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Factor Analysis and AIC

Published online by Cambridge University Press:  01 January 2025

Hirotugu Akaike
Hirotugu Akaike*
Affiliation:
The Institute of Statistical Mathematics
*
Requests for reprints should be sent to Hirotugu Akaike, The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-Ku, Tokyo 106, Japan.
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Abstract

The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting when it is viewed as the choice of a Bayesian model. This observation shows that the area of application of AIC can be much wider than the conventional i.i.d. type models on which the original derivation of the criterion was based. The observation of the Bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings.

Keywords

factor analysismaximum likelihoodinformation criterion AICimproper solutionBayesian modeling
Type
Special Section
Information
Psychometrika , Volume 52 , Issue 3 , September 1987 , pp. 317 - 332
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

The author would like to express his thanks to Jim Ramsay, Yoshio Takane, Donald Ramirez and Hamparsum Bozdogan for helpful comments on the original version of the paper. Thanks are also due to Emiko Arahata for her help in computing.

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