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On Measurement Properties of Continuation Ratio Models

Published online by Cambridge University Press:  01 January 2025

Bas T. Hemker ,
L. Andries van der Ark  and
Klaas Sijtsma
Bas T. Hemker*
Affiliation:
CITO National Institute for Educational Measurement
L. Andries van der Ark
Affiliation:
Tilburg University
Klaas Sijtsma
Affiliation:
Tilburg University
*
Requests for reprints should be sent to Bas T. Hemker, Measurement and Research Department, CITO National Institute for Educational Measurement, EO. Box 1034, 6801 MG Arnhem, THE NETHERLANDS. E-Mail: bas.hemker@citogroep
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Abstract

Three classes of polytomous IRT models are distinguished. These classes are the adjacent category models, the cumulative probability models, and the continuation ratio models. So far, the latter class has received relatively little attention. The class of continuation ratio models includes logistic models, such as the sequential model (Tutz, 1990), and nonlogistic models, such as the acceleration model (Samejima, 1995) and the nonparametric sequential model (Hemker, 1996). Four measurement properties are discussed. These are monotone likelihood ratio of the total score, stochastic ordering of the latent trait by the total score, stochastic ordering of the total score by the latent trait, and invariant item ordering. These properties have been investigated previously for the adjacent category models and the cumulative probability models, and for the continuation ratio models this is done here. It is shown that stochastic ordering of the total score by the latent trait is implied by all continuation ratio models, while monotone likelihood ratio of the total score and stochastic ordering on the latent trait by the total score are not implied by any of the continuation ratio models. Only the sequential rating scale model implies the property of invariant item ordering. Also, we present a Venn-diagram showing the relationships between all known polytomous IRT models from all three classes.

Keywords

acceleration modeladjacent category modelscontinuation ratio modelscumulative probability modelshierarchical relationships between IRT modelsinvariant item orderingmonotone likelihood ratiopolytomous IRT modelssequential modelstochastic ordering
Type
Articles
Information
Psychometrika , Volume 66 , Issue 4 , December 2001 , pp. 487 - 506
Copyright
Copyright © 2001 The Psychometric Society

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