Estimate ATE via design-based approach — design_based

This follows "Design-Based Ratio Estimators and Central Limit Theorems for Clustered, Blocked RCTs" by Peter Z. Schochet, Nicole E. Pashley, Luke W. Miratrix, and Tim Kautz.

Usage

design_based_estimators(
  formula,
  data = NULL,
  control_formula = NULL,
  weight = c("Person", "Cluster"),
  aggregated = FALSE,
  include_block_estimates = FALSE
)

Arguments

formula: Formula for outcome and treatment and nesting. If NULL, data is assumed to be in canonical form (see vignette for further discussion).
data: Data frame holding the outcome, treatment, and clustering/blocking columns referenced by `formula` (or already in canonical form if `formula` is NULL).
control_formula: What variables to control for, in the form of "~ X1 + X2".
weight: "Person" to weight the regression by individual (unweighted OLS), "Cluster" to weight so each cluster contributes equally (inverse cluster-size weights).
aggregated: TRUE means data is already aggregated (and in canonical form). FALSE means it is not.
include_block_estimates: If TRUE, also return the block-by-block estimates used to build the overall estimate, in addition to the aggregate estimate.

Value

tibble of estimates using different varieties of the methods described in the paper.

Details

It runs a weighted linear regression, as discussed in that paper. The paper discusses two possibilities: running on the aggregate, or running on the individual.

In this implementation, we run the regression on the cluster-aggregated data.

Degrees of freedom: this function receives already cluster-aggregated data, so every covariate in control_formula is, by construction, a cluster- (level 2) covariate. The degrees of freedom adjustment therefore uses number_controls(), which counts all covariates in control_formula. This is equivalent to counting level-2 covariates only, matching the technical supplement's benchmark degrees of freedom of J - K - g - 1 (g = number of level-2 covariates). Contrast with design_based_estimators_individual(), which works on individual-level data where control_formula may mix level-1 and level-2 covariates, and so explicitly uses number_level2_controls() to count only the level-2 ones.