, Volume 61, Issue 1, pp 93–108 | Cite as

Sensitivity analysis of structural equation models

  • Sik-Yum Lee
  • S. J. Wang


The main purpose of this paper is to investigate the sensitivity analysis of structural equation model when minor perturbation is introduced. Some influence measure that based on the general case weight perturbation is derived for the generalized least squares estimation. An influence measure that related to the Cook's distance is also developed for the special case deletion perturbation scheme. Using the proposed methodology, the influential observation in a data set can be detected. Moreover, the general theory can be applied to detect the influential parameters in a model. Finally, some illustrative artificial and real examples are presented.

Key words

perturbation influence graph case weight perturbation Cook's distance eigen-values and eigenvectors 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beckman, R. J., & Cook, R. D. (1983). Outliers.Technometrics, 25, 119–149.Google Scholar
  2. Bentler, P. M. (1983). Some contribution to efficient statistics for structural models: Specification and estimation of moment structures.Psychometrika, 48, 493–517.Google Scholar
  3. Bentler, P. M. (1992).EQS: Structural Equation Program Manual. Los Angeles: BMDP Statistical Software.Google Scholar
  4. Browne, M. W. (1974). Generalized least squares estimators in analysis of covariance structures.South African Statistical Journal, 8, 1–24.Google Scholar
  5. Browne, M. W. (1982). Covariance Structures. In D. M. Hawkins (Ed.),Topics in applied multivariate analysis (pp. 72–141). Cambridge: Cambridge University Press.Google Scholar
  6. Cook, R. D. (1979). Influential observations in linear regression.Journal of the American Statistical Association, 74, 169–174.Google Scholar
  7. Cook, R. D. (1986). Assessment of local influence (with discussion).Journal of the Royal Statistical Society, Series B, 48, 133–169.Google Scholar
  8. Cook, R. D., and Weisber, S. (1982).Residuals and influence in regression. New York and London: Chapman and Hall.Google Scholar
  9. Critchley, F. (1985). Influence in principal component analysis.Biometrika, 72, 627–636.Google Scholar
  10. Hayduk, L. A. (1987).Structural equation modeling with LISREL. Baltimore, MD: Johns Hopkins University.Google Scholar
  11. Hilton, T. L. (1969).Growth study annotated bibliograph (Progress Report 69-11). Princeton, NJ: Educational Testing Service.Google Scholar
  12. Huber, P. S. (1981).Robust statistics. Wiley, New York.Google Scholar
  13. IMSL (1991).FORTRAN Subroutines for statistical analysis. Houston, TX: Author.Google Scholar
  14. Johnson, W., & Geisser, S. (1983). A predictive view of the detection and characterization of influential observations in regression analysis.Journal of the American Statistical Association, 78, 137–144.Google Scholar
  15. Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices.Psychometrika, 43, 443–447.CrossRefGoogle Scholar
  16. Jöreskog, K. G., & Sörbom, D. (1988).LISREL IIV: A Guide to the program and applications, Chicago, IL: SPSS.Google Scholar
  17. Land, K. V., & Felson, A. E. (1978). Sensitivity analysis of arbitrary identified simultaneous-equation models.Sociological Methods and Research, 6(3), 283–307.Google Scholar
  18. Leamer, E. E. (1984). Global sensitivity results for generalized least squares estimate.Journal of the American Statistical Association, 79, 867–870.Google Scholar
  19. Mardia, K. V., Kent, J. T., & Bibby, J. M. (1979).Multivariate analysis. Academic Press.Google Scholar
  20. Pack, P., Jolliffe, I. T., & Morgan, B. J. T. (1988). Influential observations in principal component analysis: A case study.Journal of Applied Statistics, 15, 37–50.Google Scholar
  21. Polasek, W. (1984). Regression diagnostics for general linear regression models.Journal of the American Statistical Association, 79, 336–340.Google Scholar
  22. Tanaka, Y. (1988). Sensitivity analysis in principal component analysis: Influence on the subspace spanned by principal component.Communications in Statistics, Series A, 17, 3157–3175.Google Scholar
  23. Tanaka, Y., & Odaka, Y. (1989a). Influential observations in principal factor analysis.Psychometrika, 54, 475–485.CrossRefGoogle Scholar
  24. Tanaka, Y., & Odaka, Y. (1989b). Sensitivity analysis in maximum likelihood factor analysis.Communications in Statistics, Series A, 18, 4067–4084.Google Scholar
  25. Tanaka, Y., & Watadani, S. (1992). Sensitivity analysis in covariance structure analysis with equality constraints.Communications in Statistics, Series A, 21, 1501–1515.Google Scholar
  26. Tanaka, Y., Watadani, S., & Inoue, K. (1992). Sensitivity analysis in structural equation models. In Y. Dodge & J. Whitterker (Eds.), COMPSTAT 1992Physica-Verlag, 1, 493–498.Google Scholar
  27. Tanaka, Y., Watadani, S., & Moon, S. H. (1991). Influence in covariance structure analysis: With an application to confirmatory factor analysis.Communications in Statistics, Series A, 20, 3805–3821.Google Scholar
  28. Watadani, S., & Tanaka, Y. (1994). Statistical software SACS—Sensitivity analysis in covariance structure analysis.Technical Report of Okayama Statistical Association, 58.Google Scholar

Copyright information

© The Psychometric Society 1996

Authors and Affiliations

  • Sik-Yum Lee
    • 1
  • S. J. Wang
    • 1
  1. 1.Department of StatisticsThe Chinese University of Hong KongHong Kong

Personalised recommendations