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FACAIC: Model Selection Algorithm for the Orthogonal Factor Model using AIC and CAIC

Published online by Cambridge University Press:  01 January 2025

Hamparsum Bozdogan  and
Donald E. Ramirez
Hamparsum Bozdogan*
Affiliation:
Department of Mathematics, University of Virginia
Donald E. Ramirez
Affiliation:
Department of Mathematics, University of Virginia
*
Requests for reprints should be sent to Hamparsum Bozdogan, Department of Mathematics, University of Virginia, Charlottesville, VA 22903.
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Abstract

This paper describes the authors' FORTRAN algorithm FACAIC for choosing the number of factors for an orthogonal factor model using Akaike's Information Criterion. FACAIC utilizes the IMSL subroutine OFCOMM.

Keywords

factor analysis algorithmchoosing the number of factorsAIC and CAIC

Information

Type
Computational Psychometrics
Information
Psychometrika , Volume 53 , Issue 3 , September 1988 , pp. 407 - 415
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

The authors dedicate this algorithm to Professor Hirotugu Akaike in appreciation of his pioneering work on AIC which was originally intended for the factor analysis and other statistical model identification problems.

References

Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, AC-19, 716–723.CrossRefGoogle Scholar
Akaike, H. (1978). A Bayesian analysis of the minimum AIC procedure. Annals of the Institute of Statistical Mathematics, 30, 9–14.CrossRefGoogle Scholar
Akaike, H. (1986). Factor analysis and AIC. Psychometrika, 52, 317–332.CrossRefGoogle Scholar
Bozdogan, H. (1985). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions, Charlottesville, VA: Department of Mathematics.Google Scholar
Bozdogan, H., & Ramirez, D. E. (1986, May). The effect of multivariate nonnormality on the probability of choosing the correct number of factors using AIC and CAIC. A paper presented at the Advanced Symposium on Multivariate Statistical Modeling and Data Analysis, the 64th Meeting of the Virginia Academy of Sciences—ASA Virginia Chapter at James Madison University, Harrisonburg, Virginia.CrossRefGoogle Scholar
Bozdogan, H., & Ramirez, D. E. (1987). An expert model selection approach to determine the “best” pattern structure in factor analysis models. In Bozdogan, H., Gupta, A. K. (Eds.), Multivariate statistical modeling and data analysis (pp. 35–60). Dordrecht, Holland: D. Reidel.CrossRefGoogle Scholar
Harman, H. (1976). Modern factor analysis, Chicago, IL: The University of Chicago Press.Google Scholar
Heywood, H. B. (1931). On finite sequences of real numbers. Journal of the Royal Society, Series A, 134, 486–501.Google Scholar
Jennrich, R. I., & Robinson, S. M. (1969). A Newton-Raphson algorithm for maximum-likelihood factor analysis. Psychometrika, 34, 111–123.CrossRefGoogle Scholar
Johnson, R., & Wichern, D. (1988). Applied multivariate statistical analysis, Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
Kaiser, M. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.CrossRefGoogle Scholar
Mullen, F. (1939). Factors in the growth of girls seven to seventeen years of age. Unpublished doctoral dissertation,Department of Education, University of Chicago.Google Scholar
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.CrossRefGoogle Scholar