Hostname: page-component-89b8bd64d-n8gtw Total loading time: 0 Render date: 2026-05-06T08:24:59.108Z Has data issue: false hasContentIssue false
  • English
  • Français

Model Modification

Published online by Cambridge University Press:  01 January 2025

Dag Sörbom
Dag Sörbom*
Affiliation:
University of Uppsala
*
Requests for reprints should be sent to Dag Sörbom, University of Uppsala, Department of Statistics, PO Box 513, S-751 20 Uppsala, SWEDEN.
Get access Rights & Permissions [Opens in a new window]

Abstract

An analysis of empirical data often leads to a rejection of a hypothesized model, even if the researcher has spent considerable efforts in including all available information in the formulation of the model. Thus, the researcher must reformulate the model in some way, but in most instances there is, at least theoretically, an overwhelming number of possible actions that could be taken. In this paper a “modification index” will be discussed which should serve as a guide in the search for a “better” model. In statistical terms, the index measures how much we will be able to reduce the discrepancy between model and data, as defined by a general fit function, when one parameter is added or freed or when one equality constraint is relaxed. The modification index discussed in this paper is an improvement of the one incorporated in the LISREL V computer program in that it takes into account changes in all the parameters of the model when one particular parameter is freed.

Keywords

model modificationmaximum likelihood estimationfactor analysisstructural equation modelsstep-wise regression

Information

Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 371 - 384
Copyright
Copyright © 1989 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.)

Article purchase

Temporarily unavailable

Footnotes

The research reported in this paper has been supported by The Swedish Council for Research in the Humanities and Social Sciences under Research Program “Multivariate Statistical Analysis”, Project Director Karl G Jöreskog.

References

Aitchison, J., & Silvey, D. C. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 29, 813–828.CrossRefGoogle Scholar
BMDP (1977). Biomedical computer programs, Los Angeles: University of California Press.Google Scholar
Bollen, K. A. (1980). Issues in the comparative measurement of political democracy. American Sociological Review, 45, 370–390.CrossRefGoogle Scholar
Costner, H. L., & Schoenberg, R. (1972). Diagnosing indicator ills in multiple indicator models. In Goldberger, A. S. & Duncan, O. D. (Eds.), Structural education models in the social sciences (pp. 167–199). New York: Seminar Press.Google Scholar
Dijkstra, T. K. (1981). Latent variables in linear stochastic models. Unpublished doctoral dissertation, University of Groningen.Google Scholar
Herting, J. R., & Costner, H. L. (1985). Respecification in multiple indicator models. In Blalock, H. M. Jr. (Eds.), Causal models in the social sciences 2nd ed., (pp. 321–393). Hawthorne, NY: Aldine.Google Scholar
Holzinger, K., & Swineford, F. (1939). A study in factor analysis: The stability of a bifactor solution, Chicago: University of Chicago Press.Google Scholar
Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183–202.CrossRefGoogle Scholar
Jöreskog, K. G., & Sörbom, D. (1981). LISREL V Analysis of linear structural relationships by maximum likelihood and least squares methods, Chicago: International Educational Services.Google Scholar
Jöreskog, K. G., & Sörbom, D. (1984). LISREL VI Analysis of linear structural relationships by the method of maximum likelihood, Mooresville, IN: Scientific Software.Google Scholar
Keeves, J. P. (1972). Educational environment and student achievement, Stockholm: Almqvist & Wiksell.Google Scholar
Lohnes, P. R. (1979). Factorial modeling in support of causal inference. American Educational Research Journal, 16, 323–340.CrossRefGoogle Scholar
MacCallum, R. (1986). Specification searches in covariance structure modeling. Psychological Bulletin, 100, 107–120.CrossRefGoogle Scholar
Rao, C. R. (1948). Large sample tests of statistical hypotheses concerning several parameters with application to problems of estimation. Proceedings of the Cambridge Philosophical Society, 44, 50–57.Google Scholar
Saris, W. E., de Pijper, W. M., & Zegwaart, P. (1979). Detection of specification errors in linear structural equation models. Sociological Methodology 1979.Google Scholar
Sörbom, D. (1975). Detection of correlated errors in longitudinal data. British Journal of Mathematical and Statistical Psychology, 28, 138–151.CrossRefGoogle Scholar