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Stratified Randomized Experiments

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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

Latest Build (v.1.0.0)

Authors

Supplementary files

Installation

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
── R CMD build ───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────
✔  checking for file ‘/private/var/folders/mp/06gjwr8j56zdp5j2vgdkd4z40000gq/T/RtmpZh7j1Y/remotesfbf765906644/jutrifonov-sreg-91d11dc/DESCRIPTION’ ...
─  preparing ‘sreg’:
✔  checking DESCRIPTION meta-information
─  checking for LF line-endings in source and make files and shell scripts
─  checking for empty or unneeded directories
─  building ‘sreg_0.5.8.tar.gz’
   
* 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.                    

The function sreg()

Estimates the ATE(s) and the corresponding standard error(s) for a (collection of) treatment(s) relative to a control.

Syntax

sreg(Y, S = NULL, D, G.id = NULL, Ng = NULL, X = NULL, HC1 = TRUE)

Arguments

Data Structure

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   |

Summary

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 ` ` 1

Return Value

The function returns an object of class sreg that is a list containing the following elements:

Empirical Example

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 <- AEJapp

It 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 1

We 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 10

Now, 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 ‘ ’ 1

Besides 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 ` ` 1

The function sreg.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).

Syntax

sreg.rgen(n, Nmax = 50, n.strata,
         tau.vec = c(0), gamma.vec = c(0.4, 0.2, 1),
         cluster = TRUE, is.cov = TRUE)

Arguments

Return Value

Example

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 2.1327071

References

Bugni, 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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