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Ordering Individuals with Sum Scores: The Introduction of the Nonparametric Rasch Model

Published online by Cambridge University Press:  01 January 2025

Robert J. Zwitser  and
Gunter Maris
Robert J. Zwitser*
Affiliation:
University of Amsterdam
Gunter Maris
Affiliation:
Cito Institute for Educational Measurement and University of Amsterdam
*
Correspondence should be made to Robert J. Zwitser, University of Amsterdam, Amsterdam, The Netherlands. Email: zwitser@uva.nl
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Abstract

When a simple sum or number-correct score is used to evaluate the ability of individual testees, then, from an accountability perspective, the inferences based on the sum score should be the same as the inferences based on the complete response pattern. This requirement is fulfilled if the sum score is a sufficient statistic for the parameter of a unidimensional model. However, the models for which this holds true are known to be restrictive. It is shown that the less restrictive nonparametric models could result in an ordering of persons that is different from an ordering based on the sum score. To arrive at a fair evaluation of ability with a simple number-correct score, ordinal sufficiency is defined as a minimum condition for scoring. The monotone homogeneity model, together with the property of ordinal sufficiency of the sum score, is introduced as the nonparametric Rasch model. A basic outline for testable hypotheses about ordinal sufficiency, as well as illustrations with real data, is provided.

Keywords

ordinal inferencessum scoresufficiencynonparametric IRTnonparametric Rasch modelmonotone latent variable model
Type
Original paper
Information
Psychometrika , Volume 81 , Issue 1 , March 2016 , pp. 39 - 59
Copyright
Copyright © 2015 The Psychometric Society

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