Rerandomization to Balance Tiers of Covariates

Morgan, Kari Lock; Rubin, Donald B.

doi:10.1080/01621459.2015.1079528

Cited by 75 publications

(66 citation statements)

References 11 publications

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“…For the design, we focused on rerandomization using the Mahalanobis distance. It is conceptually straightforward to extend the results to rerandomization with tiers of covariates (Morgan and Rubin, ; Li et al ., ). Recently, Zhou et al .…”

Section: Discussionmentioning

confidence: 99%

Rerandomization and Regression Adjustment

Ding

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Randomization is a basis for the statistical inference of treatment effects without strong assumptions on the outcome‐generating process. Appropriately using covariates further yields more precise estimators in randomized experiments. R. A. Fisher suggested blocking on discrete covariates in the design stage or conducting analysis of covariance in the analysis stage. We can embed blocking in a wider class of experimental design called rerandomization, and extend the classical analysis of covariance to more general regression adjustment. Rerandomization trumps complete randomization in the design stage, and regression adjustment trumps the simple difference‐in‐means estimator in the analysis stage. It is then intuitive to use both rerandomization and regression adjustment. Under the randomization inference framework, we establish a unified theory allowing the designer and analyser to have access to different sets of covariates. We find that asymptotically, for any given estimator with or without regression adjustment, rerandomization never hurts either the sampling precision or the estimated precision, and, for any given design with or without rerandomization, our regression‐adjusted estimator never hurts the estimated precision. Therefore, combining rerandomization and regression adjustment yields better coverage properties and thus improves statistical inference. To quantify these statements theoretically, we discuss optimal regression‐adjusted estimators in terms of the sampling precision and the estimated precision, and then measure the additional gains of the designer and the analyser. We finally suggest the use of rerandomization in the design and regression adjustment in the analysis followed by the Huber–White robust standard error.

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Section: Discussionmentioning

confidence: 99%

Rerandomization and Regression Adjustment

Ding

2019

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Although the balance criterion in Step (2) can be general, Morgan and Rubin (2012) suggested using the Mahalanobis distance between covariate means in treatment and control groups, and Morgan and Rubin (2015) suggested considering tiers of covariates according to their presumed importance in predicting the outcomes in this experiment. We will discuss these two types of rerandomization in detail, and apposite statistical inference after these rerandomizations as implied by Step (6).…”

Section: Covariate Imbalance and Rerandomizationmentioning

confidence: 99%

Asymptotic theory of rerandomization in treatment–control experiments

Ding

Rubin

2018

Proc. Natl. Acad. Sci. U.S.A.

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186

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Although complete randomization ensures covariate balance on average, the chance of observing significant differences between treatment and control covariate distributions increases with many covariates. Rerandomization discards randomizations that do not satisfy a predetermined covariate balance criterion, generally resulting in better covariate balance and more precise estimates of causal effects. Previous theory has derived finite sample theory for rerandomization under the assumptions of equal treatment group sizes, Gaussian covariate and outcome distributions, or additive causal effects, but not for the general sampling distribution of the difference-in-means estimator for the average causal effect. We develop asymptotic theory for rerandomization without these assumptions, which reveals a non-Gaussian asymptotic distribution for this estimator, specifically a linear combination of a Gaussian random variable and truncated Gaussian random variables. This distribution follows because rerandomization affects only the projection of potential outcomes onto the covariate space but does not affect the corresponding orthogonal residuals. We demonstrate that, compared with complete randomization, rerandomization reduces the asymptotic quantile ranges of the difference-in-means estimator. Moreover, our work constructs accurate large-sample confidence intervals for the average causal effect.

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“…Therefore, it is necessary to deal with different combinations of estimators and re‐randomization schemes. One approach to this problem is to ask researchers for the analytic solutions of each used combination of estimator and re‐randomization scheme, à la Morgan and Rubin (, ). However, a method that can be used for a wide family of estimators and re‐randomization schemes would be much more useful.…”

Section: Introductionmentioning

confidence: 99%

“…Morgan and Rubin () develop a similar paper for re‐randomization based on the balance of certain variables.…”

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confidence: 99%

Tools for Re‐randomization

Lara

2019

Bulletin of Econ Res

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With the rising popularity of field experiments in economics, re‐randomization schemes have emerged as tools to induce balance in observable variables across treatment groups. However, re‐randomization is not fully understood and the methodologies to estimate its effects on the distribution of parameters are still under‐developed. This paper helps to close that gap by suggesting an asymptotically normal re‐randomization scheme and bootstrapping procedure to carry inference under a wide range of estimators and re‐randomization schemes.

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Rerandomization to Balance Tiers of Covariates

Cited by 75 publications

References 11 publications

Rerandomization and Regression Adjustment

Rerandomization and Regression Adjustment

Asymptotic theory of rerandomization in treatment–control experiments

Tools for Re‐randomization

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