, Volume 52, Issue 3, pp 333–343 | Cite as

Application of model-selection criteria to some problems in multivariate analysis

  • Stanley L. Sclove
Special Section


A review of model-selection criteria is presented, with a view toward showing their similarities. It is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model-selection criteria. Consideration is given to application of model-selection criteria to some problems of multivariate analysis, especially the clustering of variables, factor analysis and, more generally, describing a complex of variables.

Key words

model selection model evaluation Akaike's information criterion AIC Schwarz's criterion cluster analysis clustering variables factor analysis 


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  1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.),2nd International Symposium on Information Theory (pp. 267–281). Budapest: Akademia Kiado.Google Scholar
  2. Akaike, H. (1974). A new look at the statistical model identification.IEEE Transactions on Automatic Control, 6, 716–723.Google Scholar
  3. Akaike, H. (1981). Likelihood of a model and information criteria.Journal of Econometrics, 16, 3–14.Google Scholar
  4. Akaike, H. (1983). Statistical inference and measurement of entropy. In H. Akaike & C.-F. Wu (Eds.), Scientific inference, data analysis, and robustness (pp. 165–189). New York: Academic Press.Google Scholar
  5. Akaike, H. (1987). Factor analysis and AIC.Psychometrika, 52.Google Scholar
  6. Boekee, D. E., & Buss, H. H. (1981). Order estimation of autoregressive models.4th Aachener Kolloquium: Theorie und Anwendung der Signalverarbeitung [Proceedings of the 4th Aachen Colloquium: Theory and application of signal processing]. (pp. 126–130).Google Scholar
  7. Bozdogan, H. (1981). Multi-sample cluster analysis and approaches to validity studies in clustering individuals. Unpublished doctoral dissertation, University of Illinois at Chicago, Department of Mathematics, Chicago.Google Scholar
  8. Bozdogan, H. (1983). Determining the number of component clusters in standard multivariate normal mixture model using model-selection criteria (Technical Report UIC/DQM/A83-1, Army Research Office Contract DAAG29-82-K-0155, S. L. Sclove, Principal Investigator). Chicago: University of Illinois at Chicago.Google Scholar
  9. Bozdogan, H. (1986). Multi-sample cluster analysis as an alternative to multiple comparison procedures.Bulletin of Informatics and Cybernetics, 22 (No 1–2), 95–130.Google Scholar
  10. Bozdogan, H., & Ramirez, D. E. (1987). An expert model selection approach to determine the “best” pattern structure in factor analysis models. Unpublished manuscript.Google Scholar
  11. Bozdogan, H., & Sclove, S. L. (1984). Multi-sample cluster analysis using Akaike's information criterion.Annals of Institute Statistical Mathematics, 36, 163–180.Google Scholar
  12. Dixon, W. J., & Massey, F. J. (1969). Introduction to statistical analysis (3rd ed.). New York: McGraw-Hill.Google Scholar
  13. Kashyap, R. L. (1982). Optimal choice of AR and MA parts in autoregressive moving average models.IEEE Transactions on Pattern Analysis and Machine Intelligence, 4, 99–104.Google Scholar
  14. Rissanen, J. (1978). Modeling by shortest data description.Automatica, 14, 465–471.Google Scholar
  15. Rissanen, J. (1980). Consistent order estimates of autoregressive processes by shortest description of data. In O. L. R. Jacobs, M. H. A. Davis, M. A. H. Dempster, C. J. Harris, & P. C. Parks (Eds.),Analysis and Optimisation of Stochastic Systems (pp. 451–461). London and New York: Academic Press.Google Scholar
  16. Rissanen, J. (1983). A universal prior for integers and estimation by minimum description length.Annals of Statistics, 11, 416–431.Google Scholar
  17. Rissanen, J. (1985). Minimum-description-length principle.Encyclopedia of Statistical Sciences (Vol. 5, pp. 523–527). New York: John Wiley & Sons.Google Scholar
  18. Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics, 6, 461–464.Google Scholar
  19. Sclove, S. L. (1983a). Application of the conditional population-mixture model to image segmentation.IEEE Transactions Pattern Analysis and Machine Intelligence, 5, 428–433.Google Scholar
  20. Sclove, S. L. (1983b). Time-series segmentation: A model and a method.Information Sciences, 29, 7–25.Google Scholar
  21. Sclove, S. L. (1984). On segmentation of time series and images in the signal detection and remote sensing contexts. In E. W. Wegman & J. G. Smith (Eds.),Statistical signal processing (pp. 421–434). New York: Marcel Dekker.Google Scholar
  22. Wolfe, J. H. (1970). Pattern clustering by multivariate mixture analysis.Multivariate Behavioral Research, 5, 329–350.Google Scholar

Copyright information

© The Psychometric Society 1987

Authors and Affiliations

  • Stanley L. Sclove
    • 1
  1. 1.Department of Information and Decision Sciences, College of Business AdministrationUniversity of Illinois at ChicagoChicago

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