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Gleaning in the Field of Dual Scaling

Published online by Cambridge University Press:  01 January 2025

Shizuhiko Nishisato*
Affiliation:
University of Toronto
*
Requests for reprints should be sent to Shizuhiko Nishisato, OISE/University of Toronto, 252 Bloor Street West, Toronto, Ontario, CANADA M5S IV6, or email: snishisato@oise.utoronto.ca.

Abstract

Some historical background and preliminary technical information are first presented, and then a number of hidden, but important, methodological aspects of dual scaling are illustrated and discussed: normed versus projected weights, the amount of information accounted for by each solution, a perfect solution to the problem of multidimensional unfolding, multidimensional quantification space, graphical display, number-of-option problems, option standardization versus item standardization, and asymmetry of symmetric (dual) scaling. Contrary to the common perception that dual scaling and similar quantification methods are now mathematically transparent, the present study demonstrates how much more needs to be clarified for routine use of the method to arrive at valid conclusions. Data analysis must be carried out in such a way that common sense, intuition and sound logic will prevail.

Type
Original Paper
Copyright
Copyright © 1996 The Psychometric Society

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Footnotes

Presidential Address delivered at the Annual Meeting of the Psychometric Society, Banff Centre for Conferences, Banff, Alberta, Canada, June 27–30, 1996. The work has been supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada. I am grateful to Ira Nishisato for his comments, Ingram Olkin and Yoshio Takane for important references, and Liqun Xu for computational help.

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