Generalized probabilistic models in knowledge structure theory

01/10/2023 to 30/09/2026

Knowledge structures provide a general set-theoretic framework for the representation and assessment of knowledge, and lead to successful large-scale applications in intelligent tutoring systems. The basic local independence model (BLIM) is the standard probabilistic model of knowledge structure theory. The BLIM makes restrictive assumptions on the response error probabilities and suffers from identifiability issues, which may compromise its ability to assess the knowledge state underlying the observed responses. The project sets out to generalize the BLIM while pursuing several goals. It not only aims at providing a framework for empirically validating the the BLIM, but wants to develop a general probabilistic model that implements more plausible assumptions on the response error probabilities. Moreover, it will investigate whether appropriate generalizations can resolve the identifiability issues inherent in the BLIM. Finally, after deriving parameter estimates and implementing their computation, the generalized model will be applied to large-scale data sets to assess its empirical validity.