Rasch Models: How (In-)Coherently are they Showed and Used?

Abstract

Rasch models are widely used for the analysis of educational data. In practice, estimates of difficulties of items and abilities of examinees are reported. However, the meaning of the terms "difficulty" and "abilities" are never made explicit. The meaning of these terms does not depend on the estimations; they should be interpreted with respect to the eventual meaning of both item difficulties and individual abilities. This paper shows that the meaning of the terms "difficulty" and "ability" depends on the way in which the Rasch model is specified. In the psychometric literature, Rasch models are specified in two different ways: one specifies the observable only, whereas the other one specifies both observable and unobservable. The first specification is due to Rasch himself, the second one is due to Lord.