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Meta-Analytical SEM: Equivalence Between Maximum Likelihood and Generalized Least Squares

Author

Listed:
  • Ke-Hai Yuan

    (Nanjing University of Posts and Telecommunications University of Notre Dame)

  • Yutaka Kano

    (Osaka University)

Abstract

Meta-analysis plays a key role in combining studies to obtain more reliable results. In social, behavioral, and health sciences, measurement units are typically not well defined. More meaningful results can be obtained by standardizing the variables and via the analysis of the correlation matrix. Structural equation modeling (SEM) with the combined correlations, called meta-analytical SEM (MASEM), is a powerful tool for examining the relationship among latent constructs as well as those between the latent constructs and the manifest variables. Three classes of methods have been proposed for MASEM: (1) generalized least squares (GLS) in combining correlations and in estimating the structural model, (2) normal-distribution-based maximum likelihood (ML) in combining the correlations and then GLS in estimating the structural model (ML-GLS), and (3) ML in combining correlations and in estimating the structural model (ML). The current article shows that these three methods are equivalent. In particular, (a) the GLS method for combining correlation matrices in meta-analysis is asymptotically equivalent to ML, (b) the three methods (GLS, ML-GLS, ML) for MASEM with correlation matrices are asymptotically equivalent, (c) they also perform equally well empirically, and (d) the GLS method for SEM with the sample correlation matrix in a single study is asymptotically equivalent to ML, which has being discussed extensively in the SEM literature regarding whether the analysis of a correlation matrix yields consistent standard errors and asymptotically valid test statistics. The results and analysis suggest that a sample-size weighted GLS method is preferred for combining correlations and for MASEM.

Suggested Citation

  • Ke-Hai Yuan & Yutaka Kano, 2018. "Meta-Analytical SEM: Equivalence Between Maximum Likelihood and Generalized Least Squares," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 693-720, December.
    • Handle: RePEc:sae:jedbes:v:43:y:2018:i:6:p:693-720
    DOI: 10.3102/1076998618787799
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    References listed on IDEAS

    as
    1. Ke-Hai Yuan & Wai Chan, 2005. "On Nonequivalence of Several Procedures of Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 70(4), pages 791-798, December.
    2. De Leeuw, Jan, 1983. "Models and methods for the analysis of correlation coefficients," Journal of Econometrics, Elsevier, vol. 22(1-2), pages 113-137.
    3. Lee, Sik-Yum, 1985. "Analysis of covariance and correlation structures," Computational Statistics & Data Analysis, Elsevier, vol. 2(4), pages 279-295, February.
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