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An Entropy Approach to the Scaling of Ordinal Categorical Data

Published online by Cambridge University Press:  01 January 2025

T. R. Jefferson ,
J. H. May  and
N. Ravi
T. R. Jefferson
Affiliation:
A. B. Freeman School of Business, Tulane University
J. H. May*
Affiliation:
Joseph M. Katz Graduate School of Business, University of Pittsburgh
N. Ravi
Affiliation:
Bell Laboratories
*
Requests for reprints should be sent to Jerrold H. May, The Katz Graduate School of Business, University of Pittsburgh, 214 Mervis Hall, Roberto Clemente Drive, Pittsburgh, PA 15260.
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Abstract

This paper studies the problem of scaling ordinal categorical data observed over two or more sets of categories measuring a single characteristic. Scaling is obtained by solving a constrained entropy model which finds the most probable values of the scales given the data. A Kullback-Leibler statistic is generated which operationalizes a measure for the strength of consistency among the sets of categories. A variety of data of two and three sets of categories are analyzed using the entropy approach.

Keywords

ordinal categorical dataentropyminimum discrimination informationscalingconvex programming
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 2 , June 1989 , pp. 203 - 215
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

This research was partially supported by the Air Force Office of Scientific Research under grant AFOSR 83-0234. The support by the Air Force through grant AFOSR-83-0234 is gratefully acknowledged. The comments of the editor and referees have been most helpful in improving the paper, and in bringing several additional references to our attention.

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