Skip to main content
SpringerLink
Log in

A note on distributional properties of the Jöreskog-Sörbom fit indices

  • Notes And Comments
  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

In introducing the LISREL model for systems of linear structural equations, Jöreskog and Sörbom proposed two goodness-of-fit indices, GFI and AGFI. Their asymptotic distributions and some statistical properties are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions and goodness-of-fit indices for maximum likelihood confirmatory factor analysis.Psychometrika, 49, 155–173.

    Google Scholar 

  • Bearden, W. O., Sharma, S., & Teel, J. E. (1982). Sample size effects on chi-square and other statistics used in evaluating causal models.Journal of Marketing Research, 19, 425–430.

    Google Scholar 

  • Borwne, M. W. (1974). Generalized least squares estimator in the analysis of covariance structures.South African Statistical Journal, 8, 1–24. (Reprinted in D. J. Aigner & A. S. Goldberger (Eds.), (1977).Latent variables in socioeconomic models (pp. 207–226). Amsterdam: North Holland)

    Google Scholar 

  • Browne, M. W. (1984). Asymptotically distribution free methods for the analysis of covariance structures.British Journal of Mathematical and Statistical Psychology, 37, 62–83.

    Google Scholar 

  • Hoelter, J. W. (1983). The analysis of covariance structures: Goodness-of-fit indices.Sociological Methods and Research, 11, 325–344.

    Google Scholar 

  • Jöreskog, K. G. (1978). Structural analysis of covariance and correlation matrices.Psychometrika, 43, 443–477.

    Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1981).LISERL V: Analysis of linear structural relationship by maximum likelihood and least squares methods. Chicago: National Educational Resources.

    Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1982). Recent developments in structural equation modelling.Journal of Marketing Research, 19, 404–416.

    Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1988).LISREL 7: A guide to the program and applications. Chicago: SPSS Publications.

    Google Scholar 

  • Kendall, M. G., & Stuart, A. (1967).The advanced theory of statistics (Vol. 2). London: Griffin.

    Google Scholar 

  • Maiti, S. S., & Mukherjee, B. N. (1988).A new test of significance and goodness-of-fit measure in the analysis of linear covariance structures (Technical Report No. ASC/88/12). Calcutta: Indiah Statistical Insitute, Surveys and Computing Division, Applied Statistics.

    Google Scholar 

  • Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indexes in confirmatory factor analysis: The effect of sample size.Psychological Bulletin, 103, 391–410.

    Google Scholar 

  • McDonald, R. P. (1989). An index of goodness-of-fit based on noncentrality.Journal of Classification, 6, 97–103.

    Google Scholar 

  • McDonald, R. P., and Marsh, H. W. (in press). Choosing a multivariate model: Noncentrality and goodness-of-fit.Psychological Bulletin.

  • Mukherjee, B. N. (1970). Likelihood ratio tests of statistical hypotheses associated with patterned covariance matrices in psychology.British Journal of Mathematical and Statistical Psychology, 23, 89–120.

    Google Scholar 

  • Mukherjee, B. N. (1981). A simple approach to testing of hypotheses regarding a class of covariance structures. In J. K. Ghosh & J. Roy (Eds.),Proceedings of Indian Statistical Institute Golden Jubilee International Conference on Statistics: Applications and New Directions (pp. 442–465). Calcutt: Statistical Publishing Society.

    Google Scholar 

  • Steiger, J. H. (1989).EzPATH: A supplementary module for SYSTAT and SYSGRAPH. Evanston, IL. SYSTAT.

    Google Scholar 

  • Steiger, J. H., & Lind, J. M. (1980, May). Statistically-based tests for the number of common factors. Paper presented at the Annual Meeting of the Psychometric Society, Iowa City.

  • Tanaka, J. S., & Huba, G. J. (1985). A fit index for covariance structures model under arbitaray GLS estimation.British Journal of Mathematical and Statistical Psychology, 38, 197–208.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kalyani Univeristy, Kalyani, Nadia

    Sadhan Samar Maiti

  2. Computer Science Unit, Indian Statistical Institute, Calutta

    Bishwa Nath Mukherjee

Authors
  1. Sadhan Samar Maiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bishwa Nath Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The authors would like to acknowledge the helpful comments and suggestions from the Associate Editor and two anonymous reviewers.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maiti, S.S., Mukherjee, B.N. A note on distributional properties of the Jöreskog-Sörbom fit indices. Psychometrika 55, 721–726 (1990). https://doi.org/10.1007/BF02294619

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02294619

Key words

Search

Navigation