A Simulation Study of Mediated Effect Measures.

Area of Science:

• Statistics
• Psychometrics
• Quantitative Psychology

Background:

• Mediation analysis is crucial for understanding indirect effects in various research fields.
• Accurate estimation of mediated effects, direct effects, and their ratios is essential for valid causal inference.
• Existing analytical solutions for variance and point estimators require rigorous evaluation across different conditions.

Purpose of the Study:

• To evaluate the accuracy of analytical solutions for estimating mediated effects and related metrics.
• To compare multivariate delta method and Taylor series expansions against empirical and theoretical standards.
• To determine the minimum sample sizes required for stable and reliable estimates of mediation parameters.

Main Methods:

• Conducted statistical simulations with 500 replications for eight sample sizes (N=10 to 5000).
• Utilized three normally distributed variables and 64 parameter combinations.
• Compared approximate solutions (delta method, Taylor series) with empirical standard deviations and theoretical standard errors.

Main Results:

• Standard error estimates for indirect effects were similar for N ≥ 50, except with dichotomized independent variables.
• Accurate point and variance estimates for the proportion mediated required N ≥ 500.
• Estimates for the ratio of mediated to non-mediated effects stabilized only at N ≈ 2000 for continuous variables.

Conclusions:

• Sample size significantly impacts the reliability of mediation effect estimation.
• Researchers should consider larger sample sizes (N ≥ 500-2000) for precise mediation analysis, particularly for proportion and ratio metrics.
• Findings have implications for designing experimental and nonexperimental studies employing mediation analysis.