title: Lasso adjustments of treatment effect estimates in randomized experiments.
abstract: We provide a principled way for investigators to analyze randomized experiments when the number of covariates is large. Investigators often use linear multivariate regression to analyze randomized experiments instead of simply reporting the difference of means between treatment and control groups. Their aim is to reduce the variance of the estimated treatment effect by adjusting for covariates. If there are a large number of covariates relative to the number of observations, regression may perform poorly because of overfitting. In such cases, the least absolute shrinkage and selection operator (Lasso) may be helpful. We study the resulting Lasso-based treatment effect estimator under the Neyman-Rubin model of randomized experiments. We present theoretical conditions that guarantee that the estimator is more efficient than the simple difference-of-means estimator, and we provide a conservative estimator of the asymptotic variance, which can yield tighter confidence intervals than the difference-of-means estimator. Simulation and data examples show that Lasso-based adjustment can be advantageous even when the number of covariates is less than the number of observations. Specifically, a variant using Lasso for selection and ordinary least squares (OLS) for estimation performs particularly well, and it chooses a smoothing parameter based on combined performance of Lasso and OLS.
authors.affiliation: Department of Statistics, University of California, Berkeley, CA 94720;
authors.forename: Adam
authors.initials: A
authors.lastname: Bloniarz
authors.affiliation: Department of Statistics, University of California, Berkeley, CA 94720;
authors.forename: Hanzhong
authors.initials: H
authors.lastname: Liu
authors.affiliation: Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ 08854;
authors.forename: Cun-Hui
authors.initials: CH
authors.lastname: Zhang
authors.affiliation: Department of Statistics, University of California, Berkeley, CA 94720; Department of Political Science, University of California, Berkeley, CA 94720;
authors.forename: Jasjeet S
authors.initials: JS
authors.lastname: Sekhon
authors.affiliation: Department of Statistics, University of California, Berkeley, CA 94720; Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720 binyu@stat.berkeley.edu.
authors.forename: Bin
authors.initials: B
authors.lastname: Yu
mesh_terms: D016032:Randomized Controlled Trials as Topic; D013223:Statistics as Topic; D016896:Treatment Outcome
keywords: Lasso; Neyman–Rubin model; average treatment effect; high-dimensional statistics; randomized experiment