Hostname: page-component-5f745c7db-6bmsf Total loading time: 0 Render date: 2025-01-06T06:51:42.590Z Has data issue: true hasContentIssue false
  • English
  • Français

Bayesian Estimation in Unrestricted Factor Analysis: A Treatment for Heywood Cases

Published online by Cambridge University Press:  01 January 2025

James K. Martin  and
Roderick P. McDonald
James K. Martin
Affiliation:
Health and Welfare Canada
Roderick P. McDonald
Affiliation:
The Ontario Institute for Studies in Education
Get access Rights & Permissions [Opens in a new window]

Abstract

A Bayesian procedure is given for estimation in unrestricted common factor analysis. A choice of the form of the prior distribution is justified. It is shown empirically that the procedure achieves its objective of avoiding inadmissible estimates of unique variances, and is reasonably insensitive to certain variations in the shape of the prior distribution.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 4 , December 1975 , pp. 505 - 517
Copyright
Copyright © 1975 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

Clarke, M. R. B.. A rapidly convergent method for maximum likelihood factor analysis. British Journal of Mathematical and Statistical Psychology, 1970, 23, 43–52.CrossRefGoogle Scholar
DeGroot, M.. Optimal statistical decisions, 1970, Toronto: McGraw-Hill.Google Scholar
Emmett, W. G.. Factor analysis by Lawley's method of maximum likelihood. British Journal of Psychology, 1949, 2, 90–97.Google Scholar
Frost, B. P.. Anxiety and educational achievement. British Journal of Educational Psychology, 1968, 38, 293–301.CrossRefGoogle ScholarPubMed
Good, I. J.. The estimation of probabilities: An essay on modern Bayesian methods, 1965, Cambridge: M.I.T. Press.Google Scholar
Guttman, L.. Image theory for the structure of quantitative variates. Psychometrika, 1953, 18, 277–296.CrossRefGoogle Scholar
Guttman, L.. “Best possible” systematic estimates of communalities. Psychometrika, 1956, 21, 273–285.CrossRefGoogle Scholar
Heywood, H. B.. On finite sequences of real numbers. Proceedings of the Royal Society, Series A, 1931, 134, 486–501.Google Scholar
Hill, B. M.. Inference about variance components in the one-way model. Journal of the American Statistical Association, 1956, 60, 806–825.CrossRefGoogle Scholar
Jennrich, R. I., Robinson, S. M.. A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika, 1969, 34, 111–123.CrossRefGoogle Scholar
Jöreskog, K. G.. Some contributions to maximum likelihood factor analysis. Psychometrika, 1967, 32, 443–482.CrossRefGoogle Scholar
Lawley, D. N.. The estimation of factor loadings by the method of maximum likelihood. Proceedings of the Royal Society, Edinburgh, 1940, 60, 64–82.CrossRefGoogle Scholar
Luenberger, D. G.. Introduction to linear and nonlinear programming, 1973, Reading: Addison-Wesley.Google Scholar
McDonald, R. P., Swaminathan, H.. Structural analysis of dispersion matrices based on a very general model with a rapidty convergent procedure for the estimation of parameters, 1971, Toronto: O.I.S.E..Google Scholar
Novick, M. R., Jackson, P. H., Thayer, D. T.. Bayesian inference and the classical test theory model reliability and true scores. Psychometrika, 1971, 36, 261–288.CrossRefGoogle Scholar
Press, S. J.. Applied multivariate analysis, 1972, N. Y.: Holt, Rinehart and Winston.Google Scholar
Rao, C. R.. Estimation and tests of significance in factor analysis. Psychometrika, 1955, 20, 93–111.CrossRefGoogle Scholar