Modeling Skill Dependence in Probabilistic Competence Structures

In knowledge space theory (KST) a competence structure is a set theoretical representation of the dependencies among a given set of skills. A probabilistic model for skill dependence is proposed which respects a precise correspondence requirement between set theoretical and probabilistic representations of skill dependence. An empirical application on integer subtraction problems at the primary school shows that the proposed model fits the data pretty well. Moreover, in a comparison with an unrestricted skill based version of the basic local independence model (BLIM), the proposed model fits better than this last, indicating that the restrictions implied by the correspondence requirement are not too strong.