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.