One Step at a Time: A Statistical Approach for Distinguishing Mediators, Confounders, and Colliders using Direction Dependence Analysis (DDA)
Dexin Shi, Amanda Jane Fairchild, Wolfgang Wiedermann · 2023
In observational data, understanding the causal link when estimating the causal effect of an independent variable (x) on a dependent variable (y) often requires researchers to identify the role of a third variable in the x → y relationship. Mediation, confounding, and colliding are three key third-variable effects that yield different theoretical and methodological implications for drawing causal inferences. Commonly used covariance-based statistical methods, such as linear regression and structural equation modeling, cannot distinguish these effects in practice, however. In this study, we introduce a statistical approach for distinguishing mediators, confounders, and colliders that uses higher-order moment information from the data. We propose a two-step procedure that uses the Hilbert-Schmidt Independence Criterion (HSIC) within the Direction Dependence Analysis (DDA) framework. Results from Monte Carlo simulations show that our proposed approach accurately recovers the true data-generating process of the third variable. We provide an empirical example to demonstrate the application of our proposed approach in psychological research. Finally, we discuss implications and future directions of our work.