The derivative-based approach to nonlinear mediation models: insights and applications

Traditional mediation analysis has been developed in the context of linear models, enabling the estimation of indirect effects through the product of regression coefficients. However, in the presence of nonlinearities, defining and estimating indirect effects becomes more challenging. While nonlinear mediation models are relatively easy to address in the counterfactual-based framework, very few generalizations to nonlinear associational settings have been proposed. One of the most intuitive is the derivative-based approach that, however, seems not to be widely spread among scholars. In this paper, we deepen such an approach to nonlinear mediation models, clarifying and proposing solutions to some issues which have not been addressed by the previous literature. Specifically, we discussed discrete exposures, binary mediators and extensions of this approach to more complex settings like the multilevel one. We also propose to estimate confidence intervals for the indirect effect within a Bayesian framework and compare its performance to that of other approaches in the literature through a simulation study. Finally, a real data application is presented.