Hostname: page-component-6bf8c574d5-mggfc Total loading time: 0 Render date: 2025-02-22T05:10:30.327Z Has data issue: false hasContentIssue false
  • English
  • Français

A Bayesian Approach to Confirmatory Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Sik-Yum Lee
Sik-Yum Lee*
Affiliation:
The Chinese University of Hong Kong
*
Requests for reprints should be sent to S. Y. Lee, Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T. HONG KONG.
Get access Rights & Permissions [Opens in a new window]

Abstract

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information on parameter is incorporated in the analysis. An iterative algorithm is developed to obtain the Bayes estimates. A numerical example based on longitudinal data is presented. A simulation study is designed to compare the Bayesian approach with the maximum likelihood method.

Keywords

conjugate familyprior distributionsposterior density functionmaximum likelihood estimationlongitudinal datasimulation study
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 2 , June 1981 , pp. 153 - 160
Copyright
Copyright © 1981 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

Computer facilities were provided by the Computer Services Center, The Chinese University of Hong Kong.

References

Reference Note

Hilton, T. L. Growth study annotated bibliography, 1969, Princeton, N.J.: Educational Testing Service.Google Scholar

References

Jeffrey, H. Theory of Probability, 3rd edition, Oxford: Clarendon, 1961.Google Scholar
Jöreskog, K. G. A general approach to confirmatory maximum likelihood factor analysis. Psychometrika, 1969, 34, 183–202.CrossRefGoogle Scholar
Kshirsagar, A. M. Bartlett decomposition and Wishart distribution. Annals of Mathematical Statistics, 1959, 30, 230–241.CrossRefGoogle Scholar
Lee, S. Y. Estimation of covariance structure models with parameters subject to functional restraints. Psychometrika, 1980, 45, 309–324.CrossRefGoogle Scholar
Lee, S. Y. & Jennrich, R. I. A study of algorithms for covariance structure analysis with specific comparisons using factor analysis. Psychometrika, 1979, 44, 99–113.CrossRefGoogle Scholar
Lindley, D. V. The estimation of many parameters. In Godmake, V. P., Sprott, D. A. (Eds.), Foundations of Statistical Inference. Toronto: Holt, Rinehart and Winston. 1971, 435–455.Google Scholar
Lindley, D. V. & Smith, A. F. M. Bayes estimates for the linear model. Journal of the Royal Statistical Society, Series B, 1972, 34, 1–42.CrossRefGoogle Scholar
Martin, J. K. & McDonald, R. P. Bayesian estimation in unrestricted factor analysis: A treatment for Heywood cases. Psychometrika, 1975, 40, 505–517.CrossRefGoogle Scholar
Raiffa, H. & Schlaifer, H. Applied Statistical Decision Theory, 2nd ed., Boston: Graduate School of Business Administration, Harvard, 1961.Google Scholar
Smith, A. F. M. Bayes estimates in one-way and two-way models. Biometrika, 1973, 60, 319–329.CrossRefGoogle Scholar
Sörbom, D. & Jöreskog, K. G. Confirmatory Factor Analysis with Model Modification, User's Guide, 1976, Chicago: National Educational Resources.Google Scholar
Zellner, A. An Introduction to Bayesian Inference in Econometrics, 1971, New York: Wiley.Google Scholar