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Monte Carlo Evaluations of Goodness of Fit Indices for Structural Equation Models

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  • DAVID W. GERBING

    (Portland State University)

  • JAMES C. ANDERSON

    (Northwestern University)

Abstract

This article reviews proposed goodness-of-fit indices for structural equation models and the Monte Carlo studies that have empirically assessed their distributional properties. The cumulative contributions of the studies are summarized, and the variables under which the indices are studied are noted. A primary finding is that many of the indices used until the late 1980s, including Jöreskog and Sörbom's (1981) GFI and Bentler and Bonett's (1980) NFI, indicated better fit when sample size increased. More recently developed indices based on the chi-square noncentrality parameter are discussed and the relevant Monte Carlo studies reviewed. Although a more complete understanding of their properties and suitability requires further research, the recommended fit indices are the McDonald (1989) noncentrality index, the Bentler (1990)-McDonald and Marsh (1990) RNI (or the bounded counterpart CFI), and Bollen's (1989) DELTA2.

Suggested Citation

  • David W. Gerbing & James C. Anderson, 1992. "Monte Carlo Evaluations of Goodness of Fit Indices for Structural Equation Models," Sociological Methods & Research, , vol. 21(2), pages 132-160, November.
    • Handle: RePEc:sae:somere:v:21:y:1992:i:2:p:132-160
    DOI: 10.1177/0049124192021002002
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    References listed on IDEAS

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    1. Roderick McDonald, 1989. "An index of goodness-of-fit based on noncentrality," Journal of Classification, Springer;The Classification Society, vol. 6(1), pages 97-103, December.
    2. P. Bentler, 1983. "Some contributions to efficient statistics in structural models: Specification and estimation of moment structures," Psychometrika, Springer;The Psychometric Society, vol. 48(4), pages 493-517, December.
    3. David Gerbing & James Anderson, 1987. "Improper solutions in the analysis of covariance structures: Their interpretability and a comparison of alternate respecifications," Psychometrika, Springer;The Psychometric Society, vol. 52(1), pages 99-111, March.
    4. Gerhard Arminger & Ronald Schoenberg, 1989. "Pseudo maximum likelihood estimation and a test for misspecification in mean and covariance structure models," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 409-425, September.
    5. Kenneth Bollen, 1986. "Sample size and bentler and Bonett's nonnormed fit index," Psychometrika, Springer;The Psychometric Society, vol. 51(3), pages 375-377, September.
    6. Ledyard Tucker & Charles Lewis, 1973. "A reliability coefficient for maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 1-10, March.
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