There are several IRT models for ordered categories (e.g., Samejima 1969; Masters 1982). These have different rationales and are not reparameterisations of each other, but the practical implications for preferring one over the other are often negligible. Here we describe a continuation-ratio model (Tutz 1990; Verhelst et al. 1997). This model allows the transformation of a polytomous item into a set of dichotomous items, which facilitates model estimation. The response to a polytomous item is viewed as a set of responses to an ordered sequence of virtual dichotomous items: it is assumed that the respondent is administered virtual items until an incorrect or negative response is given. So, in this approach, an item with M categories labelled m = 0,..., M − 1, the response is dummy-coded into M − 1 dichotomous quasi-items. As an example, for an item with m = 3 categories we make two new virtual items. A score of 2 would be coded as correct responses to both virtual items. A score of 1 on the original item would be coded as a correct response to
