DAE 2024 - Session I

Session I (May 15, 8:30am-10:00am): Causal Inference and Experimental Design, organized by Tirthankar Dasgupta

Title: A Unified Framework for Rerandomization using Quadratic Forms
Speaker: Kyle Schindl, Carnegie Mellon University
Abstract: When designing a randomized experiment, one way to ensure treatment and control groups exhibit similar covariate distributions is to randomize treatment until some prespecified level of covariate balance is satisfied; this strategy is known as rerandomization. Most rerandomization methods utilize balance metrics based on a quadratic form \mathbf{v}^T \mathbf{A v}, where \mathbf{v} is a vector of covariate mean differences and \mathbf{A} is a positive semi-definite matrix. In this work, we derive general results for treatment-versus-control rerandomization schemes that employ quadratic forms for covariate balance. In addition to allowing researchers to quickly derive properties of rerandomization schemes not previously considered, our theoretical results provide guidance on how to choose the matrix \mathbf{A} in practice. We find the Mahalanobis and Euclidean distances optimize different measures of covariate balance. Furthermore, we establish how the covariates' eigenstructure and their relationship to the outcomes dictates which matrix \mathbf{A} yields the most precise mean-difference estimator for the average treatment effect. We find the Euclidean distance is minimax optimal, in the sense that the mean-difference estimator's precision is never too far from the optimal choice. Our theoretical results are verified via simulation, where we find that using the Euclidean distance typically achieves greater variance reduction than other quadratic forms.

Title: Improving Instrumental Variable Estimators with Post-stratification
Speaker: Nicole Pashley, Rutgers University
Abstract: Experiments studying get-out-the-vote (GOTV) efforts estimate the causal effect of various mobilization efforts on voter turnout. However, there is often substantial noncompliance in these studies. A usual approach is to use an instrumental variable (IV) analysis to estimate impacts for compliers, here being those actually contacted by the investigators. Unfortunately, popular IV estimators can be unstable in studies with a small fraction of compliers. This talk will explore post-stratification of the data using variables that predict complier status (and, potentially, the outcome) to mitigate this. The benefits of post-stratification in terms of bias, variance, and improved standard error estimates will be presented, along with a finite-sample asymptotic variance formula. Comparisons of the performance of different IV approaches will be made, with discussion of the advantages of our design-based post-stratification approach over incorporating compliance-predictive covariates into the two-stage least squares estimator. The benefits of our approach will be demonstrated in two GOTV applications.

Title: Kernel Discrepancy-Based Rerandomization for Controlled Experiments
Speaker: Lulu Kang, University of MA, Amherst
Abstract: Controlled experiments have been widely used in various disciplines for causal inference. Rerandomization has been proposed and advocated to improve the covariates balance. One key component in rerandomization is the balance criterion. In this article, we introduce the kernel discrepancy between the empirical distributions of the covariates in different treatment groups and show that it the upper bound of the variance of difference-in-mean estimator of the treatment effects. Accordingly, we propose using kernel discrepancy as a balance criterion. Using linear kernel function, we obtain the distribution of the kernel discrepancy for finite samples, which provides the critical value for an acceptable rerandomization. For more complicated kernel functions, we propose using empirical distributions of the kernel discrepancy to obtain the critical value. The kernel discrepancy has many merits. First, it is model-free and suitable to both continuous and categorical covariates data. Furthermore, the discrepancy-based criterion is model-free and thus makes the estimation of the treatment effect(s) robust to the model assumptions. More importantly, the proposed design is applicable to both continuous and categorical response measurements. Through simulation study and a real example, we show that the proposed design approach achieves accurate estimation even if the model assumption is not correct.