Tyranny-of-the-Minority Regression Adjustment in Randomized Experiments

Abstract

Regression adjustment is widely used in the analysis of randomized experiments to improve the estimation efficiency of the treatment effect. This article reexamines a weighted regression adjustment method termed tyranny-of-the-minority (ToM), wherein units in the minority group are given greater weights. We demonstrate that ToM regression adjustment is more robust than Lin’s regression adjustment with treatment-covariate interactions, even though these two regression adjustment methods are asymptotically equivalent in completely randomized experiments. Moreover, ToM regression adjustment can be easily extended to stratified randomized experiments and completely randomized survey experiments. We obtain the design-based properties of the ToM regression-adjusted average treatment effect estimator under such designs. In particular, we show that the ToM regression-adjusted estimator improves the asymptotic estimation efficiency compared to the unadjusted estimator, even when the regression model is misspecified, and is optimal in the class of linearly adjusted estimators. We also study the asymptotic properties of various heteroscedasticity-robust standard errors and provide recommendations for practitioners. Simulation studies and real data analysis demonstrate ToM regression adjustment’s superiority over existing methods. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.