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Probabilistic, Multidimensional Unfolding Analysis

Published online by Cambridge University Press:  01 January 2025

Joseph L. Zinnes  and
Richard A. Griggs
Joseph L. Zinnes
Affiliation:
Indiana University
Richard A. Griggs
Affiliation:
Indiana University
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Abstract

A probabilistic, multidimensional version of Coombs' unfolding model is obtained by assuming that the projections of each stimulus and each individual on each axis are normally distributed. Exact equations are developed for the single dimensional case and an approximate one for the multidimensional case. Both types of equations are expressed solely in terms of univariate normal distribution functions and are therefore easy to evaluate. A Monte Carlo experiment, involving 9 stimuli and 3 subjects in a 2 dimensional space, was run to determine the degree of accuracy of the multidimensional equation and the feasibility of using iterative methods to obtain maximum likelihood estimates of the stimulus and subject coordinates. The results reported here are gratifying in both respects.

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 3 , September 1974 , pp. 327 - 350
Copyright
Copyright © 1974 The Psychometric Society

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