Continuation Ratio Model in Item Response Theory and Selection of Models for Polytomous Items

In the continuation ratio model continuation ratio logits are used to model the probabilities of obtaining ordered categories in polytomously scored items. The continuation ratio model is an alternative to other models for ordered category items such as the graded response model, the generalized partial credit model, and the partial credit model. The theoretical development of the model, descriptions of special cases, maximum likelihood estimation of the item and ability parameters are presented. An illustration and comparisons of the models for ordered category items are presented using empirical data.