  The Elo rating system has been recognised as an effective method for
modelling students and items within adaptive educational systems. The existing
Elo-based models have the limiting assumption that items are only tagged with a
single concept and are mainly studied in the context of adaptive testing
systems. In this paper, we introduce a multivariate Elo-based learner model
that is suitable for the domains where learning items can be tagged with
multiple concepts, and investigate its fit in the context of adaptive learning.
To evaluate the model, we first compare the predictive performance of the
proposed model against the standard Elo-based model using synthetic and public
data sets. Our results from this study indicate that our proposed model has
superior predictive performance compared to the standard Elo-based model, but
the difference is rather small. We then investigate the fit of the proposed
multivariate Elo-based model by integrating it into an adaptive learning system
which incorporates the principles of open learner models (OLMs). The results
from this study suggest that the availability of additional parameters derived
from multivariate Elo-based models have two further advantages: guiding
adaptive behaviour for the system and providing additional insight for students
and instructors.
