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Assessing the Correspondence of One or More Vectors to a Symmetric Matrix Using Ordinal Regression

Published online by Cambridge University Press:  01 January 2025

Thomas J. Reynolds  and
Kenneth H. Sutrick
Thomas J. Reynolds*
Affiliation:
The University of Texas at Dallas
Kenneth H. Sutrick
Affiliation:
Murray State University
*
Requests for reprints should be sent to Thomas J. Reynolds, School of Management, University of Texas at Dallas, Richardson, TX 75080.
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Abstract

A statistical model for interpreting psychological scaling research, based on the heuristic work of Reynolds (1983), is developed. This new approach has certain advantages over the standard property fitting approach (Chang and Carroll, 1969) currently used to interpret multidimensional scaling spaces (Shepard, 1962; Torgerson, 1965). These advantages are (a) the ability to directly assess the correspondence of a descriptor vector(s) to a symmetric matrix, and (b) to provide a method in which only ordinal properties of such descriptors are required: thus standard rating, ranking, or sorting data collection methods can be used as the basis to interpret the multidimensional space resulting from the distance data.

Keywords

Data CollectionStatistical ModelPublic PolicySortingStatistical Theory
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 101 - 112
Copyright
Copyright © 1986 The Psychometric Society

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