A systematic framework for defining R-squared measures in mediation analysis.

Abstract

R-squared measures of explained variance are easy to understand, naturally interpretable, and widely used by substantive researchers. In mediation analysis, however, despite recent advances in measures of mediation effect, few effect sizes have good statistical properties. Also, most of these measures are only available for the simplest three-variable mediation model, especially for R 2 -type measures. By decomposing the mediator into two parts (i.e., the part related to the predictor and the part unrelated to the predictor), this article proposes a systematic framework to develop new effect-size measures of explained variance in mediation analysis. The framework can be easily extended to more complex mediation models and provides more delicate R 2 measures for empirical researchers. A Monte Carlo simulation study is conducted to examine the statistical properties of the proposed R 2 effect-size measure. Results show that the new R 2 measure performs well in approximating the true value of the explained variance of the mediation effect. The use of the proposed measure is illustrated with empirical examples together with program code for its implementation.

Signal-to-Noise Ratio in Estimating and Testing the Mediation Effect: Structural Equation Modeling versus Path Analysis with Weighted Composites

“…Because the reliabilities of composites are positively related to the SNR of the indirect effect and the coefficient of determination (R 2 ) for the regression models in Eq. ( 7), we suspect that other effect size measures in mediation analysis (e.g., Fairchild et al, 2009;Liu et al, 2024;MacKinnon, 2008;Lachowicz et al, 2018;Preacher & Kelley, 2011) also benefit from the use of the Bartlett-or regression-factor scores.…”

“…This is typically done by a null-hypothesis statistical test (NHST) for the indirect effect of the predictor on the outcome variable via the mediator, or by using the confidence interval (CI) approach to inference (MacKinnon et al, 2002;Shrout & Bolger, 2002) . Other approaches of quantifying mediation effects also exist (e.g., Fairchild et al, 2009;Lachowicz, Preacher & Kelley, 2018;Liu et al, 2024;Preacher & Kelley, 2011). The focus of this article is on the SNR for estimating the indirect effect.…”

A sensitivity analysis for temporal bias in cross-sectional mediation.

“…3These effect sizes were determined using partial correlations—see MacKinnon et al (2002) for more detail. Also note that there are several possible effect size measures for mediation (i.e., MacKinnon, 2008; Miočević et al, 2018), including a recently developed R 2 -based effect size (H. Liu et al, 2023).…”