Investigating Generative Factors of Score Matrices
Proceedings of the 2007 conference on Artificial Intelligence in Education: Building Technology Rich Learning Contexts That Work
IEEE Transactions on Learning Technologies
Improving matrix factorization techniques of student test data with partial order constraints
UMAP'12 Proceedings of the 20th international conference on User Modeling, Adaptation, and Personalization
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Uncovering which skills are determining the success to questions and exercises is a fundamental task in ITS. This task is notoriously difficult because most exercise and question items involve multiple skills, and because skills modeling may involve subtle concepts and abilities. Means to derive this mapping from test results data are highly desirable. They would provide objective and reproductible evidence of item to skills mapping that can either help validate predefine skills models, or give guidance to define such models. However, the progress towards this end has been relatively elusive, in particular for a conjunctive skills model, where all required skills of an item must be mastered to obtain a success. We extend a technique based on Non-negative Matrix Factorization, that was previously shown successful for single skill items, to construct a conjunctive item to skills mapping from test data with multiple skills per item. Using simulated student test data, the technique is shown to yield reliable mapping for items involving one or two skills from a set of six skills.