Hostname: page-component-6bf8c574d5-5ws7s Total loading time: 0 Render date: 2025-03-07T16:51:06.972Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of Model-Selection Criteria to Some Problems in Multivariate Analysis

Published online by Cambridge University Press:  01 January 2025

Stanley L. Sclove
Stanley L. Sclove*
Affiliation:
University of Illinois at Chicago
*
Requests for reprints should be sent to Stanley L. Sclove, Department of Information and Decision Sciences, College of Business Administration, University of Illinois at Chicago, Box 4348, Chicago, IL 60680-4348.
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

model selectionmodel evaluationAkaike's information criterionAICSchwarz's criterioncluster analysisclustering variablesfactor analysis
Type
Special Section
Information
Psychometrika , Volume 52 , Issue 3 , September 1987 , pp. 333 - 343
Copyright
Copyright © 1987 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In Petrov, B. N., Csaki, F. (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.CrossRefGoogle Scholar
Akaike, H. (1981). Likelihood of a model and information criteria. Journal of Econometrics, 16, 3–14.CrossRefGoogle Scholar
Akaike, H. (1983). Statistical inference and measurement of entropy. In Akaike, H., Wu, C.-F. (Eds.), Scientific inference, data analysis, and robustness (pp. 165–189). New York: Academic Press.CrossRefGoogle Scholar
Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52.CrossRefGoogle Scholar
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
Bozdogan, H. (1981). Multi-sample cluster analysis and approaches to validity studies in clustering individuals, Chicago: University of Illinois at Chicago, Department of Mathematics.Google Scholar
Bozdogan, H. (1983). Determining the number of component clusters in standard multivariate normal mixture model using model-selection criteria, 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 1–295–130.CrossRefGoogle Scholar
Bozdogan, H., & Ramirez, D. E. (1987). An expert model selection approach to determine the “best” pattern structure in factor analysis models. Unpublished manuscript.CrossRefGoogle Scholar
Bozdogan, H., Sclove, S. L. (1984). Multi-sample cluster analysis using Akaike's information criterion. Annals of Institute Statistical Mathematics, 36, 163–180.CrossRefGoogle 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.CrossRefGoogle Scholar
Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14, 465–471.CrossRefGoogle Scholar
Rissanen, J. (1980). Consistent order estimates of autoregressive processes by shortest description of data. In Jacobs, O. L. R., Davis, M. H. A., Dempster, M. A. H., Harris, C. J., Parks, P. C. (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.CrossRefGoogle Scholar
Rissanen, J. (1985). Minimum-description-length principle. Encyclopedia of Statistical Sciences (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.CrossRefGoogle Scholar
Sclove, S. L. (1983). Application of the conditional population-mixture model to image segmentation. IEEE Transactions Pattern Analysis and Machine Intelligence, 5, 428–433.CrossRefGoogle ScholarPubMed
Sclove, S. L. (1983). Time-series segmentation: A model and a method. Information Sciences, 29, 7–25.CrossRefGoogle Scholar
Sclove, S. L. (1984). On segmentation of time series and images in the signal detection and remote sensing contexts. In Wegman, E. W., Smith, J. G. (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.CrossRefGoogle ScholarPubMed