Factor Analysis and AIC

Akaike, Hirotugu

doi:10.1007/bf02294359

Cited by 5,264Psychometric Methodologies and TestingStatistical Methods and ApplicationsStatistical Methods and Bayesian Inference

Factor Analysis and AIC

Akaike, Hirotugu·1987·Psychometrika

DOI 10.1007/bf02294359

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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.

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The AIC was used for model comparison, with the smallest value indicating the most parsimonious model.
“The Akaike Information Criterion (AIC; Akaike, 1987) was used for the purposes of model comparison, with the smallest value being indicative of the most parsimonious model (Byrne, 2012).”
From Testing Mindfulness Mechanisms of Action on the Stress and Burnout of Social Workers (2024) · cites this paper as Akaike, 1987

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Authors: Akaike, H.
Affiliations: The Institute of Statistical Mathematics (JP)
Corresponding author: Akaike, Hirotugu
Venue: Psychometrika
Publisher: Cambridge University Press (CUP)
Published: 1987-09
Volume: 52
Issue: 3
Pages: 317-332
ISSN: 0033-3123 (ISSN-L)
1860-0980
DOI: 10.1007/bf02294359
OpenAlex: W4237377395
Cited by: 5,264
References: 15
Citations by year: 2026: 201 · 2025: 260 · 2024: 262 · 2023: 277 · 2022: 254 · 2021: 269 · 2020: 255 · 2019: 289 · 2018: 276 · 2017: 275 · 2016: 244 · 2015: 262 · 2014: 249 · 2013: 207 · 2012: 203
FWCI: 9.05
Type: journal article
Language: en
Open access: closed
Licence: www.cambridge.org/core/terms (unspecified, 13637 d)
Locations: Psychometrika (publishedVersion)
RePEc: Research Papers in Economics (submittedVersion)
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords: Akaike information criterion, factor analysis, model selection, Bayesian model, number of factors, factor loadings, prior distributions, improper solutions, maximum likelihood estimation, autoregressive model order selection

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