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Nonlinear Programming Approach to Optimal Scaling of Partially Ordered Categories

Published online by Cambridge University Press:  01 January 2025

Shizuhiko Nishisato  and
P. S. Arri
Shizuhiko Nishisato
Affiliation:
The Ontario Institute for Studies in Education
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Abstract

A modified technique of separable programming was used to maximize the squared correlation ratio of weighted responses to partially ordered categories. The technique employs a polygonal approximation to each single-variable function by choosing mesh points around the initial approximation supplied by Nishisato's method. The major characteristics of this approach are: (i) it does not require any grid refinement; (ii) the entire process of computation quickly converges to the acceptable level of accuracy, and (iii) the method employs specific sets of mesh points for specific variables, whereby it reduces the number of variables for the separable programming technique. Numerical examples were provided to illustrate the procedure.

Type
Original Paper
Information
Psychometrika , Volume 40 , Issue 4 , December 1975 , pp. 525 - 548
Copyright
Copyright © 1975 The Psychometric Society

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Footnotes

*

This study was supported by the Canada Council (Grant No. 73-0399) to S. Nishisato. The authors are indebted to Dr. B. F. Green, Jr., Dr. J. Abrham, and anonymous reviewers for their advice and suggestions.

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