Effect size measures for mediation models: Quantitative strategies for communicating indirect effects.

TLDR

Mediation analysis is widely used to investigate causal processes, yet methods for conveying the magnitude and practical importance of indirect effects remain underdeveloped. This article sets out desiderata for effect‑size measures, reviews existing approaches, evaluates them against these criteria, and proposes new methods to better communicate mediation effect sizes. We introduce a residual‑based index that captures variance explained in both mediator and outcome, a second index that expresses the indirect effect as a proportion of its theoretical maximum, and provide user‑friendly R tools for numerical and visual presentation.

Abstract

The statistical analysis of mediation effects has become an indispensable tool for helping scientists investigate processes thought to be causal. Yet, in spite of many recent advances in the estimation and testing of mediation effects, little attention has been given to methods for communicating effect size and the practical importance of those effect sizes. Our goals in this article are to (a) outline some general desiderata for effect size measures, (b) describe current methods of expressing effect size and practical importance for mediation, (c) use the desiderata to evaluate these methods, and (d) develop new methods to communicate effect size in the context of mediation analysis. The first new effect size index we describe is a residual-based index that quantifies the amount of variance explained in both the mediator and the outcome. The second new effect size index quantifies the indirect effect as the proportion of the maximum possible indirect effect that could have been obtained, given the scales of the variables involved. We supplement our discussion by offering easy-to-use R tools for the numerical and visual communication of effect size for mediation effects.