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The Elo rating system has been recognised as an effective method formodelling students and items within adaptive educational systems. The existingElo-based models have the limiting assumption that items are only tagged with asingle concept and are mainly studied in the context of adaptive testingsystems. In this paper, we introduce a multivariate Elo-based learner modelthat is suitable for the domains where learning items can be tagged withmultiple concepts, and investigate its fit in the context of adaptive learning.To evaluate the model, we first compare the predictive performance of theproposed model against the standard Elo-based model using synthetic and publicdata sets. Our results from this study indicate that our proposed model hassuperior predictive performance compared to the standard Elo-based model, butthe difference is rather small. We then investigate the fit of the proposedmultivariate Elo-based model by integrating it into an adaptive learning systemwhich incorporates the principles of open learner models (OLMs). The resultsfrom this study suggest that the availability of additional parameters derivedfrom multivariate Elo-based models have two further advantages: guidingadaptive behaviour for the system and providing additional insight for studentsand instructors.

A Multivariate Elo-based Learner Model for Adaptive Educational Systems