Allowing for correlations between correlations in random-effects meta-analysis of correlation matrices

Area of Science:

• Psychology
• Statistics
• Behavioral Science

Background:

• Meta-analysis of correlation matrices often overlooks covariances between correlation estimates.
• Existing methods may not fully account for the complex relationships within correlation data.

Purpose of the Study:

• To evaluate methods for incorporating covariances between correlation estimates in meta-analysis.
• To assess the impact of accounting for these covariances on psychological research findings, specifically exercise behavior change prediction.

Main Methods:

• Exploration of generalized least squares, maximum marginal likelihood, and Bayesian approaches.
• Application to a 6-dimensional response dataset from psychological studies on exercise behavior.
• Simulation study to assess the validity of the asymptotic normal assumption.

Main Results:

• Accounting for correlations between correlations is unnecessary for individual correlation analyses.
• It is potentially important when analyzing composite measures involving multiple correlations.
• The asymptotic normal assumption appears reasonable based on simulation results.

Conclusions:

• Model-based approaches (maximum marginal likelihood or Bayesian) are recommended due to potential instability in generalized least squares methods.
• These advanced methods offer more robust analysis of correlation matrices in meta-analysis.
• The findings guide researchers in selecting appropriate meta-analytic techniques for correlation data.