Kees Jan van Garderen from the University of Amsterdam will present "Small Sample Corrected Augmented LR Test for Mediation"

Abstract  
This paper addresses testing for mediation when the low power problem near the origin is exacerbated by small sample size. The mediation effect q1q2 under the null of no mediation has a singularity when both coefficients are zero. Van Garderen and Van Giersbergen (2024) address this problem by augmenting the LR test in their g-test. We derive the exact distribution for the t-ratios and exploit this to adjust the augmentation region such that the size condition is also met in finite samples, not only asymptotically. The width of this new trapezoidal augmentation region is determined optimally. This new test is a-coherent, which permits p-values, show to be easily calculated. The test also applies when testing for moderation of the first- and second-stage of the causal graph. Simulations confirm power improvement and size control, even with non-normal errors and robustness is further confirmed using nonlinear models with binary outcomes.