The LOOP Estimator: Adjusting for Covariates in Randomized Experiments

Friday July 13, 2pm, Carslaw 829

Johann Gagnon-Bartsch
University of Michigan, Department of Statistics

The LOOP Estimator: Adjusting for Covariates in Randomized Experiments

When conducting a randomized controlled trial, it is common to specify in advance, as part of the trial protocol, the statistical analyses that will be used to analyze the data. Typically these analyses will involve adjusting for small imbalances in baseline covariates. However, this poses a dilemma, since adjusting for too many covariates can hurt precision more than it helps, and it is often unclear which covariates are predictive of outcome prior to conducting the experiment. For example, both post-stratification and OLS regression adjustments can actually increase variance (relative to a simple difference in means) if too many covariates are used. OLS is also biased under the Neyman-Rubin model. Here we introduce the LOOP ("Leave-One-Out Potential outcomes") estimator of the average treatment effect. We leave out each observation and then impute that observation's treatment and control potential outcomes using a prediction algorithm, such as a random forest. This estimator is exactly unbiased under the Neyman-Rubin model, generally performs at least as well as the unadjusted estimator, and the experimental randomization largely justifies the statistical assumptions made. Importantly, the LOOP estimator also enables us to take advantage of automatic variable selection, and thus eliminates the guess work of selecting covariates prior to conducting the trial.

Johann Gagnon-Bartsch is an Assistant Professor of Statistics in the Department of Statistics at the University of Michigan. Gagnon-Bartsch received his bachelor’s degree from Stanford University with majors in Math, Physics, and International Relations. He completed a PhD at Berkeley in Statistics, and then spent three more years as a visiting assistant professor in the Berkeley Statistics department. Gagnon-Bartsch’s research focuses on causal inference, machine learning, and nonparametric methods with applications in the biological and social sciences.