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Meta-regression with categorical moderators and dependent effect sizes: A simulation study.

Belén Fernández-Castilla1, José Antonio López-López2,3, María Rubio-Aparicio2

  • 1Department of Methodology of Health and Behavioral Sciences, Faculty of Psychology, https://ror.org/02msb5n36Universidad Nacional de Educación a Distancia, Spain.

Research Synthesis Methods
|May 14, 2026
PubMed
Summary
This summary is machine-generated.

This meta-regression simulation found that combining three-level models with robust variance estimation (RVE) offers the best balance for detecting categorical moderators in meta-analyses, especially with unbalanced effect size distributions.

Keywords:
dependent effect sizesmultilevel modelspowerrobust variance estimationsimulationType I error

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Area of Science:

  • Statistics
  • Meta-analysis
  • Psychometrics

Background:

  • Categorical moderators are frequently analyzed in meta-analysis using meta-regression.
  • Handling multiple effect sizes within studies requires advanced meta-regression techniques.
  • Existing methods include multivariate models, three-level models, and correlated-effects models with robust variance estimation (RVE).

Purpose of the Study:

  • To compare the performance of various meta-regression methods when dealing with categorical moderators and multiple effect sizes.
  • To evaluate methods such as three-level models, correlated-effects models with RVE, and correlated-effects models with RVE and cluster wild bootstrapping (CWB).
  • To assess method performance under different simulation conditions, including moderator type and effect size distribution balance.

Main Methods:

  • A simulation study generated Cohen's d values under a multivariate model.
  • A binary moderator variable was incorporated, representing either study-level or effect size-level characteristics.
  • Simulated factors included the number of studies, number of outcomes per study, and moderator distribution balance; methods were compared for bias, Type I error, and power.

Main Results:

  • All methods showed reduced power when the moderator was study-level and the effect size distribution was highly unbalanced.
  • Robust variance estimation (RVE)-based methods controlled Type I error but were often overconservative.
  • Three-level models offered higher power but resulted in inflated Type I error rates.

Conclusions:

  • A combination of three-level models and robust variance estimation (RVE) provided the optimal balance between Type I error control and statistical power.
  • Method performance is sensitive to the nature of the moderator (study-level vs. effect size-level) and the distribution of effect sizes.
  • Careful selection of meta-regression techniques is crucial for accurate moderator analysis in meta-analysis.