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Department of Statistics, UCLA

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The Mediation Formula: A guide to the assessment of causal pathways in nonlinear models


Mediation analysis aims to uncover causal pathways along which changes are transmitted from stimulus to response. Recent advances in causal inference have given rise to a general and easy-to-use estimator for assessing the extent to which the effect of one variable on another is mediated by a third, thus setting a causally-sound standard for mediation analysis of empirical data. This estimator, called Mediation Formula, is applicable to nonlinear models with both discrete and continuous variables, and permits the evaluation of path-specific effects with minimal assumptions regarding the data-generating process. We demonstrate the use of the Mediation Formula in simple examples and illustrate why parametric methods of analysis yield distorted results, even when parameters are known precisely. We stress the importance of distinguishing between the necessary and sufficient interpretations of “mediated-effect” and show how to estimate the two components in systems with categorical variables, including logistic, probit, and nonparametric regressions.

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