Evaluation of an Approximate Method for Synthesizing Covariance Matrices for Use in Meta-Analytic SEM

Meta-analytic structural equation modeling (MA-SEM) is increasingly being used to assess model-fit for variables' interrelations synthesized across studies. MA-SEM researchers have analyzed synthesized correlation matrices using structural equation modeling (SEM) estimation that is designed for covariance matrices. This can produce incorrect model-fit chi-square statistics, standard error estimates (Cudeck, 1989), or both for parameters that are not scale free or that describe a scale-noninvariant model unless corrected SEM estimation is used to analyze the correlations. This study introduced univariate and multivariate approximate methods for synthesizing covariance matrices for use in MA-SEM. A simulation study assessed the approximate methods by estimating parameters in a scale-noninvariant model using synthesized covariances versus synthesized correlations with and without the appropriate corrections. Standard error bias was noted only for uncorrected analyses of pooled correlations. Chi-square model-fit statistics were overly conservative except when covariance matrices were analyzed. Benefits and limitations of this approximate method are presented and discussed.