Abstract
The process of performing meta-analytic structural equation modeling (MASEM) consists of two stages. First, correlation coefficients that have been gathered from studies have to be combined to obtain a pooled correlation matrix of the variables of interest. Next, a structural equation model can be fitted on this pooled matrix. Several methods are proposed to pool correlation coefficients. In this chapter, the univariate approach, the generalized least squares (GLS) approach, and the Two Stage SEM approach are introduced. The univariate approaches do not take into account that the correlation coefficients may be correlated within studies. The GLS approach has the limitation that the Stage 2 model has to be a regression model. Of the available approaches, the Two Stage SEM approach is favoured for its flexibility and good statistical performance in comparison with the other approaches.
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Notes
- 1.
I put an example of an analysis with two groups (studies) on my website (http://suzannejak.nl/masem) to illustrate the function of the D-matrices.
References
Becker, B. J. (1992). Using results from replicated studies to estimate linear models. Journal of Educational Statistics, 17, 341–362.
Becker, B. J. (1995). Corrections to “Using results from replicated studies to estimate linear models”. Journal of Educational Statistics, 20, 100–102.
Becker, B. J. (2000). Multivariate meta-analysis. In H. E. A. Tinsley & S. D. Brown (Eds.), Handbook of applied multivariate statistics and mathematical modeling (pp. 499–525). San Diego: Academic Press.
Becker, B. J. (2009). Model-based meta-analysis. In H. Cooper, L. V. Hedges, & J. C. Valentine (Eds.), The Handbook of Research Synthesis and Meta-analysis (pp. 377–398) (2nd ed.). New York: Russell Sage Foundation.
Becker, B. J., Fahrbach, K. (1994). A comparison of approaches to the synthesis of correlation matrices. In annual meeting of the American Educational Research Association, New Orleans, LA.
Beretvas, S. N., & Furlow, C. F. (2006). Evaluation of an approximate method for synthesizing covariance matrices for use in meta-analytic SEM. Structural Equation Modeling, 13, 153–185.
Boker, S., Neale, M., Maes, H., Wilde, M., Spiegel, M., Brick, T., et al. (2011). OpenMx: An open source extended structural equation modeling framework. Psychometrika, 76, 306–317.
Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37(1), 62–83.
Card, N. A. (2012). Applied meta-analysis for social science research. New York: Guilford.
Cheung, M. W.-L. (2015). MetaSEM: An R package for meta-analysis using structural equation modeling. Frontiers in Psychology, 5(1521). doi:10.3389/fpsyg.2014.01521
Cheung, M. W.-L., & Chan, W. (2005). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10, 40–64.
Cheung, M. W.-L., & Chan, W. (2009). A two-stage approach to synthesizing covariance matrices in meta-analytic structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 16(1), 28–53.
Cheung, S. F. (2000). Examining solutions to two practical issues in meta-analysis: Dependent correlations and missing data in correlation matrices. Unpublished doctoral dissertation, Chinese University of Hong Kong.
Corey, D. M., Dunlap, W. P., & Burke, M. J. (1998). Averaging correlations: Expected values and bias in combined Pearson rs and Fisher’s z transformations. The Journal of General Psychology, 125(3), 245–261.
Furlow, C. F., & Beretvas, S. N. (2005). Meta-analytic methods of pooling correlation matrices for structural equation modeling under different patterns of missing data. Psychological Methods, 10(2), 227–254.
Hafdahl, A. R., & Williams, M. A. (2009). Meta-analysis of correlations revisited: Attempted replication and extension of Field’s (2001) simulation studies. Psychological Methods, 14(1), 24–42. doi10.1037/a0014697
Hedges, L. V., & Olkin, I. (1985). Statistical models for meta-analysis. New York, NY: Academic Press.
Hunter, J. E., & Schmidt, F. L. (1990). Methods of meta-analysis. Correcting error and bias in research findings. Newbury Park, CA: Sage Publications.
Olkin, I., & Siotani, M. (1976). Asymptotic distribution of functions of a correlation matrix. In S. Ikeda, et al. (Eds.), Essays in probability and statistics. Tokyo: Shinko Tsusho Co., Ltd.
Oort, F. J. & Jak, S. (2015). Maximum likelihood estimation in meta-analytic structural equation modeling. doi:10.6084/m9.figshare.1292826
Schulze, R. (2004). Meta-analysis: A comparison of approaches. Toronto: Hogrefe & Huber Publishers.
Viswesvaran, C., & Ones, D. S. (1995). Theory testing: Combining psychometric meta-analysis and structural equations modeling. Personnel Psychology, 48(4), 865–885.
Wothke, W. (1993). Nonpositive definite matrices in structural modeling. In K. A. Bollen & J. S. Long (Eds.), Testing structural equation models (pp. 256–293). Newbury Park, CA: Sage.
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Jak, S. (2015). Methods for Meta-Analytic Structural Equation Modeling. In: Meta-Analytic Structural Equation Modelling. SpringerBriefs in Research Synthesis and Meta-Analysis. Springer, Cham. https://doi.org/10.1007/978-3-319-27174-3_2
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