Package {sreg}

Replication data for: Iron Deficiency and Schooling Attainment in Peru (Chong et al, 2016)

Description

The data is taken from Chong et al. (2016), who study the effect of iron deficiency anemia (i.e., anemia caused by a lack of iron) on school-age children’s educational attainment and cognitive ability in Peru.

Usage

data("AEJapp")

Format

A data frame with 215 observations on the 62 variables.

Source

Chong, A., Cohen, I., Field, E., Nakasone, E., and Torero, M. (2016). Replication data for: Iron Deficiency and Schooling Attainment in Peru. Nashville, TN: American Economic Association [publisher], 2016. Ann Arbor, MI: Inter-university Consortium for Political and Social Research [distributor], 2019-10-12. doi:10.3886/E113624V1.

References

Chong, A., Cohen, I., Field, E., Nakasone, E., and Torero, M. (2016). Iron Deficiency and Schooling Attainment in Peru. American Economic Journal: Applied Economics, 8(4), 222–255. doi:10.1257/app.20140494.

Examples

data(AEJapp)

Plot Method for 'sreg' Objects

Description

Visualize estimated ATEs and confidence intervals for objects of class sreg.

Usage

## S3 method for class 'sreg'
plot(
  x,
  treatment_labels = NULL,
  title = "Estimated ATEs with Confidence Intervals",
  bar_fill = NULL,
  point_shape = 23,
  point_size = 3,
  point_fill = "white",
  point_stroke = 1.2,
  point_color = "black",
  label_color = "black",
  label_size = 4,
  bg_color = NULL,
  grid = TRUE,
  zero_line = TRUE,
  y_axis_title = NULL,
  x_axis_title = NULL,
  ...
)

Arguments

Value

Invisibly returns the ggplot object. Called for its side effects (i.e., generating a plot).

Examples

set.seed(22)
data <- sreg.rgen(
  n = 120, tau.vec = c(0.2, 0.5), n.strata = 4,
  cluster = FALSE
)
fit <- sreg(Y = data$Y, S = data$S, D = data$D)

plot(fit)

p <- plot(
  fit,
  treatment_labels = c("Program A", "Program B"),
  title = "Estimated treatment effects",
  x_axis_title = "ATE relative to control",
  bar_fill = c("#3B82F6", "#14B8A6")
)
class(p)

Print sreg Objects

Description

Print the summary table of estimation results for sreg objects.

Usage

## S3 method for class 'sreg'
print(x, ...)

Arguments

Value

No return value, called for side effects.

Examples

set.seed(21)
data <- sreg.rgen(
  n = 80, tau.vec = c(0.2, 0.5), n.strata = 4,
  cluster = FALSE
)
fit <- sreg(
  Y = data$Y, S = data$S, D = data$D,
  X = data[c("x_1", "x_2")]
)
print(fit)

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,
  small.strata = FALSE,
  k = NULL
)

Arguments

Details

Supplying G.id selects cluster-level assignment; otherwise, treatment is treated as assigned at the individual level. Setting small.strata = FALSE selects the large-strata procedure. With small.strata = TRUE, a common observed stratum size selects the small-strata procedure, whereas varying stratum sizes select the mixed procedure. The optional k validates the common size in a uniform small-strata design and identifies the small-stratum size in a general mixed design.

Under cluster-level assignment, adjustment is performed using cluster-level covariates. Covariates supplied with one row per individual are replaced by their within-cluster means. The package computes the mean outcome among the available observations from each cluster and uses Ng as its represented cluster size. If Ng = NULL, the represented cluster size is set equal to the number of available observations in that cluster.

When covariates are supplied in a mixed design, they are used in both the small- and large-strata components. If the large-strata component cannot support the required treatment-by-stratum regressions, sreg() returns an error suggesting fewer covariates or X = NULL.

Value

An object of class sreg that is a list containing the following elements:

• tau.hat: a numeric vector of ATE estimates, one for each active treatment arm relative to control

• se.rob: a numeric vector of estimated standard errors

• t.stat: a numeric vector of test statistics

• p.value: a numeric vector of corresponding p-values

• CI.left, CI.right: numeric vectors containing the lower and upper endpoints of the 95% asymptotic confidence intervals

• as.CI: the confidence-interval endpoints combined as c(CI.left, CI.right)

• data: the data used for estimation, including the outcome, strata, treatment, and any supplied cluster or covariate variables

• lin.adj: the covariates used for linear adjustment, or NULL when no adjustment is used

• small.strata: a logical value recording the requested strata procedure

• HC1: a logical value recording whether the HC1 finite-sample correction was applied

• mixed.design: present and TRUE for mixed designs

• res.small, res.big: for mixed designs, the fitted sreg objects for the small- and large-strata components

Depending on the selected design, the object may additionally contain the estimated adjustment coefficients in ols.iter or beta.hat.

Author(s)

Authors:

Juri Trifonov jutrifonov@u.northwestern.edu

Yuehao Bai yuehao.bai@usc.edu

Azeem Shaikh amshaikh@uchicago.edu

Max Tabord-Meehan m.tabordmeehan@utoronto.ca

Maintainer:

Juri Trifonov jutrifonov@u.northwestern.edu

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.2201.13004.

Bai, Y., Jiang, L., Romano, J. P., Shaikh, A. M., and Zhang, Y. (2024). Covariate adjustment in experiments with matched pairs. Journal of Econometrics, 241(1), doi:10.1016/j.jeconom.2024.105740.

Bai, Y. (2022). Optimality of Matched-Pair Designs in Randomized Controlled Trials. American Economic Review, 112(12), doi:10.1257/aer.20201856.

Bai, Y., Romano, J. P., and Shaikh, A. M. (2022). Inference in Experiments With Matched Pairs. Journal of the American Statistical Association, 117(540), doi:10.1080/01621459.2021.1883437.

Liu, J. (2024). Inference for Two-stage Experiments under Covariate-Adaptive Randomization. doi:10.48550/arXiv.2301.09016.

Cytrynbaum, M. (2024). Covariate Adjustment in Stratified Experiments. Quantitative Economics, 15(4), 971–998, doi:10.3982/QE2475.

Examples

### Large strata with covariate adjustment
set.seed(1)
large_data <- sreg.rgen(
  n = 120, tau.vec = c(0.2, 0.5), n.strata = 4,
  cluster = FALSE
)
fit_large <- sreg(
  Y = large_data$Y, S = large_data$S, D = large_data$D,
  X = large_data[c("x_1", "x_2")]
)
fit_large$tau.hat
fit_large$se.rob

### Uniform triplets: k is observed and may be omitted from sreg()
set.seed(2)
small_data <- sreg.rgen(
  n = 60, tau.vec = c(0.2, 0.5), cluster = FALSE,
  small.strata = TRUE, k = 3, treat.sizes = c(1, 1, 1)
)
fit_small <- sreg(
  Y = small_data$Y, S = small_data$S, D = small_data$D,
  small.strata = TRUE
)
fit_small$tau.hat

### Mixed design with general k-tuples: specify k in sreg()
set.seed(3)
mixed_data <- sreg.rgen(
  n = 60, tau.vec = 0.5, cluster = FALSE,
  mixed.strata = TRUE, n.small = 40, k = 4,
  treat.sizes = c(2, 2), n.strata = 2
)
fit_mixed <- suppressWarnings(sreg(
  Y = mixed_data$Y, S = mixed_data$S, D = mixed_data$D,
  small.strata = TRUE, k = 4
))
fit_mixed$mixed.design

### Cluster-randomized design
set.seed(4)
cluster_data <- sreg.rgen(
  n = 24, tau.vec = 0.5, n.strata = 3, cluster = TRUE
)
fit_cluster <- sreg(
  Y = cluster_data$Y, S = cluster_data$S, D = cluster_data$D,
  G.id = cluster_data$G.id, Ng = cluster_data$Ng
)
fit_cluster$tau.hat

Generate a Pseudo-Random Sample under the Stratified Block Randomization Design

Description

The function generates the observed outcomes, treatment assignments, strata indicators, cluster indicators, cluster sizes, and covariates for estimating the treatment effect within the context of a stratified block randomization design under the covariate-adaptive randomization (CAR).

Usage

sreg.rgen(
  n,
  Nmax = 50,
  n.strata = 10,
  tau.vec = c(0),
  gamma.vec = c(0.4, 0.2, 1),
  cluster = TRUE,
  is.cov = TRUE,
  small.strata = FALSE,
  k = 3,
  treat.sizes = c(1, 1, 1),
  mixed.strata = FALSE,
  n.small = NULL,
  allocation.probs = NULL,
  stratum.effects = NULL,
  treatment.effects.by.stratum = NULL
)

Arguments

Value

A data.frame with one row per generated individual. Under individual-level assignment it contains n rows; under cluster-level assignment, n is the number of generated clusters and the number of rows equals the total number of individuals generated across those clusters. The returned columns are:

• Y: the observed outcome

• S: the stratum indicator

• D: the treatment indicator indexed by \{0, 1, 2, \ldots\}, where D = 0 denotes control

• G.id: the cluster indicator, included when cluster = TRUE

• Ng: the generated cluster size, included when cluster = TRUE

• x_1, x_2: generated covariate columns, included when is.cov = TRUE

Examples

### Large-strata individual-level design
set.seed(11)
large_data <- sreg.rgen(
  n = 80, tau.vec = 0.5, n.strata = 4, cluster = FALSE
)

### Uniform matched pairs
set.seed(12)
pair_data <- sreg.rgen(
  n = 40, tau.vec = 0.5, cluster = FALSE,
  small.strata = TRUE, k = 2, treat.sizes = c(1, 1)
)

### Mixed design with 4-tuples and large strata
set.seed(13)
mixed_data <- sreg.rgen(
  n = 60, tau.vec = 0.5, cluster = FALSE,
  mixed.strata = TRUE, n.small = 40, k = 4,
  treat.sizes = c(2, 2), n.strata = 2
)
sort(table(mixed_data$S))

### For cluster assignment, n counts clusters rather than observations
set.seed(14)
cluster_data <- sreg.rgen(
  n = 20, tau.vec = 0.5, n.strata = 2, cluster = TRUE
)
length(unique(cluster_data$G.id))