Abstract

Meta-analytic structural equation modeling (MASEM) combines the ideas of meta-analysis and structural equation modeling for the purpose of synthesizing correlation or covariance matrices and fitting structural equation models on the pooled correlation or covariance matrix. Cheung and Chan (Psychological Methods 10:40–64, 2005b, Structural Equation Modeling 16:28–53, 2009) proposed a two-stage structural equation modeling (TSSEM) approach to conducting MASEM that was based on a fixed-effects model by assuming that all studies have the same population correlation or covariance matrices. The main objective of this article is to extend the TSSEM approach to a random-effects model by the inclusion of study-specific random effects. Another objective is to demonstrate the procedures with two examples using the metaSEM package implemented in the R statistical environment. Issues related to and future directions for MASEM are discussed.
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Abstract

Structural equation modeling (SEM) is widely used as a statistical framework to test complex models in behavioral and social sciences. When the number of publications increases, there is a need to systematically synthesize them. Methodology of synthesizing findings in the context of SEM is known as meta-analytic SEM (MASEM). Although correlation matrices are usually preferred in MASEM, there are cases in which synthesizing covariance matrices is useful, especially when the scales of the measurement are comparable. This study extends the 2-stage SEM (TSSEM) approach proposed by M. W. L. Cheung and Chan (2005b) to synthesizing covariance matrices in MASEM. A simulation study was conducted to compare the TSSEM approach with several approximate methods. An empirical example is used to illustrate the procedures and future directions for MASEM are discussed.
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Abstract

To synthesize studies that use structural equation modeling (SEM), researchers usually use Pearson correlations (univariate r), Fisher z scores (univariate z), or generalized least squares (GLS) to combine the correlation matrices. The pooled correlation matrix is then analyzed by the use of SEM. Questionable inferences may occur for these ad hoc procedures. A 2-stage structural equation modeling (TSSEM) method is proposed to incorporate meta-analytic techniques and SEM into a unified framework. Simulation results reveal that the univariate-r, univariate-z, and TSSEM methods perform well in testing the homogeneity of correlation matrices and estimating the pooled correlation matrix. When fitting SEM, only TSSEM works well. The GLS method performed poorly in small to medium samples.
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Abstract

There has been a significant increase in the usage of structural equation modeling (SEM) as the prime analysis technique in these few decades. To synthesize the studies for SEM, researchers usually employ meta-analytic procedures with Hunter-Schmidt (H-S) approach (Hunter & Schmidt, 1990), Hedges-Olkin (H-O) approach (Hedges & Olkin, 1985) or generalized least squares (GLS) approach (Becker, 1992) on correlation matrices. The synthesized correlation matrix is subjected to the analysis of SEM. Hunter-Schmidt and Hedges-Olkin approaches have several potential problems: (a) the resultant correlation matrix is nonpositive definite because of the pairwise aggregation of correlation coefficients in the presence of missing data; (b) the arbitrary choice of sample size (median, total, arithmetic or geometric means) in fitting SEM makes the chi-square statistics and standard errors incorrect; (c) treating correlation matrix as covariance matrix makes the statistical inferences questionable. In response to these problems, a framework on conducting meta-analytic structural equation modeling was proposed. In the first part, a two-stage structural equation modeling (TSSEM) approach based on the multiple-group and correlation analyses was proposed as the analysis technique. The empirical performance of TSSEM against H-S, H-O and GLS were assessed by simulation studies. Results revealed that H-S, H-O and TSSEM performed very well in testing the homogeneity of correlation matrices and estimating the pooled correlation matrix when the rejection counts and parameter estimates of GLS were over-estimated. When fitting SEM, however, the chi-square test statistics of H-S, H-O and GLS approaches were over-estimated while their standard errors were under-estimated. The TSSEM worked well in most conditions. In the second part, cluster analytic procedures were proposed to group correlation matrices into homogenous groups when the correlation matrices were heterogeneous. Simulation studies showed that the Euclidian distance as the proximity matrix and Ward's minimum variance method as the clustering method performed the best. A real example was used to illustrate how to apply these procedures on real data set. Future directions for research would also be discussed.
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Abstract

To assess how culture influences the behavior of people, multilevel models are an immediate choice for modeling the relationship at the levels of the individual and culture. The authors propose structural equation modeling (SEM) to test the universality of psychological processes at the individual and culture levels. Specifically, the structural equivalence of the measurement (where the instrument is measuring the same construct across countries) is first tested with meta-analytic SEM. If the measurement is structurally equivalent, cross-level equivalence (where the instrument is measuring similar constructs at different levels) will then be tested with multilevel SEM. A large data set on social axioms with 7,590 university students from 40 cultural groups was used to illustrate the procedures. The results showed that the structural equivalence of the social axioms was well supported at the individual level across 40 cultural groups, whereas the cross-level equivalence was partially supported. The superiority of the SEM approach and the theoretical meaning of its solution are discussed.
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