Item Relational Structure Theory Based on Liu’s Improved Nonparametric IRT Theory

In this paper, an extensional item relational structure theory based on the improved nonparametric item response theory is proposed. Item relational structure theory (Takeya, 1991) was developed to detect item relational structures of a group of subjects. The differences of these structures and experts knowledge structures can provide more information for planning remedial instruction, developing instruction materials, or educational researches. In this study, Lius improved nonparametric item response theory ( Liu, 2000, 2013) without the local independence assumption is used to estimate the joint probability of two items, and construct personal item relational structures. A Mathematics example is also provided in this paper to illustrate the advantages of the proposed method

Liu’s Polytomous Item Relational Structure Theory Based on Q-Matrix Theory

In this paper, an improved polytomous item relational structure theory based on Q-matrix theory is proposed, using Tatsuoka’s Q-matrix theory, we can construct the test with all efficient items which are fitting in with the given relational structure of cognitive attributes, and then, before the test, using Liu’s before-test item ordering theory, an ideal relational structural graph of itemscan be constructed, and the real efficient items can be obtained accordingly. After testing the students, an after-test structure of items can be estimated by using the Liu’s polytomous item relational structure theory. Furthermore, using Liu’s criterion related validity index, we can evaluate the estimated item relational structure of the test, and the results could be useful for cognitive diagnosis and remedial instruction.

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.