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Some Properties of Hoelter's CN

Author

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  • KENNETH A. BOLLEN

    (University of North Carolina at Chapel Hill)

  • JERSEY LIANG

    (University of Michigan)

Abstract

Reviews, critiques, and simulation studies are available for the chi-square and other measures of goodness of fit for structural equation models. The main exception is Hoelter's critical N (CN) statistic. In this article we present some of the properties of CN, explain why a fixed cutoff value for CN often favors large samples over small ones, and illustrate some of these characteristics with simulated and empirical data. We also describe the ambiguities involved in treating CN as a gauge of the power of the chi-square test.

Suggested Citation

  • Kenneth A. Bollen & Jersey Liang, 1988. "Some Properties of Hoelter's CN," Sociological Methods & Research, , vol. 16(4), pages 492-503, May.
    • Handle: RePEc:sae:somere:v:16:y:1988:i:4:p:492-503
    DOI: 10.1177/0049124188016004003
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    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. Antonia Abbey & Frank Andrews, 1985. "Modeling the psychological determinants of life quality," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 16(1), pages 1-34, January.
    5. 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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    1. Tang, Liang (Rebecca) & Jang, Soocheong (Shawn) & Morrison, Alastair, 2012. "Dual-route communication of destination websites," Tourism Management, Elsevier, vol. 33(1), pages 38-49.

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