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A Simple Multivariate Probabilistic Model for Preferential and Triadic Choices

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 Guelph
Daniel M. Ennis*
Affiliation:
Philip Morris Research Center
*
Requests for reprints should be sent to Daniel Ennis, Philip Morris Research Center, PO Box 26583, Richmond, Virginia, 23261.
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Abstract

Multidimensional probabilistic models of behavior following similarity and choice judgements have proven to be useful in representing multidimensional percepts in Euclidean and non-Euclidean spaces. With few exceptions, these models are generally computationally intense because they often require numerical work with multiple integrals. This paper focuses attention on a particularly general triad and preferential choice model previously requiring the numerical evaluation of a 2n-fold integral, where n is the number of elements in the vectors representing the psychological magnitudes. Transforming this model to an indefinite quadratic form leads to a single integral. The significance of this form to multidimensional scaling and computational efficiency is discussed.

Keywords

multivariate triadsduo-triocanonical quadratic formschoice modelsmultidimensional scalingpreferenceunfolding
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 1 , March 1991 , pp. 69 - 75
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

The authors would like to thank Jean-Claude Falmagne and Norman Johnson for suggestions and advice concerning quadratic forms.

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