Estimate ATE via Middleton & Aronow unbiased approach — middleton_aronow

This follows Middleton, J. A., & Aronow, P. M. (2015). Unbiased Estimation of the Average Treatment Effect in Cluster-Randomized Experiments. 6(1–2), 312. doi: 10.1515/spp-2013-0002

Usage

middleton_aronow_estimator(
  formula,
  data = NULL,
  control_formula = NULL,
  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".
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

They introduce a Raj Difference estimator that is an extension of a Horvitz-Thompson estimator where, in effect, we divide the sum of the outcomes by a fixed constant rather than the realized sample size to avoid biasing our estimate.

Note that the control_formula is ignored–these estimators do not adjust for additioanl controls at this time.