Abstract: Nowadays, polytomous items are widely used in psychological and educational tests. Polytomous items are more attractive than dichotomous items because they can provide more information for the examinees. With respect to polytomous items, there are many models to use such as the Grade Response Model (GRM), which was proposed by Samejima (1969), the Nominal Categories Model (NCM), which was proposed by Bock (1972), and the Partial Credit Model (PCM), which was proposed by Masters (1982). It is known that the GRM and PCM can be used observed ordered levels of response and the NCM is suitable for those nominal categories items.
However, it is a common fact that most polytomous items are not always scored in ordered categories or nominal ones. What models can be used for those polytomous items with responses scored in mixed categories? What scoring models to propose? It is the main purpose of the paper to discuss these problems.
In the paper, the notion of item node is given firstly. Then, given assumption that the probability of a correct response on an item node can be fit by the two-parameter Logistic model, three polytomous scoring models, one of which is GRM, are outlined for three different types of items. In conclusion, the model for a polytomous item based on item node can be derived.

Key words: polytomous scoring model, item node, GRM, two-parameter Logistic Model