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Combining Correlation Matrices: Simulation Analysis of Improved Fixed-Effects Methods

University of Missouri–Columbia

The originally proposed multivariate meta-analysis approach for correlation matrices—analyze Pearson correlations, with each study’s observed correlations replacing their population counterparts in its conditional-covariance matrix—performs poorly. Two refinements are considered: Analyze Fisher Z-transformed correlations, and substitute better estimates of correlations in the conditional covariances. Fixed-effects methods with and without each refinement were examined in a Monte Carlo study; number of studies and the distribution of within-study sample sizes were varied. Both refinements improved element-wise point and interval estimates, as well as Type I error control for homogeneity tests, especially with many small studies. Practical recommendations and suggestions for future methodological work are offered. An appendix describes how to transform Fisher-Z (co)variances to the Pearson-r metric.

Key Words: meta-analysis; correlation; generalized least squares; Monte Carlo study

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