Skip to main content
Log in

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

  • Special Section
  • Published:
Psychometrika Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • 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 

  • Akaike, H. (1974). A new look at the statistical model identification.IEEE Transactions on Automatic Control, 6, 716–723.

    Google Scholar 

  • Akaike, H. (1981). Likelihood of a model and information criteria.Journal of Econometrics, 16, 3–14.

    Google Scholar 

  • 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 

  • Akaike, H. (1987). Factor analysis and AIC.Psychometrika, 52.

  • 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).

  • 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 Unpublished doctoral dissertation, University of Illinois at Chicago, Department of Mathematics, Chicago.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 

  • 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 

  • 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 

  • Bozdogan, H., & Ramirez, D. E. (1987). An expert model selection approach to determine the “best” pattern structure in factor analysis models. Unpublished manuscript.

  • 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 

  • Dixon, W. J., & Massey, F. J. (1969). Introduction to statistical analysis (3rd ed.). New York: McGraw-Hill.

    Google Scholar 

  • 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 

  • Rissanen, J. (1978). Modeling by shortest data description.Automatica, 14, 465–471.

    Google Scholar 

  • 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 

  • Rissanen, J. (1983). A universal prior for integers and estimation by minimum description length.Annals of Statistics, 11, 416–431.

    Google Scholar 

  • Rissanen, J. (1985). Minimum-description-length principle.Encyclopedia of Statistical Sciences (Vol. 5, pp. 523–527). New York: John Wiley & Sons.

    Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model.Annals of Statistics, 6, 461–464.

    Google Scholar 

  • 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 

  • Sclove, S. L. (1983b). Time-series segmentation: A model and a method.Information Sciences, 29, 7–25.

    Google Scholar 

  • 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 

  • Wolfe, J. H. (1970). Pattern clustering by multivariate mixture analysis.Multivariate Behavioral Research, 5, 329–350.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sclove, S.L. Application of model-selection criteria to some problems in multivariate analysis. Psychometrika 52, 333–343 (1987). https://doi.org/10.1007/BF02294360

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02294360

Key words

Navigation