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 the first virtual item and an incorrect response to the second virtual item. A score of 0 would be coded as an incorrect response to the first virtual item and the second virtual item would be coded as not administered (missing). Now the responses to all virtual items can be modelled by an IRT model for dichotomous items, such as the models given by Eqs. 1, 2 or 3 and can be estimated by any IRT software package that can handle dichotomous items in combination with missing data. There are also IRT packages that estimate models for polytomous items directly (e.g., Multilog; Thissen et al. 2003).
