level
data.clean <- data.frame(Y, D, S)
data.clean <- data.clean %>%
mutate(D = ifelse(D == 3, 0, D))
Y <- data.clean$Y
D <- data.clean$D
S <- data.clean$S
head(data.clean)
Y D S
1 11.2 1 1
2 12.4 0 3
3 11.9 0 5
4 13.1 0 1
5 13.4 2 2
6 10.7 0 1We can take a look at the frequency table of D and
S:
table(D = data.clean$D, S = data.clean$S)
S
D 1 2 3 4 5
0 15 19 16 12 10
1 16 19 15 10 10
2 17 20 15 11 10Now, it is straightforward to replicate the results from (Bugni et
al, 2019) using sreg:
result <- sreg::sreg(Y = Y, S = S, D = D)
print(result)Saturated Model Estimation Results under CAR
Observations: 215
Number of treatments: 2
Number of strata: 5
---
Coefficients:
Tau As.se T-stat P-value CI.left(95%) CI.right(95%) Significance
1 -0.05113 0.20645 -0.24766 0.80440 -0.45577 0.35351
2 0.40903 0.20651 1.98065 0.04763 0.00427 0.81379 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1Besides that, sreg allows adding linear adjustments
(covariates) to the estimation procedure:
pills <- data$pills_taken
age <- data$age_months
data.clean <- data.frame(Y, D, S, pills, age)
data.clean <- data.clean %>%
mutate(D = ifelse(D == 3, 0, D))
Y <- data.clean$Y
D <- data.clean$D
S <- data.clean$S
X <- data.frame("pills" = data.clean$pills, "age" = data.clean$age)
result <- sreg::sreg(Y, S, D, G.id = NULL, X = X)
print(result)
Saturated Model Estimation Results under CAR
Observations: 215
Number of treatments: 2
Number of strata: 5
Covariates used in linear adjustments: pills, age
---
Coefficients:
Tau As.se T-stat P-value CI.left(95%) CI.right(95%) Significance
1 -0.02862 0.17964 -0.15929 0.87344 -0.38071 0.32348
2 0.34609 0.18362 1.88477 0.05946 -0.01381 0.70598 .
---
Signif. codes: 0 `***` 0.001 `**` 0.01 `*` 0.05 `.` 0.1 ` ` 1sreg.rgen()Generates the observed outcomes, treatment assignments, strata indicators, cluster indicators, cluster sizes, and covariates for estimating the treatment effect following the stratified block randomization design under covariate-adaptive randomization (CAR).
sreg.rgen(n, Nmax = 50, n.strata,
tau.vec = c(0), gamma.vec = c(0.4, 0.2, 1),
cluster = TRUE, is.cov = TRUE)n - a total number of observations in
a sample;Nmax - a maximum size of generated
clusters (maximum number of observations in a cluster);n.strata - an integer
specifying the number of strata;tau.vec - a numeric \(1 \times |\mathcal A|\) vector
of treatment effects, where \(|\mathcal
A|\) represents the number of treatments;gamma.vec - a numeric \(1 \times 3\) vector of
parameters corresponding to covariates;cluster - a TRUE/FALSE
argument indicating whether the dgp should use a cluster-level treatment
assignment or individual-level;is.cov - a TRUE/FALSE
argument indicating whether the dgp should include covariates or
not.Y - a numeric \(n \times 1\) vector of the
observed outcomes;S - a numeric \(n \times 1\) vector of strata
indicators;D - a numeric \(n \times 1\) vector of
treatments indexed by \(\\{0, 1, 2,
\ldots\\}\), where D = 0 denotes the control;G.id - a numeric \(n \times 1\) vector of cluster
indicators;Ng - a numeric
vector/matrix/data.frame of cluster sizes; if
NULL then Ng is assumed to be equal to the
number of available observations in every cluster;X - a data.frame with
columns representing the covariate values for every observation.library(sreg)
data <- sreg.rgen(n = 1000, tau.vec = c(0), n.strata = 4, cluster = TRUE)
> head(data)
Y S D x_1 x_2
1 1.717293 1 0 4.772092 2.4138491
2 2.553695 2 0 5.413440 2.0551019
3 2.237556 3 2 6.611161 0.9300293
4 1.825809 3 1 2.735503 1.7839981
5 5.536280 2 2 2.469239 2.0495611
6 1.628753 2 0 4.887561 2.1327071Bugni, F. A., Canay, I. A., and Shaikh, A. M. (2018). Inference Under Covariate-Adaptive Randomization. Journal of the American Statistical Association, 113(524), 1784–1796, doi:10.1080/01621459.2017.1375934.
Bugni, F., Canay, I., Shaikh, A., and Tabord-Meehan, M. (2024+). Inference for Cluster Randomized Experiments with Non-ignorable Cluster Sizes. Forthcoming in the Journal of Political Economy: Microeconomics, doi:10.48550/arXiv.2204.08356.
Jiang, L., Linton, O. B., Tang, H., and Zhang, Y. (2023+). Improving Estimation Efficiency via Regression-Adjustment in Covariate-Adaptive Randomizations with Imperfect Compliance. Forthcoming in Review of Economics and Statistics, doi:10.48550/arXiv.2204.08356.
These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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