Bayesian Student Models Based on Item to Item Knowledge Structures
Bayesian networks are commonly used in cognitive student modeling and assessment. They typically represent the item-concepts relationships, where items are observable responses to questions or exercises and concepts represent latent traits and skills. Bayesian networks can also represent concepts-concepts and concepts-misconceptions relationships. We explore their use for modeling item-item relationships, in accordance with the theory of knowledge spaces. We compare two Bayesian frameworks for that purpose, a standard Bayesian network approach and a more constrained framework that relies on a local independence assumption. Their performance is compared over their respective ability to predict item outcome and through simulations over two data sets. The simulation results show that both approaches can effectively perform accurate predictions, but the constrained approach shows higher predictive power than a Bayesian Network. We discuss the applications of item to item structure for cognitive modeling within different contexts.
KeywordsBayesian Network Directed Acyclic Graph Knowledge Structure Knowledge State Structural Learning
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- 5.Desmarais, M.C., Pu, X.: A bayesian inference adaptive testing framework and its comparison with item response theory. International Journal of Artificial Intelligence in Education 15, 291–323 (2005)Google Scholar
- 8.Dowling, C.E., Hockemeyer, C.: Automata for the assessment of knowledge. IEEE Transactions on Knowledge and Data Engineering (2001)Google Scholar
- 10.François, O., Leray, P.: Etude comparative d’algorithmes d’apprentissage de structure dans les réseaux bayésiens. In: RJCIA 2003, pp. 167–180 (2003)Google Scholar
- 11.Jensen, F.V.: An introduction to Bayesian Networks. UCL Press, London (1996)Google Scholar
- 14.Mislevy, R.J., Almond, R.G., Yan, D., Steinberg, L.S.: Bayes nets in educational assessment: Where the numbers come from. In: Laskey, K.B., Prade, H. (eds.) Proceedings of the 15th Conference on Uncertainty in Artificial Intelligence (UAI 1999), pp. 437–446. Morgan Kaufmann Publishers, San Francisco (1999)Google Scholar
- 15.Murphy, K.P.: The Bayes net toolbox for MATLAB. Technical report, University of California at Berkeley; Berkeley, CA, October 12 (2001)Google Scholar
- 16.Neapolitan, R.E.: Learning Bayesian Networks. Prentice Hall, New Jersey (2004)Google Scholar
- 17.Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, 2nd edn. MIT Press, Cambridge (2000)Google Scholar