Meta-analytic methods of pooling correlation matrices for structural equation modeling under different patterns of missing data
MetadataShow full item record
This study compared the effects of different methods of synthesizing correlations for meta-analytic structural equation modeling (SEM) under various patterns of missingness on the estimation of correlation parameters and the resulting SEM parameters and fit indices. Univariate weighting methods for synthesizing correlations are frequently used. An alternative multivariate method for pooling correlation matrices involves using generalized least squares (GLS), where the dependencies of the correlations within the same matrix are taken into consideration (Becker, 1992). Since previous research has reported poor performance with GLS versus univariate weighting procedures, a revised GLS method, W-COV GLS, was used. Both the W-COV GLS procedure and univariate weighting were compared using correlations transformed with Fisher’s z versus untransformed correlations. There is frequently a problem when synthesizing correlation matrices due to the effects of missing data. One type of missing data scenario is the file-drawer problem (Rosenthal, 1979) in which a potential selection bias may occur whereby correlations that are non-significant are not reported. The performance of the different synthesis methods were assessed under different degrees and types of missingness including an approximation of the file-drawer problem using listwise and pairwise deletion to handle missing data. Results from this study indicated comparable performance of univariate weighting with the z transformation and W-COV GLS procedures, both with and without the transformation, for estimating the correlation parameters and ensuing parameters of the structural model. However, the W-COV GLS procedure performed slightly better in estimating the standard errors of the paths in the structural model and for the chi-squared test of data-model fit. When data were MCAR then there was almost no relative bias detected but when data were MNAR there were unacceptably high levels of relative bias in estimation of the correlation and SEM model parameters as well as high model rejection rates regardless of method used to synthesize correlations. Pairwise deletion resulted in higher incorrect rejection rates and larger bias in the standard error estimates for the SEM model than did listwise deletion. Inaccurate standard error estimates were found for several of the paths and attributed to the use of a correlation matrix with SEM.