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Conditions for Rasch-Dichotomizability of the Unidimensional Polytomous Rasch Model

Published online by Cambridge University Press:  01 January 2025

Edward E. Roskam  and
Paul G. W. Jansen
Edward E. Roskam*
Affiliation:
Nijmegen Institute for Cognition and Information (NICI) Division of Mathematical Models, University of Nijmegen
Paul G. W. Jansen
Affiliation:
Industrial Psychology Branch, The Netherlands Telecommunications Services, The Hague
*
Requests for reprints should be sent to Edward Roskam, Psychological Laboratory, University of Nijmegen, Montessorilaan 3, PO Box 9104, 6500 HE Nijmegen, THE NETHERLANDS.
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Abstract

Jansen and Roskam (1986) discussed the compatibility of the unidimensional polytomous Rasch model with dichotomization of the response continuum. They derived a rather strict condition in which dichotomization of multicategory data that fit the unidimensional polytomous Rasch model, results in dichotomous data which fit the dichotomous Research model with effectively the same subject parameter. In this paper a more general dichotomization condition is derived for the polytomous Rasch model, which appears less restrictive, but upholds that the intrinsic logic of the unidimensional polytomous Rasch model defies dichotomization in general. The robustness of dichotomous analysis investigated in a simulation study. It shows a close relation with the two-parameters (Birnbaum) model. Theoretical and methodological implications are discussed.

Keywords

latent trait theorydichotomizatonpolytomous Rasch modelgraded responsesrating data
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 2 , June 1989 , pp. 317 - 332
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

The authors are indebted to H. Müller (personal communication, August 1986), for giving an example which pointed toward the core equation in this paper. The authors also acknowledge the critical comments of Th. Bezambinder and P. Wakker, and of Psychometrika's reviewers to an earlier version of this paper.

References

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