Skip to main content

Heterogeneity

  • Chapter
  • First Online:
Meta-Analytic Structural Equation Modelling

Part of the book series: SpringerBriefs in Research Synthesis and Meta-Analysis ((BRIEFSSYNTHES))

Abstract

Fixed effects models assume that all differences between correlation coefficients are due to sampling fluctuations, and do not allow inference beyond the studies included in the meta-analysis. Random effects models are more appropriate when researchers wish to make more general statements. Differences between studies’ coefficients may occur for other reasons than sampling, for example because other measurement instruments were used or because characteristics of the samples are different. Random effects meta-analytic structural equation modeling takes the study level variance into account. This chapter shows how one can test for heterogeneity of correlation coefficients, and how to quantify the size of the heterogeneity. If heterogeneity is present, the fixed effects model is not appropriate. One option is to explain all heterogeneity with study level variables, for example using subgroup analysis. Random effects analysis can also be combined with subgroup analysis, by fitting a random effects model to subgroups of studies.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Becker, B. J. (1992). Using results from replicated studies to estimate linear models. Journal of Educational Statistics, 17, 341–362.

    Article  Google Scholar 

  • Becker, B. J. (1995). Corrections to using results from replicated studies to estimate linear models. Journal of Educational Statistics, 20, 100–102.

    Article  Google Scholar 

  • 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 (2nd ed., pp. 377–398). New York (NY): Russell Sage Foundation.

    Google Scholar 

  • Becker, B. J., & Fahrbach, K. (1994). A comparison of approaches to the synthesis of correlation matrices. New Orleans, LA: In annual meeting of the American Educational Research Association.

    Google Scholar 

  • Cheung, M. W.-L. (2013). Multivariate meta-analysis as structural equation models. Structural Equation Modeling, 20(3), 429–454.

    Article  MathSciNet  Google Scholar 

  • Cheung, M. W.-L. (2014). Fixed- and random-effects meta-analytic structural equation modeling: Examples and analyses in R. Behavior Research Methods, 46, 29–40.

    Article  Google Scholar 

  • Cheung, M. W.-L., & Chan, W. (2005a). Meta-analytic structural equation modeling: A two-stage approach. Psychological Methods, 10, 40–64.

    Article  Google Scholar 

  • Cheung, M. W.-L., & Chan, W. (2005b). Classifying correlation matrices into relatively homogeneous subgroups: A cluster analytic approach. Educational and Psychological Measurement, 65, 954–979.

    Article  MathSciNet  Google Scholar 

  • 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.

    Google Scholar 

  • Cochran, W. (1954). The combination of estimates from different experiments. Biometrics, 10(1), 101–129.

    Article  MathSciNet  Google Scholar 

  • DerSimonian, R., & Laird, N. (1986). Meta-analysis in clinical trials. Controlled Clinical Trials, 7(3), 177–188.

    Article  Google Scholar 

  • Hedges, L. V., & Vevea, J. L. (1998). Fixed-and random-effects models in meta-analysis. Psychological Methods, 3(4), 486–504.

    Article  Google Scholar 

  • Higgins, J., & Thompson, S. G. (2002). Quantifying heterogeneity in a meta-analysis. Statistics in Medicine, 21(11), 1539–1558.

    Article  Google Scholar 

  • Higgins, J., Thompson, S. G., Deeks, J. J., & Altman, D. G. (2003). Measuring inconsistency in meta-analysis. British Medical Journal, 327, 557–560.

    Article  Google Scholar 

  • Jackson, D., White, I. R., & Riley, R. D. (2012). Quantifying the impact of between-study heterogeneity in multivariate meta-analyses. Statistics in Medicine, 31(29), 3805–3820.

    Article  MathSciNet  Google Scholar 

  • Roorda, D. L, Jak, S., Oort, F. J., & Koomen, H. M. Y. (under review). Teacher-student relationships and students’ achievement: Using a meta-analytic approach to test the mediating role of school engagement.

    Google Scholar 

  • Takkouche, B., Cadarso-Suárez, C., & Spiegelman, D. (1999). Evaluation of old and new tests of heterogeneity in epidemiologic meta-analysis. American Journal of Epidemiology, 150(2), 206–215.

    Article  Google Scholar 

  • Viechtbauer, W. (2007). Hypothesis tests for population heterogeneity in meta-analysis. British Journal of Mathematical and Statistical Psychology, 60(1), 29–60.

    Article  MathSciNet  Google Scholar 

  • Xiong, C., Miller, J. P., & Morris, J. C. (2010). Measuring study-specific heterogeneity in meta-analysis: application to an antecedent biomarker study of Alzheimer’s disease. Statistics in biopharmaceutical research, 2(3), 300–309.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Suzanne Jak .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 The Author(s)

About this chapter

Cite this chapter

Jak, S. (2015). Heterogeneity. 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_3

Download citation

Publish with us

Policies and ethics