The Rasch Rating Model and the Disordered Threshold Controversy

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Adams, Raymond J, Wu, Margaret and Wilson, Mark (2012) The Rasch Rating Model and the Disordered Threshold Controversy. Educational and Psychological Measurement, 72 (4). pp. 547-573. ISSN 0013-1644 (print) 1552-3888 (online)


The Rasch rating (or partial credit) model is a widely applied item response model that is used to model ordinal observed variables that are assumed to collectively reflect a common latent variable. In the application of the model there is considerable controversy surrounding the assessment of fit. This controversy is most notable when the set of parameters that are associated with the categories of an item have estimates that are not ordered in value in the same order as the categories. Some consider this disordering to be inconsistent with the intended order of the response categories in a variable and often term it reversed deltas. This article examines a variety of derivations of the model to illuminate the controversy. The examination of the derivations shows that the so-called parameter disorder and order of the response categories are separate phenomena. When the data fit the Rasch rating model the response categories are ordered regardless of the (order of the) values of the parameter estimates. In summary, reversed deltas are not necessarily evidence of a problem. In fact the reversed deltas phenomenon is indicative of specific patterns in the relative numbers of respondents in each category. When there are preferences about such relative numbers in categories, the patterns of deltas may be a useful diagnostic.

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Item type Article
DOI 10.1177/0013164411432166
Official URL
Subjects Historical > FOR Classification > 1701 Psychology
Historical > Faculty/School/Research Centre/Department > College of Education
Keywords ResPubID25702, partial credit model, Rasch model, Rasch rating model
Citations in Scopus 79 - View on Scopus
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