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The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis

Author

Listed:
  • Ke-Hai Yuan

    (University of Notre Dame)

  • Peter M. Bentler

    (University of California, Los Angeles)

  • Wei Zhang

    (University of Notre Dame)

Abstract

The maximum likelihood (ML) method, based on the normal distribution assumption, is widely used in mean and covariance structure analysis. With typical nonnormal data, the ML method will lead to biased statistics and inappropriate scientific conclusions. This article develops a simple but informative case to show how ML results are influenced by skewness and kurtosis. Specifically, the authors discuss how skewness and kurtosis in a univariate distribution affect the standard errors of the ML estimators, the covariances between the estimators, and the likelihood ratio test of hypotheses on mean and variance parameters. They also describe corrections that have been developed to allow appropriate inference. Enough details are provided so that this material can be used in graduate instruction. For each result, the corresponding results in the higher dimensional case are pointed out, and references are provided.

Suggested Citation

  • Ke-Hai Yuan & Peter M. Bentler & Wei Zhang, 2005. "The Effect of Skewness and Kurtosis on Mean and Covariance Structure Analysis," Sociological Methods & Research, , vol. 34(2), pages 240-258, November.
    • Handle: RePEc:sae:somere:v:34:y:2005:i:2:p:240-258
    DOI: 10.1177/0049124105280200
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    References listed on IDEAS

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    1. Ke-Hai Yuan & Peter Bentler, 2002. "On robusiness of the normal-theory based asymptotic distributions of three reliability coefficient estimates," Psychometrika, Springer;The Psychometric Society, vol. 67(2), pages 251-259, June.
    2. Yuan, Ke-Hai & Bentler, Peter M., 1999. "On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions," Statistics & Probability Letters, Elsevier, vol. 42(2), pages 107-113, April.
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    Cited by:

    1. Zhiyong Zhang, 2013. "Bayesian growth curve models with the generalized error distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(8), pages 1779-1795, August.

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