On regression adjustments in experiments with several treatments

By David Freedman. 2008

189 citations recorded by the source corpus.

Regression adjustments are often made to experimental data. Since randomization does not justify the models, bias is likely; nor are the usual variance calculations to be trusted. Here, we evaluate regression adjustments using Neyman's nonparametric model. Previous results are generalized, and more intuitive proofs are given. A bias term is isolated, and conditions are given for unbiased estimation in finite samples.

Subfields: Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f3b190add98b24241be6249263909a7c8fe0e790

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Citations in the corpus

Regression Discontinuity Designs Using Covariates (2018, result): “rojections on the additional covariates. Remarkably, however, these results are in perfect agreement with those in the literature on analysis of experiments obtained using Neyman’s repeated sampling (Freedman, 2008; Lin, 2013), where it is also found that incorporating covariates in randomized contr”
In Pursuit of Balance: Randomization in Practice in Development Field Experiments (2008, unknown): “See Freedman (2008) and Deaton (2008) for further discussion.”
A paradox from randomization-based causal inference (2014, methodology): “Although linear regression has been criticized for analyzing experimental data (Freedman, 2008), the least square estimator β̂OLS = τ̂ is unbiased for the average causal effect τ .”
SHARP BOUNDS ON THE VARIANCE IN RANDOMIZED EXPERIMENTS (2014, methodology): “MR0448746 [3] Freedman, D. A. (2008).”
A Class of Unbiased Estimators of the Average Treatment Effect in Randomized Experiments (2013, methodology): “Freedman [6, 7, 36] rekindled interest in the design-based analysis of randomized experiments.”
Regression-adjusted average treatment effect estimates in stratified randomized experiments (2019, background): “[11] Freedman, D.”
High-dimensional regression adjustments in randomized experiments (2016, background): “…the number of samples grows to inﬁnity, it is now well-established that regression adjustments are always asymptotically helpful—even in misspeciﬁed models—provided we add full treatment-by-covariate interactions to the regression design and use robust standard errors [2, 3, 4, 5, 6, 7, 8, 9, 10].”
Contamination Bias in Linear Regressions (2021, unknown): “5The contamination bias issue is also distinct from the Freedman (2008a, 2008b) critique of regression to analyze randomized trials, which concerns estimation, not identification.”
General Forms of Finite Population Central Limit Theorems with Applications to Causal Inference (2016, methodology): “Although the simple difference-in-means estimator of the average causal effect is unbiased, carefully using the covariates often improves the efficiency (Freedman 2008a, b; Lin 2013).”
Revisiting regression adjustment in experiments with heterogeneous treatment effects (2020, background): “As mentioned in the introduction, both early [Neyman (1923) and Fisher (1935)] and recent [Freedman (2008a) Freedman (2008b) and Lin (2013)] approaches to estimating ATEs assume that the entire population is the sample.”
A Nonparametric Bayesian Analysis of Heterogenous Treatment Effects in Digital Experimentation (2014, methodology): “es and the response. This result provides some perspective on the recent controversy as to whether or not one should use covariates to adjust estimates of the ATE after a randomized controlled trial. Freedman (2008 a,b) provided an inﬂuential critique, arguing that the assumption of randomization is”
Opiates for the Matches: Matching Methods for Causal Inference (2009, background): “The regression standard errors can be severely biased, and the multiple regression estimator may have higher asymptotic variance than simply estimating Equation 3 (for details see Freedman 2008b,c).”
From Local to Global: External Validity in a Fertility Natural Experiment (2015, unknown): “The sampling and random assignment processes imply that (cid:2) τ ( 1 ) is statistically independent of (cid:2) τ 1 , and the within-context distribution is asymptotically normal and centered on τ ( 1 ) (Abadie et al. 2014; Freedman 2008; Lin 2013).”