User guide

Estimation and inference

This guide illustrates estimation of an average treatment effect under stratified randomization. A simulated example introduces the data structure, linear covariate adjustment, and interpretation of the reported estimates and standard errors.

01 · Installation

install.packages("sreg")
library(sreg)

install.packages("remotes")
remotes::install_github("jutrifonov/sreg")

net install sreg, from("/path/to/sreg-stata") replace
help sreg

python -m pip install "git+https://github.com/jutrifonov/sreg-python.git"

from sreg import sreg, sreg_rgen

02 · Data and estimand

For the individual-randomized example, let Y(1) and Y(0) denote potential outcomes under treatment and control. The estimand is the average treatment effect, τ = E[Y(1) − Y(0)]. With multiple active treatments, the package estimates an ATE for each treatment relative to control.

The simulation has 1,000 individuals in four strata and a treatment effect of 0.5. The generator returns observed outcomes Y, stratum indicators S, assignments D, and covariates x_1 and x_2. Treatment is assigned at the individual level within strata.

set.seed(42)
dat <- sreg.rgen(
  n = 1000,
  tau.vec = c(0.5),
  n.strata = 4,
  cluster = FALSE
)

head(dat)
table(dat$S, dat$D)

set rng mt64
set seed 42
sreg_rgen, n(1000) individual strata(4) tau(.5) clear

list Y S D x_1 x_2 in 1/6
tabulate S D

dat = sreg_rgen(
    n=1000,
    tau_vec=(0.5,),
    n_strata=4,
    cluster=False,
    random_state=42,
)

print(dat.head())
print(dat.groupby(["S", "D"]).size())

The random seed makes a simulation repeatable within a given implementation and environment. The same seed does not generate identical data across R, Stata, and Python. Compare estimates across languages using the same input dataset.

03 · Estimation and covariate adjustment

The following specification estimates the ATE with linear adjustment for x_1 and x_2. The default uses the large-strata procedure and applies the HC1 finite-sample correction to the variance estimator.

Covariates should be selected with reference to the experimental design and the intended adjustment specification. The package's adjustment procedure and corresponding variance estimator are described in the methodological references.

fit <- sreg(
  Y = dat$Y,
  S = dat$S,
  D = dat$D,
  X = dat[c("x_1", "x_2")]
)
print(fit)

fit_unadjusted <- sreg(Y = dat$Y, S = dat$S, D = dat$D)
print(fit_unadjusted)

sreg Y x_1 x_2, treatment(D) strata(S)

sreg Y, treatment(D) strata(S)

fit = sreg(
    Y=dat["Y"],
    S=dat["S"],
    D=dat["D"],
    X=dat[["x_1", "x_2"]],
)
print(fit)

fit_unadjusted = sreg(Y=dat["Y"], S=dat["S"], D=dat["D"])
print(fit_unadjusted)

04 · Interpretation and inference

Each row corresponds to an active treatment relative to control. The reported standard error is obtained from the variance estimator for the specified randomization design and adjustment procedure.

In this simulation, the true ATE is 0.5. The estimation error varies across simulated samples. The efficiency properties of covariate adjustment concern the relevant asymptotic variance; they do not imply that estimated standard errors decrease in every finite sample.

Confidence intervals and tests rely on an asymptotic approximation. The HC1 correction does not make inference exact in finite samples. When several treatment effects are reported, the individual 95% intervals are marginal intervals, rather than a simultaneous confidence region.

fit$tau.hat
fit$se.rob
cbind(lower = fit$CI.left, upper = fit$CI.right)

sreg Y x_1 x_2, treatment(D) strata(S)
matrix list e(b)
matrix list e(V)
sregplot

print(fit["tau_hat"])
print(fit["se_rob"])
ax = fit.plot()

05 · Specification for empirical applications

For an empirical application, supply observed outcomes, treatment assignments, randomization strata, and any covariates used for adjustment. Code control as 0 and active treatments as consecutive integers 1, 2, …. Stratum codes 1, 2, … provide a common format across implementations.

The specification must correspond to the assignment mechanism. Strata partition assignment units before randomization; clusters are groups of individuals assigned jointly to treatment. These identifiers have distinct roles in estimation and variance calculation.

Large strata

The example uses the large-strata procedure. For an unstratified experiment, omit the strata argument. The distinction between large and small strata concerns the stratification structure underlying the inference procedure, not the overall sample size alone.

Matched pairs and k-tuples

Select the small-strata estimator when the design uses small matched groups. The option is small.strata = TRUE in R, smallstrata in Stata, and small_strata=True in Python. In a uniform design the common group size can be inferred; an explicit k validates it.

Mixed small and large strata

Use the small-strata option to select mixed inference for varying stratum sizes. Specify k to identify the small component when it consists of 4-tuples or larger. At least 25% of strata must have the selected small-stratum size. See the estimator formulas and your implementation's reference before using this specification.

Cluster assignment

Supply cluster identifiers and represented cluster sizes: G.id and Ng in R, cluster() and clustersize() in Stata, or G_id and Ng in Python. For small or mixed strata, k counts clusters per small stratum. Individual-varying covariates are aggregated to cluster means for adjustment.

Empirical application

The Peru encouragement experiment provides a complete application using the package's AEJapp data: treatment recoding, unadjusted and age-adjusted estimates, confidence intervals, and plotting in R, Stata, and Python.

Reference documentation

Software citation

Cite the software version used in the analysis and the methodological papers corresponding to the estimator and randomization design. The project authors are Juri Trifonov, Yuehao Bai, Azeem Shaikh, and Max Tabord-Meehan.

citation("sreg")

Based on the R, Stata, and Python package documentation. Installation routes and advanced features may differ by release.