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

Robert J. Zwitser () and Gunter Maris
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Robert J. Zwitser: University of Amsterdam
Gunter Maris: University of Amsterdam

Psychometrika, 2016, vol. 81, issue 1, No 5, 39-59

Abstract: 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 inferences; sum score; sufficiency; nonparametric IRT; nonparametric Rasch model; monotone latent variable model (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s11336-015-9481-x

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