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Mathematical Formulation of Multivariate Euclidean Models for Discrimination Methods

Published online by Cambridge University Press:  01 January 2025

Kenneth Mullen  and
Daniel M. Ennis
Kenneth Mullen
Affiliation:
Department of Mathematics and Statistics, University of Guleph
Daniel M. Ennis*
Affiliation:
Philip Morris Research Center
*
Request for reprints should be sent to Daniel M. Ennis, Philip Morris Research Center, PO Box 26583, Richmond, VA 23261.
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Abstract

Multivariate models for the triangular and duo-trio methods are described in this paper. In both cases, the mathematical formulation of Euclidean models for these methods is derived and evaluated for the bivariate case using numerical quadrature. Theoretical results are compared with those obtained using Monte Carlo simulation which is validated by comparison with previously published theoretical results for univariate models of these methods. This work is discussed in light of its importance to the development of a new theory for multidimensional scaling in which the traditional assumption can be eliminated that proximity measures and perceptual distances are monotonically related.

Keywords

triangularduo-triomultidimensional scalingproximity measures
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 2 , March 1987 , pp. 235 - 249
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

We thank J. Frijters, J. Tindall, H. A. David, R. Pangborn, and J. and E. Kapenga for useful discussions and criticism; M. Waugh, D. Zima, D. Paulson, and S. Osborne for computer support; and J. Day and Y. Lancaster for manuscript preparation assistance.

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