Advertisement

Bayesian Factor Analysis Model and Choosing the Number of Factors Using a New Informational Complexity Criterion

  • Hamparsum Bozdogan
  • Kazuo Shigemasu
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

This paper introduces two forms of informational complexity ICOMP criteria of Bozdogan (1988, 1990,1994) as a decision rule for model selection and evaluation in Bayesian Confirmatory Factor Analysis (BAYCFA) model due to Press and Shigemasu (1989) in contemporaneously choosing the number of factors and determining the “bestapproximating factor pattern structure. A Monte Carlo simulation example with a known factor pattern structure and known actual number of factors is shown to demonstrate the utility and versatility of the new approach in recovering the true structure.

Key words

Bayesian Confirmatory Factor Analysis Choosing the Number of Factors Informational Complexity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle, in: Second International Symposium on Information Theory B.N. Petrov and F. Csaki (Eds.) Budapest: Academiai Kiado, 267–281.Google Scholar
  2. Bozdogan, H. (1988). ICOMP: A new model selection criterion, in: Classification and Related Methods of Data Analysis, Hans H. Bock (Ed.), Amsterdam: North -Holland, 599–608.Google Scholar
  3. Bozdogan, H. (1990). On the information-based measure of covariance complexity and its application to the evaluation of multivariate linear models, Communications in Statistics, Theory and Methods, 19 (1), 221–278.CrossRefGoogle Scholar
  4. Bozdogan, H. (1994). Mixture-model cluster analysis using a new informational complexity and model selection criteria, in: Multivariate Statistical Modeling, Volume 2, Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling H. Bozdogan (Ed.), Dordrecht: Kluwer Academic Publishers, the Netherlands, 69–113.Google Scholar
  5. Hartigan, J. (1975). Clustering algorithms, John Wiley and Sons, New York.Google Scholar
  6. Mulaik, S. A. (1989). Personal correspondence.Google Scholar
  7. Press, S. J. (1982). Applied multivariate analysis: using Bayesian and frequentist methods of inference, Malabar, Florida: Robert E. Krieger Publishing Co., Inc. Press S. J. and Shigemasu, K. (1989). Bayesian inference in factor analysis, in: Contributions to Probability and Statistics: Essays in Honor of Ingram Olkin, L. Gleser, M. Perlman, S.J. Press, and A. Sampson (Eds.), New York: Springer- Verlag, 271–287.Google Scholar
  8. Rissanen, J. (1978). Modeling by shortest data description, Automatica, 14, 465– 471.Google Scholar
  9. Schwarz, G. (1978). Estimating the dimension of a model, Annals of Statistics, 6, 461–464.CrossRefGoogle Scholar
  10. Van Emden, M.H. (1971). An analysis of complexity. Amsterdam: Math. Centre Tracts 35.Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1998

Authors and Affiliations

  • Hamparsum Bozdogan
    • 1
  • Kazuo Shigemasu
    • 2
  1. 1.Department of StatisticsThe University of TennesseeKnoxvilleUSA
  2. 2.Department of Life SciencesThe University of TokyoTokyo 153Japan

Personalised recommendations