Polytomous item relational structure theory based on empirical distribution critical value

The threshold limit value of Takeya's item relational structure theory is a fixed value, which is lacking of statistical meaning, in our previous paper, an improved threshold limit value by using the empirical distribution critical value was proposed, it was showed that the new theory is more sensitive and effective than the old one. However, for constructing the item relational structure, both of them can only be used for dichotomous items, not for polytomous items. In this paper, the empirical distribution critical value based polytomous item relational structure theory is proposed, it is a generalization of our previously improved theory. A calculus example was also provided in this paper to illustrate the advantages of the proposed method.