Statistical Mediation Analysis in Regression Discontinuity Design for Causal Inference

Regression discontinuity designs (RDDs) are the most robust quasi-experimental design, but current statistical models are limited to estimates for the simple causal relationship between only two variables: the independent and dependent variables. In practice, intervening variables (or mediators) are often observed as part of the causal chain. Mediators explain the why and how a treatment or intervention works. Therefore, mediation and RDD analysis combined can be a useful tool in identifying key components or processes that make intervention programs effective while making causal inferences for improving student achievement, despite natural constraints, limitations, and ethical considerations. Without an integrated framework of assumptions for conducting mediation analysis within RDDs, researchers are more susceptible to making incorrect causal inferences. Therefore, this study includes an integrated framework for conducting mediation analysis in RDD to facilitate rigorous causal inferences despite constraints in applied research settings. Secondary data analysis using the Head Start Impact Study (HSIS) compared results between a randomized controlled trial (RCT) and synthetic RD data set. A Monte Carlo simulation study was conducted to determine performance and statistical validity of mediation in RDD under varying conditions. Two main assumptions necessary for drawing correct causal inferences are the independence assumption and SUTVA. Results from the secondary data analysis showed that RDD estimates are more often smaller than their RCT counterparts. Additionally, 95% confidence intervals (CIs) constructed for RDD estimates made opposite significance conclusions than the RCT estimates. The simulation study revealed that type I error rate and power for all mediation effects were within or reached the robustness criteria, but bias and coverage were more often outside the robustness range. Imbalance provided a more thorough understanding of where the true effect was landing in comparison to the CIs. The findings of this study serve to inform future research practice by providing researchers guidelines for making valid causal inferences under identified conditions and identifying causal mechanisms in programs to increase what is working and reduce ineffective components. Advisors: James A. Bovaird & Lorey A. Wheele