On Estimating Causal Mediation Effects from a Single Regression Equation
Saunders, Christina Tripp
Mediation modeling is prevalent in the biomedical and social sciences. This work describes a novel framework for mediation analysis that yields closed-form expressions for mediation effects and uncertainty estimates, accommodates flexible modeling, and increases computational efficiency. The first paper describes a classical regression framework for estimating causal mediation effects from the fit of a single regression equation, rather than from the traditional system of three equations. The vector of changes in exposure pathway coefficients, which we named the ``essential mediation components" (EMCs), is used to estimate mediation effects. Since the portion eliminated (and in several settings, the indirect effect) is a simple function of the EMCs, the analytical expression for its model-based variance follows directly. Importantly, requiring the fit of just one equation permits the use of a rich suite of analytical tools that are not as easily implemented on a system of equations. The second paper extends the approach to non-nested mediation systems and complex behavioral research hypotheses, including models with multiple mediators, interactions, and nonlinearities. We show how to visualize mediation effects and measure joint mediation. Further, we note that even under a linear model, the difference and product of coefficients approaches do not always yield the same total effect estimate. The third paper considers extensions of the new framework to generalized linear models and examines its implications. Using a large-scale example from genetic epidemiology, we compare the single-model approach to existing methods. This new framework imparts substantial gains in computational efficiency and meaningful insight into the formation and evaluation of complex mediation hypotheses.