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A Method of Optimal Scaling for Multivariate Ordinal Data and its Extensions

Published online by Cambridge University Press:  01 January 2025

Takayuki Saito  and
Tatsuo Otsu
Takayuki Saito*
Affiliation:
Department of Behavioral Science, Hokkaido University
Tatsuo Otsu
Affiliation:
Fuyo Data Processing & Systems Development, Ltd.
*
Requests for reprints should be sent to Takayuki Saito, Department of Behavioral Science, Hokkaido University, Bungakubu, Kita 10 Nishi 7, Sapporo 060, JAPAN.
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Abstract

This paper develops a method of optimal scaling for multivariate ordinal data, in the framework of a generalized principal component analysis. This method yields a multidimensional configuration of items, a unidimensional scale of category weights for each item and, optionally, a multidimensional configuration of subjects. The computation is performed by alternately solving an eigenvalue problem and executing a quasi-Newton projection method. The algorithm is extended for analysis of data with mixed measurement levels or for analysis with a combined weighting of items. Numerical examples and simulations are provided. The algorithm is discussed and compared with some related methods.

Keywords

categorical dataOSMODprincipal component analysisquasi-Newton projection method
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 1 , March 1988 , pp. 5 - 25
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

Earlier results of this research appeared in Saito and Otsu (1983). The authors would like to acknowledge the helpful comments and encouragement of the editor.

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