Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2025-01-06T03:03:05.748Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Investigation of Local Identifiability: A Counterexample

Published online by Cambridge University Press:  01 January 2025

A. Shapiro  and
M. W. Browne
A. Shapiro*
Affiliation:
University of South Africa
M. W. Browne
Affiliation:
University of South Africa
*
Reprint requests should be addressed to Alexander Shapiro, Department of Mathematics, University of South Africa, P. O. Box 392, 0001 Pretoria, Republic of South Africa.
Get access Rights & Permissions [Opens in a new window]

Abstract

An assertion that the parameters of a covariance structure are locally identified at a certain point only if the rank of the Jacobian matrix at that point equals the number of parameters, is shown to be false by means of a counterexample.

Keywords

covariance structuresidentifiabilityJacobian matrixrank
Type
Notes And Comments
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 303 - 304
Copyright
Copyright © 1983 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 authors are indebted to Dr. R. P. McDonald for constructive comments on an earlier draft of this note.

References

Reference Note

Shapiro, A. On local identifiability in the analysis of moment structures. Submitted for publication.Google Scholar

References

Anderson, T. W. & Rubin, H. Statistical inference in factor analysis. In Neyman, J. (Eds.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability (Vol. V) . Berkeley: University of California Press. 1956, 111–150.Google Scholar
Fisher, F. M. The identification problem in economics, New York: McGraw-Hill, 1966.Google Scholar
McDonald, R. P. A note on the investigation of local and global identifiability. Psychometrika, 1982, 47, 101–103.CrossRefGoogle Scholar
McDonald, R. P. & Krane, W. R. A note on local identifiability and degrees of freedom in the asymptotic likelihood ratio test. British Journal of Mathematical and Statistical Psychology, 1977, 30, 198–203.CrossRefGoogle Scholar
McDonald, R. P. & Krane, W. R. A Monte Carlo study of local identifiability and degrees of freedom in the asymptotic likelihood ratio test. British Journal of Mathematical and Statistical Psychology, 1979, 32, 121–132.CrossRefGoogle Scholar
Wald, A. Note on the identification of economic relations. In Koopmans, T. C. (Eds.), Statistical Inference in Dynamic Economic Models. New York: Wiley. 1950, 238–257.Google Scholar