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

Author

Listed:
  • Chiara Di Maria

    (University of Palermo)

  • Claudio Rubino

    (University of Palermo)

  • Alessandro Albano

    (University of Palermo
    Sustainable Mobility Center (Centro Nazionale per la Mobilità Sostenibile – CNMS))

Abstract

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.

Suggested Citation

  • Chiara Di Maria & Claudio Rubino & Alessandro Albano, 2024. "The derivative-based approach to nonlinear mediation models: insights and applications," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4383-4405, October.
    • Handle: RePEc:spr:qualqt:v:58:y:2024:i:5:d:10.1007_s11135-024-01860-7
    DOI: 10.1007/s11135-024-01860-7
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    References listed on IDEAS

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    1. Donald B. Rubin, 2005. "Causal Inference Using Potential Outcomes: Design, Modeling, Decisions," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 322-331, March.
    2. Marco Doretti & Martina Raggi & Elena Stanghellini, 2022. "Exact parametric causal mediation analysis for a binary outcome with a binary mediator," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 87-108, March.
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