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Latent Trait Models and Dichotomization of Graded Responses

Published online by Cambridge University Press:  01 January 2025

Paul G. W. Jansen  and
Edward E. Roskam
Paul G. W. Jansen
Affiliation:
Industrial Psychology Branch, The Netherlands Postal and Telecommunications Services, the Hague
Edward E. Roskam*
Affiliation:
University of Nijmegen
*
Requests for reprints should be sent to Edward Roskam, Department of Psychology, Mathematical Psychology Group, University of Nijmegen, Montessorilaan 3, P.O. Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Abstract

This paper discusses the compatibility of the polychotomous Rasch model with dichotomization of the response continuum. It is argued that in the case of graded responses, the response categories presented to the subject are essentially an arbitrary polychotomization of the response continuum, ranging for example from total rejection or disagreement to total acceptance or agreement of an item or statement. Because of this arbitrariness, the measurement outcome should be independent of the specific polychotomization applied, for example, presenting a specific multicategory response format should not affect the measurement outcome. When such is the case, the original polychotomous model is called “compatible” with dichotomization.

A distinction is made between polychotomization or dichotomization “before the fact,” that is, in constructing the response format, and polycho- or dichotomization “after the fact,” for example in dichotomizing existing graded response data.

It is shown that, at least in case of dichotomization after-the-fact, the polychotomous Rasch model is not compatible with dichotomization, unless a rather special condition of the model parameters is met. Insofar as it may be argued that dichotomization before the fact is not essentially different from dichotomization after the fact, the value of the unidimensional polychotomous Rasch model is consequently questionable. The impact of our conclusion on related models is also discussed.

Keywords

latent trait theorydichotomizationpolychotomous Rasch modelgraded responsesrating data
Type
Original Paper
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 69 - 91
Copyright
Copyright © 1986 The Psychometric Society

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