The Application of Bayesian Networks in Cognitive Diagnosis with Small Sample Size
In this study,Bayesian networks(BN)are proposed to conduct cognitive diagnosis in a small sample.The combination of IRP(Ideal Response Pattern)and EM parameter estimating methods can overcome the shortcomings of IRP and EM algorithms respectively,and can realize the BN application in a small sample size.The Monte Carlo simulation study is used to examine the performance of the BN-IRP-EM method in a small sample size,compared with the hamming distance method.In the simulation study,the pattern match ratio and average attribute match ratio are used as criteria to evaluate the classification accuracy of different approaches.To demonstrate the effectiveness of the BN-IRP-EM method,the BN based purely on the IRP method is adopted as the controlling method,another controlling method is the hamming distance(H-D)method.The results are as follows:the classification rate of the BN-IRP method is slightly higher than that of the H-D method which is based on the same IRP information except for some conditions.The classification rate of the BN-IRP-EM method is higher than the BN-IRP method and the H-D method in all circumstances.In the BN-IRP-EM condition,due to the incorporation of the empirical information,the classification rate is gradually increasing with the increase in sample size.These outcomes demonstrated that the BN-IRP-EM method could be used in a small sample size and can promote the application of CDA in classroom assessment.