关键词: 额外信息, 贝叶斯定理, 机器学习诊断法, 判准率

Abstract: With the emerging era of big data, cognitive diagnostic assessment (CDA) can no longer be limited to the mining of single test information but should acquire a large amount of information of students through various methods, which will aid in distinguishing the knowledge state of students synthetically. Existing research on CDA involves preliminary studies that are based on parametric models incorporating process information, and they require additional parameters to be included in the original model. As a result, the model not only becomes more complex but also is not necessarily universal. Moreover, to deal with different types of data, such a model needs to be refactored. Therefore, how to simplify the method to combine process information is a topic worthy of extensive research. Among machine-learning-based diagnostic methods, the probabilistic neural network (PNN) diagnostic method combines the advantages of neural networks and non-parametric methods. The existing algorithm of the PNN uses Euclidean distance discrimination (EDD). Nevertheless, Kang and Yang (2019) found that the Manhattan distance discrimination (MDD) method has a higher accuracy rate than EDD. Based on this, this study has the following objectives: (1) The Euclidean distance in the PNN algorithm is modified to the Manhattan distance to improve the accuracy of the PNN diagnostic method. (2) In the second layer of the PNN algorithm, Bayes' theorem is added such that additional information can be fused in the model and the state of students’ knowledge can be comprehensively identified. Accordingly, the study proposes a relatively concise cognitive diagnostic method (termed MB-PNN) that can incorporate additional information. Further, the effectiveness and suitability of the MB-PNN are examined through simulation and empirical research. The results demonstrate the following: (1) Under the same conditions, the accuracy rate of the M-PNN is higher than that of the PNN, indicating that replacing the Euclidean Distance in the PNN with the Manhattan Distance is an effective approach. (2) Under the same conditions, the accuracy rate of the MB-PNN is higher than those of the M-PNN and PNN, indicating that the diagnosis accuracy based on multiple information is higher than that based on single information. (3) The MB-PNN retains the original non-parametric advantages of the PNN and is basically not affected by the distribution of knowledge state and the sample size. (4) The MB-PNN can optimally distinguish different types of students and is more suited for application in CDA. The study provides possible research ideas for cognitive diagnosis and evaluation based on multimodal education big data.

Key words: additional information, Bayes', theorem, machine learning diagnosis method, accuracy rate