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A New Incremental Fit Index for General Structural Equation Models

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  • KENNETH A. BOLLEN

    (University of North Carolina at Chapel Hill)

Abstract

Assessing overall model fit is an important problem in general structural equation models. One of the most widely used fit measures is Bentler and Bonett's (1980) normed index. This article has three purposes: (1) to propose a new incremental fit measure that provides an adjustment to the normed index for sample size and degrees of freedom, (2) to explain the relation between this new fit measure and the other ones, and (3) to illustrate its properties with an empirical example and a Monte Carlo simulation. The simulation suggests that the mean of the sampling distribution of the new fit measure stays at about one for different sample sizes whereas that for the normed fit index increases with N. In addition, the standard deviation of the new measure is relatively low compared to some other measures (e.g., Tucker and Lewis's (1973) and Bentler and Bonett's (1980) nonnormed index). The empirical example suggests that the new fit measure is relatively stable for the same model in different samples. In sum, it appears that the new incremental measure is a useful complement to the existing fit measures.

Suggested Citation

  • Kenneth A. Bollen, 1989. "A New Incremental Fit Index for General Structural Equation Models," Sociological Methods & Research, , vol. 17(3), pages 303-316, February.
    • Handle: RePEc:sae:somere:v:17:y:1989:i:3:p:303-316
    DOI: 10.1177/0049124189017003004
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    References listed on IDEAS

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    1. James Steiger & Alexander Shapiro & Michael Browne, 1985. "On the multivariate asymptotic distribution of sequential Chi-square statistics," Psychometrika, Springer;The Psychometric Society, vol. 50(3), pages 253-263, September.
    2. James Anderson & David Gerbing, 1984. "The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 49(2), pages 155-173, June.
    3. 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.
    4. 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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