Abstract
In the attribute hierarchy method, cognitive attributes are assumed to be organized hierarchically. Content specialists usually conduct a task analysis on a sample of items to specify the cognitive attributes required by the correctly answered items, and to order these attributes to create an attribute hierarchy. However, the problem-solving performance of experts and novices was almost certain to be different. Additionally, experts’ knowledge is highly organized in deeply integrated schemas, while a novice views domain knowledge and problem-solving knowledge separately. Thus, this may bring uncertainty into the attribute hierarchy and lead to different attribute hierarchies for a test. Formally, a Bayesian network is a probabilistic graphical model that represents a set of random latent attributes or variables and their conditional dependencies via a directed acyclic graph. For example, a Bayesian network can be used to represent the probabilistic relationships between latent attributes in the attribute hierarchy. The purpose of this study is to apply Bayesian network for modeling uncertainty in an attribute hierarchy. The Bayesian network created from the attribute hierarchy, which is regarded as a flexible high-order model, is incorporated into three cognitive diagnostic models. The new model has an advantage of taking an account of subjectivity of the attribute hierarchy specified by experts with the uncertainty of item responses. Fraction subtraction data were analyzed to evaluate the performance of the new model.
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Acknowledgements
This research is supported by the National Natural Science Foundation of China (Grant No. 31500909, 31360237, and 31160203), the Key Project of National Education Science “Twelfth Five Year Plan” of Ministry of Education of China (Grant No. DHA150285), the National Natural Science Foundation of Jiangxi (Grant No. 20161BAB212044), the Education Science Foundation of Jiangxi (Grant No. 13YB032), the Social Science Foundation of Jiangxi (Grant No. 17JY10), the National Social Science Fund of China (Grant No. 16BYY096), the Humanities and Social Sciences Research Foundation of Ministry of Education of China (Grant No. 12YJA740057), and the Youth Growth Fund and the Doctoral Starting up Foundation of Jiangxi Normal University. The authors would like to thank the editor Steve Culpepper for the valuable comments.
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Song, L., Wang, W., Dai, H., Ding, S. (2018). Bayesian Network for Modeling Uncertainty in Attribute Hierarchy. In: Wiberg, M., Culpepper, S., Janssen, R., González, J., Molenaar, D. (eds) Quantitative Psychology. IMPS 2017. Springer Proceedings in Mathematics & Statistics, vol 233. Springer, Cham. https://doi.org/10.1007/978-3-319-77249-3_26
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