A class of probabilistic unfolding models for polytomous responses

By revisiting the approaches used to present the Rasch model for polytomous response, this paper uses the principle of the rating formulation (Andrich . 1978) to construct a class of unfolding models for polytomous responses i n terms of a set of latent dichotomous unfolding variables. By anchoring th e dichotomous unfolding variables involved at the same location, this paper presents a formulation of a very general class of unfolding models for ord ered polytomous responses, of which the unfolding models for ordered polyto mous responses proposed hitherto are special cases. Within this class, the analytic and measurement properties of the probabilistic Functions are well interpreted in terms of the latitudes of acceptance parameters of the dich otomous unfolding models. Based on the general form of this: class of unfol ding models, some new models are readily specified. (C) 2001 Academic Press .