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A Beta Unfolding Model for Continuous Bounded Responses

Published online by Cambridge University Press:  01 January 2025

Yvonnick Noel
Yvonnick Noel*
Affiliation:
University of Brittany, Rennes 2
*
Requests for reprints should be sent to Yvonnick Noel, University of Brittany Rennes 2, Department of Psychology, Place du Recteur Henri Le Moal, CS 24307, 35043 Rennes Cedex, France. E-mail: yvonnick.noel@uhb.fr
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Abstract

An unfolding model for continuous bounded responses is proposed, derived both from a hypothetical interpolation response mechanism and from the hypothesis of two opposite sources of item refusal being collapsed. These two sources of refusal are made explicit in a three-component Dirichlet response model and then collapsed to obtain a (two-component) beta response model. The two natural parameters of the beta are interpreted as acceptance and refusal parameters and expressed as functions of person-item distances on a latent continuum. The potentially bimodal shape of the beta is exploited to model chaotic response choices among ambivalent subjects.

Keywords

item response theoryunfolding analysisbeta distributioncontinuous bounded responsesbimodality
Type
Original Paper
Information
Psychometrika , Volume 79 , Issue 4 , October 2014 , pp. 647 - 674
Copyright
Copyright © 2013 The Psychometric Society

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Footnotes

An R script for estimating the BUM parameters is available upon request from the author.

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