Hostname: page-component-5f745c7db-sbzbt Total loading time: 0 Render date: 2025-01-06T06:53:18.187Z Has data issue: true hasContentIssue false
  • English
  • Français

Sensitivity Analysis of Structural Equation Models

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee  and
S. J. Wang
Sik-Yum Lee*
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
S. J. Wang
Affiliation:
Department of Statistics, The Chinese University of Hong Kong
*
Request for reprints should be sent to Sik-Yum Lee, Department of Statistics, The Chinese University of Hong Kong, Shatin, N.T., HONG KONG.
Get access Rights & Permissions [Opens in a new window]

Abstract

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.

Keywords

perturbationinfluence graphcase weight perturbationCook's distanceeigen-values and eigenvectors
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 1 , March 1996 , pp. 93 - 108
Copyright
© 1996 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The research of the first author was supported by a Hong Kong UPGC grant. The authors are greatly indebted to two reviewers for some very valuable comments for improvement of the paper.

References

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