Abstract: It’s very significant to correctly identify the hierarchical relation among attributes correctly when constructing a diagnosis test. As we know, there are various methods to identify the hierarchical relation among attributes in different cognitive diagnosis models (CDMs). Rule Space Model (RSM) is a kind of great influence CDM which was developed by Tatsuoka and her associates. In RSM, the task of attribute identification is performed after the test items have already been developed. And then an incidence Q matrix can be determined which reflects hierarchical relation. However, in Leighton, Gierl and Hunka’s (2004) Attribute Hierarchy Method (AHM) the organization of attributes(attributes, number of attributes and attribute hierarchical relation) should be determined before developing the test items. In RSM and AHM the importance of correctly identifying the attributes and their hierarchical relation cannot be overstated, and the attributes and their hierarchical relations serve as the most important input variables to the models because they provide the basis for interpreting the results. The hierarchical relation among attributes describes the domain knowledge structures. Understanding the domain knowledge structures in highly specific detail provides a rational basis for proposing and evaluating potential improvements in the measurement of general proficiency. Otherwise, improvement remains largely a trial-and-error process. It has been proved that is not reliable to get the hierarchical relation by analyzing the test items, even the resulting hierarchical relations are not unique.
Now, structure learning of Bayesian Networks would be introduced to study the hierarchical relation from the examinees’ attribute mastery patterns. On the one hand, this paper conducted a simulation study in which Cui, Leighton and Zheng (2006)’s attribute hierarchical relation was employed, and the sample size of 5000 was used. In the simulated study, different sliping rates was considered for the purpose of testing the robustness of Bayesian structure learning. On the other hand, this paper conducted an empirical study to research the attributes which were commonly used in different numeration representation system converting, and the sample size was 189. Also the hierarchical relation generated by Bayesian structure learning and the hierarchical relation extracted by domain expert was compared.
The result of simulation study and empirical study all showed the Bayesian Networks was a very useful tool in determining the hierarchical relation among attributes in the realm of education measurement and psychometrics. It is proved that the result for reference is valuable through structure learning of Bayesian Networks in simulated experiments and practical application. Meanwhile, the Bayesian Networks also can be used to test the hierarchical relation in RSM.

Key words: rule space model, cognitive diagnosis, Bayesian networks, structure learning