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On Bayesian Estimation in Unrestricted Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Raymond F. Koopman
Raymond F. Koopman*
Affiliation:
Simon Fraser University
*
Requests for reprints should be sent to R. F. Koopman, Psychology Dept., Simon Fraser University, Burnaby, B.C., Canada V5A 1S6.
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Abstract

It is shown that the common and unique variance estimates produced by Martin & McDonald’s Bayesian estimation procedure for the unrestricted common factor model have a predictable sum which is always greater than the maximum likelihood estimate of the total variance. This fact is used to justify a suggested simple alternative method of specifying the Bayesian parameters required by the procedure.

Keywords

communalitiesuniquenessescommon varianceunique varianceHeywood casesunbiased estimatesmissing data
Type
Notes and Comments
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 109 - 110
Copyright
Copyright © 1978 The Psychometric Society

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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
Martin, J. K., & McDonald, R. P. Bayesian estimation in unrestricted factor analysis: a treatment for Heywood cases. Psychometrika, 1975, 40, 505–517.CrossRefGoogle Scholar