Abstract
BackgroundIn the first stage of meta-analytic structural equation modeling (MASEM), researchers synthesized studies using univariate meta-analysis (UM) and multivariate meta-analysis (MM) approaches. The MM approaches are known to be of better performance than the UM approaches in the meta-analysis with equal sized studies. However in real situations, where the studies might be of different sizes, the empirical performance of these approaches is yet to be studied in the first and second stages of MASEM. The present study aimed to evaluate the performance of the UM and MM methods, having unequal sample sizes in different primary studies. Testing the homogeneity of correlation matrices and the empirical power, estimating the pooled correlation matrix and also, estimating parameters of a path model were investigated using these approaches by simulation.ResultsThe results of the first stage showed that Type I error rate was well under control at 0.05 level when the average sample sizes were 200 or more, irrespective of the types of the methods or the sample sizes used. Moreover, the relative percentage biases of the pooled correlation matrices were also lower than 2.5% for all methods. There was a dramatic decrease in the empirical power for all synthesis methods when the inequality of the sample sizes was increased. In fitting the path model at the second stage, MM methods provided better estimation of the parameters.ConclusionsThis study showed the different performance of the four methods in the statistical power, especially when the sample sizes of primary studies were highly unequal. Moreover, in fitting the path model, the MM approaches provided better estimation of the parameters.
Highlights
In the first stage of meta-analytic structural equation modeling (MASEM), researchers synthesized studies using univariate meta-analysis (UM) and multivariate meta-analysis (MM) approaches
In two-stage structural equation modeling (TSSEM) approach, correlations are pooled by multiple group SEM techniques at stage one and the pooled matrix is used for the analysis of SEM in the second stage
Results of stage 2 Table 4 summarizes the results of Chi square test statistics and their standard deviations for evaluation of model fit of four methods in all conditions of sample sizes
Summary
In the first stage of meta-analytic structural equation modeling (MASEM), researchers synthesized studies using univariate meta-analysis (UM) and multivariate meta-analysis (MM) approaches. In real situations, where the studies might be of different sizes, the empirical performance of these approaches is yet to be studied in the first and second stages of MASEM. Univariatez (UNIz) and Univariate-r (UNIr), introduced by Hedges and Olkin [9] and Hunter and Schmidt [10], are the most popularly used UM techniques in MASEM researches. These approaches synthesize correlation matrices among k studies by taking the weighted average of correlation, ri. One problem associated with these approaches is that they fail to take into account the dependencies between correlations This can cause a bias estimation of the pooled correlation matrix [11]. In TSSEM approach, correlations are pooled by multiple group SEM techniques at stage one and the pooled matrix is used for the analysis of SEM in the second stage
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