Factor Analysis and AIC

1987/09/01 by Hirotugu Akaike · 5,190 citations
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Modeling Techniques #Akaike information criterion #Applied mathematics #Autoregressive model #Bayesian inference #Bayesian information criterion #Bayesian probability #Computer science #Deviance information criterion #Econometrics #Factor (programming language) #Factor analysis #Information Criteria #Marginal likelihood #Mathematics #Maximum likelihood #Model selection #Statistical Methods and Applications #Statistics

paper · doi:10.1007/bf02294359

published in Psychometrika 52(3), 317-332 (Springer Science+Business Media)

openalex publication_date 1987/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

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