Performance Comparison of Item-to-Item Skills Models with the IRT Single Latent Trait Model

Assessing a learner's mastery of a set of skills is a fundamental issue in intelligent learning environments. We compare the predictive performance of two approaches for training a learner model with domain data. One is based on the principle of building the model solely from observable data items, such as exercises or test items. Skills modelling is not part of the training phase, but instead dealt with at later stage. The other approach incorporates a single latent skill in the model. We compare the capacity of both approaches to accurately predict item outcome (binary success or failure) from a subset of item outcomes. Three types of item-to-item models based on standard Bayesian modeling algorithms are tested: (1) Naive Bayes, (2) Tree-Augmented Naive Bayes (TAN), and (3) a K2 Bayesian Classifier. Their performance is compared to the widely used IRT-2PL approach which incorporates a single latent skill. The results show that the item-to-item approaches perform as well, or better than the IRT-2PL approach over 4 widely different data sets, but the differences vary considerably among the data sets. We discuss the implications of these results and the issues relating to the practical use of item-to-item models.