Lasso adjustments of treatment effect estimates in randomized experiments
By Adam E. Bloniarz, Hanzhong Liu, Cun-Hui Zhang, Jasjeet S. Sekhon, Bin Yu. 2015
189 citations recorded by the source corpus.
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.
Subfields: Statistics and Probability
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Citations in the corpus
- The State of Applied Econometrics - Causality and Policy Evaluation (2016, neutral): “Some researchers have raised concerns with the regression approach in small samples (Freedman [2006, 2008], Young [2015], Athey and Imbens [2016], Imbens and Rubin [2015]), but generally such analyses are justified at least in large samples, even in settings with many covariates (Bloniarz et al. [20”
- Randomization Tests for Weak Null Hypotheses in Randomized Experiments (2018, methodology): “In fact, many parametric or non-parametric tests are approximations to the FRT (Eden and Yates 1933; Pitman 1937; Kempthorne 1952; Box and Andersen 1955; Collier and Baker 1966; Bradley 1968; Lehmann 1975). Another formulation of the FRT relies on exchangeability of outcomes under different treatmen”
- Regression-adjusted average treatment effect estimates in stratified randomized experiments (2019, methodology): “[5], we adjust the degrees of freedom.”
- Regression‐assisted inference for the average treatment effect in paired experiments (2016, background): “Bloniarz et al. (2016) describe related work with completely randomized experiments.”
- The Design of Field Experiments With Survey Outcomes: A Framework for Selecting More Efficient, Robust, and Ethical Designs (2017, background): “Baseline survey •Measures covariates at baseline capable of decreasing sampling variability and allowing theories with predictions for heterogeneous effects to be tested (Gerber and Green 2012; Bloniarz et al. 2016).”
- Covariate-adjusted Fisher randomization tests for the average treatment effect (2020, background): “It is of great interest to extend the theory to high dimensional settings (Bloniarz et al. 2016; Lei and Ding 2020), nonlinear models (Zhang et al.”
- A Survey on Causal Inference (2020, background): “les, are only predictive to the outcome, and some others might be irrelevant variables. Adjusting on the adjustment variables by Lasso, although it cannot reduce the bias, helps decrease the variance [17, 116]. While including the irrelevant variables would cause overfitting. Basedontheseparatenessa”
- Rerandomization and regression adjustment (2019, methodology): “It is interesting to extend the discussion to covariate adjustment in more complicated settings, such as high dimensional covariates (Bloniarz et al. 2016; Wager et al. 2016; Lei and Ding 2018), logistic regression for binary outcomes (Zhang et al.”