Comparing Two IRT Models for Conjunctive Skills
A step in ITS often involve multiple skills. Thus a step requiring a conjunction of skills is harder than steps that require requiring each individual skill only. We developed two Item-Response Models – Additive Factor Model (AFM) and Conjunctive Factor Model (CFM) – to model the conjunctive skills in the student data sets. Both models are compared on simulated data sets and a real assessment data set. We showed that CFM was as good as or better than AFM in the mean cross validation errors on the simulated data. In the real data set CFM is not clearly better. However, AFM is essentially performing as a conjunctive model.
KeywordsConjunctive Model Cross Validation Error Cognitive Tutoring Latent Trait Model Multiple Skill
Unable to display preview. Download preview PDF.
- 1.Kurt VanLehn, K.K., Skogsholm, A., Nwaigwe, A., Hausmann, R.G.M., Weinstein, A., Billings, B.: Whats in a step? Toward general, abstract representations of tutoring system log data. In: Conati, C., McCoy, K., Paliouras, G. (eds.) UM 2007. LNCS (LNAI), vol. 4511. Springer, Heidelberg (2007)Google Scholar
- 2.Mitrovic, A., Koedinger, K.R., Martin, B.: A Comparative Analysis of Cognitive Tutoring and Constraint-Based Modeling. In: User Modeling 2003. Springer, Heidelberg (2003)Google Scholar
- 3.Cen, H., Koedinger, K., Junker, B.: Learning Factors Analysis - A General Method for Cognitive Model Evaluation and Improvement. In: 8th International Conference on Intelligent Tutoring Systems (2006)Google Scholar
- 4.Embretson, S.: Multicomponent Response Models. In: Linden, W.V.D., Hambleton, R.K. (eds.) Handbook of Modern Item Response Theory. Springer, Heidelberg (1997)Google Scholar
- 5.Koedinger, K.R., Nathan, M.J.: The real story behind story problems: Effects of representations on quantitative reasoning. The Journal of the Learning Sciences (2003)Google Scholar