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A Beta Unfolding Model for Continuous Bounded Responses

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  • Yvonnick Noel

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. Copyright The Psychometric Society 2014

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  • Yvonnick Noel, 2014. "A Beta Unfolding Model for Continuous Bounded Responses," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 647-674, October.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:4:p:647-674
    DOI: 10.1007/s11336-013-9361-1
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    References listed on IDEAS

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    1. Fumiko Samejima, 1973. "Homogeneous case of the continuous response model," Psychometrika, Springer;The Psychometric Society, vol. 38(2), pages 203-219, June.
    2. J. Ramsay, 1980. "The joint analysis of direct ratings, pairwise preferences, and dissimilarities," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 149-165, June.
    3. Michael Greenacre & Michael Browne, 1986. "An efficient alternating least-squares algorithm to perform multidimensional unfolding," Psychometrika, Springer;The Psychometric Society, vol. 51(2), pages 241-250, June.
    4. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    5. Fumiko Samejima, 1974. "Normal ogive model on the continuous response level in the multidimensional latent space," Psychometrika, Springer;The Psychometric Society, vol. 39(1), pages 111-121, March.
    6. Robert Mislevy, 1984. "Estimating latent distributions," Psychometrika, Springer;The Psychometric Society, vol. 49(3), pages 359-381, September.
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    Cited by:

    1. Nathan D. Minchen & Jimmy de la Torre & Ying Liu, 2017. "A Cognitive Diagnosis Model for Continuous Response," Journal of Educational and Behavioral Statistics, , vol. 42(6), pages 651-677, December.
    2. Matthias Kloft & Raphael Hartmann & Andreas Voss & Daniel W. Heck, 2023. "The Dirichlet Dual Response Model: An Item Response Model for Continuous Bounded Interval Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 888-916, September.

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