The Rasch Rating Model and the Disordered Threshold Controversy

Abstract

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 mod..