, Volume 52, Issue 3, pp 317–332 | Cite as

Factor analysis and AIC

  • Hirotugu Akaike
Special Section


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.

Key words

factor analysis maximum likelihood information criterion AIC improper solution Bayesian modeling 


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Copyright information

© The Psychometric Society 1987

Authors and Affiliations

  • Hirotugu Akaike
    • 1
  1. 1.The Institute of Statistical MathematicsTokyoJapan

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