ABSTRACT
Early item response models were concerned with the simple dichotomous case where items were either solved or not. But items often carry more information when the response is in ordered categories with higher categories meaning better performance. Various models that exploit the information in ordered categories have been proposed in recent years. The model considered here is appropriate for items that are solved in a stepwise manner such that higher levels can be reached only if previous levels were reached earlier. Items of this structure are quite common, in particular, in ability tests. A simple example that illustrates items of this type is as follows.
