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Improper Solutions in Structural Equation Models

Author

Listed:
  • FEINIAN CHEN

    (University of North Carolina at Chapel Hill)

  • KENNETH A. BOLLEN

    (University of North Carolina at Chapel Hill)

  • PAMELA PAXTON

    (Ohio State University)

  • PATRICK J. CURRAN

    (University of North Carolina at Chapel Hill)

  • JAMES B. KIRBY

    (Agency for Healthcare Research and Quality)

Abstract

In this article, the authors examine the most common type of improper solutions: zero or negative error variances. They address the causes of, consequences of, and strategies to handle these issues. Several hypotheses are evaluated using Monte Carlo simulation models, including two structural equation models with several misspecifications of each model. Results suggested several unique findings. First, increasing numbers of omitted paths in the measurement model were associated with decreasing numbers of improper solutions. Second, bias in the parameter estimates was higher in samples with improper solutions than in samples including only proper solutions. Third, investigations of the consequences of using constrained estimates in the presence of improper solutions indicated that inequality constraints helped some samples achieve convergence. Finally, the use of confidence intervals as well as four other proposed tests yielded similar results when testing whether the error variance was greater than or equal to zero.

Suggested Citation

  • Feinian Chen & Kenneth A. Bollen & Pamela Paxton & Patrick J. Curran & James B. Kirby, 2001. "Improper Solutions in Structural Equation Models," Sociological Methods & Research, , vol. 29(4), pages 468-508, May.
    • Handle: RePEc:sae:somere:v:29:y:2001:i:4:p:468-508
    DOI: 10.1177/0049124101029004003
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    References listed on IDEAS

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    1. Albert Satorra, 1990. "Robustness issues in structural equation modeling: a review of recent developments," Quality & Quantity: International Journal of Methodology, Springer, vol. 24(4), pages 367-386, November.
    2. 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.
    3. Otto Driel, 1978. "On various causes of improper solutions in maximum likelihood factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 225-243, June.
    4. Albert Satorra & Willem Saris, 1985. "Power of the likelihood ratio test in covariance structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 83-90, March.
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    1. Reinartz, Werner & Haenlein, Michael & Henseler, Jörg, 2009. "An empirical comparison of the efficacy of covariance-based and variance-based SEM," International Journal of Research in Marketing, Elsevier, vol. 26(4), pages 332-344.

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