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Forced Classification: A Simple Application of a Quantification Method

Published online by Cambridge University Press:  01 January 2025

Shizuhiko Nishisato
Shizuhiko Nishisato*
Affiliation:
The Ontario Institute for Studies in Education The University of Toronto
*
Requests for a reprint should be addressed to S. Nishisato, Department of Measurement, Evaluation and Computer Applications, the Ontario Institute for Studies in Education, 252 Bloor Street West, Toronto, Ontario, Canada M5S 1V6.
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Abstract

This study formulates a property of a quantification method, the principle of equivalent partitioning (PEP). When the PEP is used together with Guttman's principle of internal consistency (PIC) in a simple way, the combination offers an interesting way of analyzing categorical data in terms of the variate(s) chosen by the investigator, a type of canonical analysis. The study discusses applications of the technique to multiple-choice, rank-order, and paired comparison data.

Keywords

dual scalingforced classificationanalyses des correspondancesmultiple correspondence analysisdiscriminant analysiscanonical analysisprojection operator
Type
Original Paper
Information
Psychometrika , Volume 49 , Issue 1 , March 1984 , pp. 25 - 36
Copyright
Copyright © 1984 The Psychometric Society

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Footnotes

This study was supported by the Natural Sciences and Engineering Research Council of Canada (Grant No. A7942). Comments on the earlier drafts from anonymous reviewers and the editor were much appreciated.

References

Reference Notes

Bock, R. D. (1960). Methods and applications of optimal scaling. The University of North Carolina Psychometric Laboratory Research Memorandum, No. 26.Google Scholar
Carroll, J. D. & Chang, J. J. (1964). Nonparametric multidimensional analysis of paired comparison data. Paper presented at the joint meeting of the Psychometric and the Psychonomic Societies, Niagara Falls, N. Y.Google Scholar
de Leeuw, J. (1973). Canonical analysis of categorical data, the Netherlands: University of Leiden.Google Scholar
Gifi, A. (1981). Nonlinear multivariate analysis (pre-publication edition), the Netherlands: Department of Data Theory, University of Leiden.Google Scholar
Greenacre, M. J. (1978). Some objective methods of graphical display of a data matrix (the English translation of the 1978 doctoral thesis, written in French). Special report, Department of Statistics and Operations Research, University of South Africa.Google Scholar
Heiser, W. J. (1981). Unfolding analysis of proximity data, the Netherlands: University of Leiden.Google Scholar
Nishisato, S. (1973). Optimal scaling of partially ordered categories. Paper presented at the annual meeting of the Psychometric Society, University of Chicago, Ill.Google Scholar
Tenenhaus, M. (1981). Principal component analysis of qualitative variables, Jouy-en-Josas, France: Les cahiers de recherche, Centre d'Enseignement Superieur des Affaires.Google Scholar
Tenenhaus, M. & Young, F. W. (1983). Multiple correspondence analysis and the principal components of qualitative data. The L. L. Thurstone Psychometric Laboratory Report No. 170.Google Scholar

References

Bechtel, G. A., Tucker, L. R., & Chang, W. (1971). A scalar product model for the multidimensional scaling of choice. Psychometrika, 36, 369–388.CrossRefGoogle Scholar
Benzécri, J. P. (1969). Statistical anslysis as a tool to make patterns emerge from data. In Watanabe, S. (Eds.), Methodologies of pattern recognition (pp. 35–74). New York: Academic Press.CrossRefGoogle Scholar
Benzécri, J. P. (1979). Sur l'analyse d'un tableau dont l'une des collones a un poid prédominant. Les Cahiers de l'Analyse des Données, 4, 413–416.Google Scholar
Benzécri, J. P. (1977). Histoire et préhistoire de l'analyse des données: L'analyse des correspondances. Les Cahiers de l'Analyse des Données, 2, 9–40.Google Scholar
Benzécri, J. P. et al. (1973). L'analyse des données: II. L'analyse des correspondances, Paris: Dunod.Google Scholar
Bouroche, J. M. & Saporta, G. (1981). L'analyse des données, Paris: Presses Universitaire.Google Scholar
Bock, R. D. & Jones, L. V. (1968). Measurement and prediction of judgment and choice, San Francisco: Holden-Day.Google Scholar
Bradley, R. A., Katti, S. K. & Coons, I. J. (1962). Optimal scaling for ordered categories. Psychometrika, 27, 355–374.CrossRefGoogle Scholar
Carroll, J. D. (1972). Individual differences and multidimensional scaling. In Shepard, R. N., Romney, A. K. & Nerlove, S. B. (Eds.), Multidimensional scaling: Theory and applications in the behavioral sciences (Vol. 1), New York: Seminar Press.Google Scholar
de Leeuw, J., Young, F. W. & Takane, Y. (1976). Additive structure in qualitative data: An alternating least squares method with optimal scaling features. Psychometrika, 41, 471–504.CrossRefGoogle Scholar
Fisher, R. A. (1940). The precision of discriminant functions. Annals of Eugenics, 10, 422–429.CrossRefGoogle Scholar
Greenacre, M. J. (1981). Practical correspondence analysis. In Barne, V. H. (Eds.), Interpreting multivariate data (pp. 119–146). Chicester: Wiley.Google Scholar
Guttman, L. (1941). The quantification of a class of attributes: a theory and method of scale construction. In the Committee on Social Adjustment (Eds.), The prediction of personal adjustment (pp. 319–348). New York: Social Science Research Council.Google Scholar
Guttman, L. (1946). An approach for quantifying paired comparison and rank order. Annals of Mathematical Statistics, 17, 144–163.CrossRefGoogle Scholar
Hayashi, C., Higuchi, I. & Komazawa, T. (1970). Joho shori to tokei suri, Tokyo: Sangyo Tosho (in Japanese)Google Scholar
Hill, M. O. (1974). Correspondence analysis: A neglected multivariate method. Applied Statistics, 23, 340–354.CrossRefGoogle Scholar
Hirschfeld, H. O. (1935). A connection between correlation and contingency. Cambridge Philosophical Society Proceedings, 31, 520–524.CrossRefGoogle Scholar
Horst, P. (1935). Measuring complex attitudes. Journal of Social Psychology, 6, 369–374.CrossRefGoogle Scholar
Komazawa, T. (1978). Tagenteki data bunseki no kiso, Tokyo: Asakura Shoten (in Japanese)Google Scholar
Komazawa, T. & Hayashi, C. (1982). Suryoka riron to data shori, Tokyo: Asakura Shoten (in Japanese)Google Scholar
Lebart, L. (1979). Exemple d'analyse d'un tableau dont l'une des colonnes a un poid prédominant. Les Cahiers de l'Analyse des Données, 4, 417–422.Google Scholar
Lebart, L., Morineau, A. & Tabard, N. (1977). Technique de la description statistique, Paris: Dunod.Google Scholar
Maung, K. (1941). Measurement of association in contingency table with special reference to the pigmentation of hair and eye colours of Scottish school children. Annals of Eugenics, 11, 189–223.CrossRefGoogle Scholar
McDonald, R. P. (1968). A unified treatment of the weighting problem. Psychometrika, 33, 351–381.CrossRefGoogle ScholarPubMed
McDonald, R. P., Torii, Y. & Nishisato, S. (1979). Some results on proper eigenvalues and eigenvectors with applications to scaling. Psychometrika, 44, 211–227.CrossRefGoogle Scholar
Meulman, J. (1982). Homogeneity analysis of incomplete data, Leiden: DSWO Press.Google Scholar
Nishisato, S. (1975). Oyo shinri shakudoho: Shitsuteki data no bunseki to kaishaku (applied psychological scaling: analysis and interpretation of qualitative data), Tokyo: Seishin Shobo (in Japanese)Google Scholar
Nishisato, S. (1978). Optimal scaling of paired comparison and rank-order data: An alternative to Guttman's formulation. Psychometrika, 43, 263–271.CrossRefGoogle Scholar
Nishisato, S. (1979). Dual (optimal scaling and its history. Mathematical Sciences, 190, 76–83 (in Japanese)Google Scholar
Nishisato, S. (1980). Analysis of categorical data: Dual scaling and its applications, Toronto: University of Toronto Press.CrossRefGoogle Scholar
Nishisato, S. (1982). Shitsuteki data no suryoka: Sotsui shakudoho to sono oyo (quantifying qualitative data: dual scaling and its applications), Tokyo: Asakura Shoten (in Japanese)Google Scholar
Nishisato, S. & Arri, P. S. (1975). Nonlinear programming approach to optimal scaling of partially ordered categories. Psychometrika, 40, 525–548.CrossRefGoogle Scholar
Nishisato, S. & Sheu, W. (1980). Piecewise method of reciprocal averages for dual scaling of multiple-choice data. Psychometrika, 45, 467–478.CrossRefGoogle Scholar
Perreault, W. D. Jr., Young, F. W. (1980). Alternating least squares optimal scaling: Analysis of nonmetric data in marketing research. Journal of Marketing Research, 17, 1–13.CrossRefGoogle Scholar
Richardson, M. & Kuder, G. F. (1933). Making a rating scale that measures. Personnel Journal, 12, 36–40.Google Scholar
Saporta, G. (1979). Théories et méthodes de la statistique, Paris: Technip.Google Scholar
Shye, S. (1978). Theory construction and data analysis, Tel Aviv: Jossey-Bass.Google Scholar
Slater, P. (1960). The analysis of personal preferences. British Journal of Statistical Psychology, 3, 119–135.CrossRefGoogle Scholar
Takeuchi, K. & Yanai, H. (1972). Tahenryo kaiseki no kiso: Senkei kukan eno shaei ni yoru hoho, Tokyo: Toyo Keizai Simposha (in Japanese)Google Scholar
Takeuchi, K., Yanai, H. & Mukherjee, B. N. (1982). The foundations of multivariate analysis: A unified approach by means of projection onto linear subspaces, New Delhi: Wiley Eastern.Google Scholar
Tatsuoka, M. M. (1971). Multivariate analysis in educational and psychological research, New York: Wiley.Google Scholar
Tenenhaus, M. (1977). Analyse en composantes principales, d'un ensemble de variables nominales ou numériques. Revue de Statistique Appliquée, 25, 39–56.Google Scholar
Torgerson, W. S. (1958). Theory and methods of scaling, New York: Wiley.Google Scholar
Traub, R. E. (1979). Analysis of test data, San Francisco: Jossey-Bass.Google Scholar
Tucker, L. R. (1960). Intra-individual and inter-individual multidimensionality. In Gulliksen, H., Messick, S. (Eds.), Psychological scaling, New York: Wiley.Google Scholar
Yanai, H. & Takane, Y. (1977). Tahenryo kaisekiho, Tokyo: Asakura Shoten (in Japanese)Google Scholar
Young, F. W. (1981). Quantitative analysis of qualitative data. Psychometrika, 46, 357–388.CrossRefGoogle Scholar
Young, F. W. Scaling. (1984). Annual Review of Psychology, 35 (in press).CrossRefGoogle ScholarPubMed