Hostname: page-component-74656f9884-rdgjk Total loading time: 0 Render date: 2026-11-09T06:31:44.704Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Structural Models for the Circumplex

Published online by Cambridge University Press:  01 January 2025

Robert Cudeck
Robert Cudeck*
Affiliation:
University of Minnesota
*
Requests for reprints should be sent to Robert Cudeck, Department of Psychology, University of Minnesota, 75 East River Road, Minneapolis, MN 55455.
Get access Rights & Permissions [Opens in a new window]

Abstract

Jöreskog (1974) developed a latent variable model for the covariance structure of the circumplex which, under certain conditions, includes a model for a patterned correlation matrix (Browne, 1977). This model is of limited usefulness, however, in that it employs a known matrix that is rank deficient for many problems. Furthermore, the model is inappropriate for the circumplex which contains negative covariances. This paper presents alternative models for the perfect circumplex and quasi-circumplex that avoids these difficulties, and that includes the important model for a patterned correlation circumplex matrix. Two numerical examples are provided.

Keywords

patterned correlationsconfirmatory factor analysis

Information

Type
Notes and Comments
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 143 - 147
Copyright
Copyright © 1986 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

This research was supported in part by a grant from the Graduate School of the University of Minnesota. I wish to thank M. W. Browne for suggesting the final model presented in this paper. James Steiger and the Editor also made several valuable suggestions.

References

Anderson, T. W. (1960). Some stochastic process models for intelligence test scores. In Arrow, K. J., Karlin, S., Suppes, P. (Eds.), Mathematical methods in the social sciences, 1959 (pp. 205–220). Stanford, CA.: Stanford University Press.Google Scholar
Browne, M. W. (1977). The analysis of patterned correlation matrices by generalized least squares. British Journal of Mathematical and Statistical Psychology, 30, 113–124.CrossRefGoogle Scholar
Davis, P. J. (1979). Circulant matrices, New York: Wiley.Google Scholar
Guttman, L. A. (1954). A new approach to factor analysis: The radex. In Lazarsfeld, P. F. (Eds.), Mathematical thinking in the social sciences (pp. 258–348). New York: Columbia University Press.Google Scholar
Jöreskog, K. B. (1969). A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 34, 183–202.CrossRefGoogle Scholar
Jöreskog, K. G. (1974). Analyzing psychological data by structural analysis of covariance matrices. In Atkinson, R. C., Krantz, D. H., Luce, R. D., Suppes, P. (Eds.), Contemporary developments in mathematical psychology (Vol. 2 (pp. 1–56). San Francisco: W. H. Freeman.Google Scholar
Jöreskog, K. G., Sörbom, D. (1981). LISREL VI user's guide 3rd ed.,, Mooresville, IN: Scientific Software.Google Scholar
Lawley, D. N., Maxwell, A. E. (1971). Factor analysis as a statistical method, London: Butterworth.Google Scholar
Lee, S.-Y., Jennrich, R. I. (1984). The analysis of structural equation models by means of derivative free nonlinear least squares. Psychometrika, 49, 521–528.CrossRefGoogle Scholar
Lorr, M., McNair, D. M. (1963). An interpersonal behavior circle. Journal of Abnormal and Social Psychology, 67, 68–75.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Wiggins, J. S., Steiger, J. H., Gaelick, L. (1981). Evaluating circumplexity in personality data. Multivariate Behavioral Research, 16, 263–289.Google Scholar