Abstract
This paper presents recently discovered properties of mutual information between concepts and dichotomous test items. The properties generalize some common intuitions for comparing test items, and provide principled foundations for designing item-selection heuristics for student assessments in computer-assisted educational systems. We compare performance profiles achieved by systems that adopt mutual information and the Mahalanobis distance in the assessment task. Experimental results reveal that, all else being equal, the mutual information based methods offer better performance profiles. In addition, experimental results suggest that, when computing mutual information online is considered computationally costly, heuristics that are designed based on our theoretical findings serve as a good delegate for exact mutual information.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Yan, D., Almond, R.G., Mislevy, R.J.: Empirical comparisons of cognitive diagnostic models. unpublished draft of Educational Testing Service (2003), http://www.ets.org/research/dload/aera03-yan.pdf
Rost, J., Langeheine, R. (eds.): Applications of Latent Trait and Latent Class Models in the Social Sciences. Waxmann (1997)
Birenbaum, M., Kelly, A.E., Tatsuoka, K.K., Gutvirtz, Y.: Attribute-mastery patterns from rule space as the basis for student models in algebra. Int’l J. of Human-Computer Studies 40, 497–508 (1994)
VanLehn, K., Martin, J.: Evaluation of an assessment system based on Bayesian student modeling. Int’l J. of Artificial Intelligence in Education 8, 179–221 (1997)
Liu, C.L.: Using mutual information for adaptive student assessments. In: Proc. of the 4th IEEE Int’l Conf. on Advanced Learning Technologies, pp. 585–589 (2004)
Jensen, F.V.: Bayesian Networks and Decision Graphs. Springer, Heidelberg (2001)
Wellman, M.P.: Fundamental concepts of qualitative probabilistic networks. Artificial Intelligence 44, 257–303 (1990)
Hambleton, R.K., Swaminathan, H., Rogers, H.J.: Fundamentals of Item Response Theory. SAGE Publications, Thousand Oaks (1991)
Liu, C.L., Wang, Y.T., Liu, Y.C.: A Bayesian network-based simulation environment for investigating assessment issues in intelligent tutoring systems. In: Proc. of the Int’l Computer Symposium, pp. 234–239 (2004)
Mislevy, R.J., Almond, R.G., Yan, D., Steinberg, L.S.: Bayes nets in educational assessment: Where do the numbers come from? In: Proc. of the 15th Conf. on Uncertainty in Artificial Intelligence, pp. 437–446 (1999)
Cover, T.M., Thomas, J.A.: Elements of Information Theory. John Wiley & Sons, Chichester (1991)
Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification. Wiley, Chichester (2001)
VanLehn, K., Ohlsson, S., Nason, R.: Applications of simulated students: An exploration. Int’l J. of Artificial Intelligence in Education 5, 135–175 (1994)
Collins, J.A., Greer, J.E., Huang, S.X.: Adaptive assessment using granularity hierarchies and Bayesian nets. In: Proc. of the 3rd Int’l Conf. on Intelligent Tutoring System, pp. 569–577 (1996)
Mayo, M., Mitrovic, A.: Optimising ITS behaviour with Bayesian networks and decision theory. Int’l J. of Artificial Intelligence in Education 12, 124–153 (2001)
Lauritzen, S.L.: The EM algorithm for graphical association models with missing data. Computational Statistics & Data Analysis 19, 191–201 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, CL. (2005). Some Theoretical Properties of Mutual Information for Student Assessments in Intelligent Tutoring Systems. In: Hacid, MS., Murray, N.V., Raś, Z.W., Tsumoto, S. (eds) Foundations of Intelligent Systems. ISMIS 2005. Lecture Notes in Computer Science(), vol 3488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11425274_54
Download citation
DOI: https://doi.org/10.1007/11425274_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25878-0
Online ISBN: 978-3-540-31949-8
eBook Packages: Computer ScienceComputer Science (R0)