Hostname: page-component-745bb68f8f-b6zl4 Total loading time: 0 Render date: 2025-01-07T18:37:37.221Z Has data issue: false hasContentIssue false

A Note to Bollen's Alternative Fit Measure

Published online by Cambridge University Press:  01 January 2025

Ingo Balderjahn*
Affiliation:
Technical University of Berlin
*
Requests for reprints should be sent to Ingo Balderjahn, Technical University of Berlin, Department of Quantitative Methods, FranktinstraBe 28/28, D-1000 Berlin 10, WEST GERMANY.

Abstract

The problem of dependence of the nonnormed fit index on sample size in covariance structure analysis is discussed. Contrary to Bollen (1986) we show that the mean of the nonnormed fit index is independent of sample size for true and almost true models whereas Bollen's alternative index does depend on sample size.

Type
Notes And Comments
Copyright
Copyright © 1988 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.)

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, 155173.CrossRefGoogle Scholar
Balderjahn, I. (1987). Der Einsatz von LISREL zur Kreuzvalidierung von Kovarianzstrukturmodellen [The use of LISREL to cross-validate covariance structure models. Paper presented at the 4th Conference on Scientific Use of Statistical Software in Heidelberg, West Germany.Google Scholar
Bollen, K. A. (1986). Sample size and Bentler and Bonetts nonnormed fit index. Psychometrika, 51, 375377.CrossRefGoogle Scholar
Browne, M. W. (1982). Covariance structures. In Hawkins, D. M. (Eds.), Topics in applied multivariate analysis (pp. 72141). Cambridge: University Press.CrossRefGoogle Scholar
Bentler, P. M., Bonett, D. G. (1980). Significance tests and goodness-of-fit in the analysis of covariance structures. Psychological Bulletin, 88, 588606.CrossRefGoogle Scholar
Satorra, A., Saris, W. E. (1985). Power of the likelihood ratio test in covariance structure analysis. Psychometrika, 50, 8390.CrossRefGoogle Scholar
Steiger, J. H., Shapiro, A., Browne, M. W. (1985). On the multivariate asymptotic distribution of sequential Chi-square statistics. Psychometrika, 50, 253264.CrossRefGoogle Scholar
Tucker, L. R., Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 110.CrossRefGoogle Scholar