sreg {sreg}

Estimate Average Treatment Effects (ATEs) and Corresponding Standard Errors

Description

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

Usage

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

Arguments

Y

a numeric n \times 1 vector/matrix/data.frame/tibble of the observed outcomes

S

a numeric n \times 1 vector/matrix/data.frame/tibble of strata indicators indexed by \{1, 2, 3, \ldots\}; if NULL then the estimation is performed assuming no stratification

D

a numeric n \times 1 vector/matrix/data.frame/tibble of treatments indexed by \{0, 1, 2, \ldots\}, where \code{D} = 0 denotes the control

G.id

a numeric n \times 1 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 n \times 1 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. (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)

HC1

a TRUE/FALSE logical argument indicating whether the small sample correction should be applied to the variance estimator

Value

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

Author(s)

Authors:

Juri Trifonov [e-mail]

Yuehao Bai [e-mail]

Azeem Shaikh [e-mail]

Max Tabord-Meehan [e-mail]

Maintainer:

Juri Trifonov [e-mail]

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.

Examples

library("sreg")
library("dplyr")
library("haven")
### Example 1. Simulated Data.
data <- sreg.rgen(n = 1000, tau.vec = c(0), n.strata = 4, cluster = FALSE)
Y <- data$Y
S <- data$S
D <- data$D
X <- data.frame("x_1" = data$x_1, "x_2" = data$x_2)
result <- sreg(Y, S, D, G.id = NULL, Ng = NULL, X)
print(result)
### Example 2. Empirical Data.
?AEJapp
data("AEJapp")
data <- AEJapp
head(data)
Y <- data$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$S
table(D = data.clean$D, S = data.clean$S)
result <- sreg(Y, S, D)
print(result)
pills <- data$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(Y, S, D, G.id = NULL, X = X)
print(result)