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Problems with EM Algorithms for ML Factor Analysis

Published online by Cambridge University Press:  01 January 2025

P. M. Bentler  and
Jeffrey S. Tanaka
P. M. Bentler*
Affiliation:
University of California, Los Angeles
Jeffrey S. Tanaka
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to P. M. Bentler, Department of Psychology, University of California, Los Angeles, California 90024.
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Abstract

Rubin and Thayer recently presented equations to implement maximum likelihood (ML) estimation in factor analysis via the EM algorithm. They present an example to demonstrate the efficacy of the algorithm, and propose that their recovery of multiple local maxima of the ML function “certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.” It is shown here, in contrast, that these second derivatives verify that Rubin and Thayer did not find multiple local maxima as claimed. The only known maximum remains the one found by Jöreskog over a decade earlier. The standard errors obtained from the second derivatives and the Fisher information matrix thus remain appropriate where ML assumptions are met. The advantages of the EM algorithm over other algorithms for ML factor analysis remain to be demonstrated.

Keywords

factor analysisEM algorithmsmaximum likelihood
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 247 - 251
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

Supported in part by grants DA00017 and DA01070 from the U.S. Public Health Service.

References

Reference Note

Schoenberg, R. Personal communication.Google Scholar

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