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EM Algorithms for ML Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Donald B. Rubin  and
Dorothy T. Thayer
Donald B. Rubin*
Affiliation:
Educational Testing Service
Dorothy T. Thayer
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Donald B. Rubin, Educational Testing Service, Rosedale Road, Princeton, New Jersey, 08540.
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Abstract

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least squares regression operations; the largest matrix inversion required is for a q × q symmetric matrix where q is the matrix of factors. The example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other; such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.

Keywords

factor analysisEM algorithmsmaximum likelihood
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 1 , March 1982 , pp. 69 - 76
Copyright
Copyright © 1982 The Psychometric Society

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References

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