extended · article · 1995

Conceptual Notes on Models for Discrete Polytomous Item Responses

Gideon J. Mellenbergh; Ivor W. Molenaar

The following types of discrete item responses are distinguished : nominal-dichotomous, ordinal-dichotomous, nominal-polytomous, and ordinal-polytomous. Bock (1972) presented a model for nominal-polytomous item responses that, when applied to dichotomous responses, yields Birnbaum's (1968) two-parameter logistic model. Applying Bock's model to ordinal-polytomous items leads to a conceptual problem. The ordinal nature of the response variable must be preserved; this can be achieved using three different methods. A number of existing models are derived using these three methods. The structure of these models is similar, but they differ in the interpretation and qualities of their parameters. Informa-tion, parameter invariance, log-odds differences invariance, and model violation also are discussed. Information and parameter invariance of dichotomous item response theory (nt'r) also apply t...