Attribute Hierarchical Structure Estimation Based On Three Structure Learning Algorithms

The cognitive attributes examined by diagnostic tests are usually not independent,and often have a hierarchical relationship,and they are interconnected in the form of a network.The psychological order or hierarchical relationship between cognitive attributes is called Attribute Hierarchy(AH).In the actual test scenario,it is challenging to accurately obtain the attribute hierarchy relationship,and the attribute hierarchies obtained based on experience is prone to wrong or inconsistent settings.Based on this,this research estimates the attribute hierarchy from a data-driven perspective.On the one hand,it provides a more realistic and possible statistical method for large-scale diagnostic testing.On the other hand,it reduces the subjectivity caused by human judgment and provides objective supplementary evidence when there are inconsistent settings in artificial definition.Based on three Bayesian network structure learning algorithms,this paper derives the relationship between attributes from the data of students’ mastery of attributes.Take the student’s master pattern as input,and use Bayesian network structure learning algorithms: K2 algorithm,HC algorithm and MMHC algorithm to learn the attribute hierarchy.In order to examine the accuracy of the three Bayesian network structure learning algorithms under different conditions,this paper carried out a series of studies.The main factors considered are: attribute level(dichotomous attributes or polytomous attributes),The number of attributes,the quality of the questions,the number of questions,the sample size,the threshold under the K2 algorithm,and the true attribute hierarchy.Three researches were specifically carried out.Research 1: Research on hierarchical structure learning based on algorithms that require attribute topological sorting(K2 algorithm),Research 2: Research on hierarchical structure learning based on algorithms that do not require attribute topological sorting(HC and MMHC),Research 3: Research on empirical data.Research indicates:(1)The K2 algorithm has a high correct recovery rate for the learning of the attribute hierarchies.Under the condition of the dichotomous attributes,the attribute hierarchies can be obtained totally correct under the appropriate conditions,and the correct recovery rate can reach more than 80% under the appropriate conditions under the polytomous attributes condition.The results of the HC algorithm and the MMHC algorithm are close.The correct recovery rate can reach more than 95% under the appropriate conditions under the dichotomous attributes,and over 90% under the appropriate conditions under the polytomous attributes;(2)Under the dichotomous attributes,as the number of attributes increases,the correct recovery rate decreases.The better the quality of the question,the correct recovery rate increases slightly,and the sample size has a little effect on the correct recovery rate;under the polytomous attributes condition,the question quality and the number of questions has a greater impact on the correct recovery rate,the lower the quality of the question,the fewer the number of questions,the lower the correct recovery rate;(3)Under the K2 algorithm,the higher the threshold,the higher the recovery rate of linear,divergent and convergent types.When the threshold is 0.05,that is,when the scoring standard is the strictest,the recovery rate is the highest.The opposite is true for the unstructured type.The higher the threshold,the lower the recovery rate;(4)Because the score is equivalent or the algorithm itself falls into a local optimum,the accuracy of the HC algorithm and the MMHC algorithm in identifying the convergence type is low,and even the sample size may inhibit the estimation accuracy;(5)In the study of empirical data,the data of a probability theory teaching experiment at the University of Tubingen was selected,and the result showed that the attribute hierarchy obtained under the strict standard of the K2 algorithm is more logical.The results obtained by the Bayesian network structure learning algorithm do reflect the " attribute hierarchy of the participants" to a certain extent,and it is complementary to the attribute-hierarchy specified by experts.