The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability theta). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly…

The adequacy of several approaches to estimation of proficiency distributions for the Trial State Assessment (TSA) in eighth grade mathematics of the National Assessment of Educational Progress was examined. These approaches are more restrictive than the estimation procedures originally used, with the same kind of plausible-values approach that…

The dimensional structure of the 1987 Advanced Placement (AP) French language examination was tested in four populations using a series of confirmatory linear factor analysis models. To mitigate problems with the linear factor analysis of multiple choice items, the linear factor analysis of item parcel scores, made of small mutually exclusive…