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

Hongyun Liu1, Ke-Hai Yuan2, Hui Li1

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This study introduces a new framework for calculating explained variance in mediation analysis, offering improved R-squared measures. These novel effect sizes are statistically robust and applicable to complex models, aiding researchers in quantifying mediation effects.

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Area of Science:

  • Psychometrics
  • Statistical Modeling
  • Quantitative Psychology

Background:

  • R-squared measures are widely used for explained variance but lack robust statistical properties in mediation analysis.
  • Existing effect size measures for mediation are often limited to simple models and may not be R-squared based.

Purpose of the Study:

  • To propose a systematic framework for developing new R-squared effect-size measures in mediation analysis.
  • To extend explained variance measures beyond the basic three-variable mediation model.
  • To offer statistically sound and interpretable effect sizes for mediation.

Main Methods:

  • Decomposing the mediator into predictor-related and unrelated components.
  • Developing a novel R-squared effect-size measure based on this decomposition.
  • Conducting a Monte Carlo simulation to evaluate the measure's statistical properties.

Main Results:

  • The proposed R-squared measure effectively approximates the true explained variance of the mediation effect.
  • The framework allows for the development of more nuanced R-squared measures.
  • The new measure demonstrates good statistical properties in simulations.

Conclusions:

  • The new framework provides a valuable tool for quantifying explained variance in mediation analysis.
  • The proposed R-squared effect size measure is a statistically sound and practical advancement.
  • This approach enhances the analysis of mediation in both simple and complex models.