Title: Non-Identifiability in Probabilistic Knowledge Structures and Cognitive Diagnostic Models Author: Jürgen Heller Affiliation: University of Tuebingen Abstract: As an indispensable prerequisite for unambiguously assessing the cognitive state of an individual, the identifiability of probabilistic knowledge structures has received some attention recently. Extending results available for the basic local independence model (BLIM) to its competence-based extension (CBLIM), non-identifiability is shown to be due to quite independent properties of the underlying skill function (assigning subsets of skills to items, each of which sufficient for solving them). These different sources of non-identifiability can be characterized through its associated problem function (specifying the items that can be solved within a subset of skills) on the one hand, and through structural aspects of the delineated knowledge structure on the other hand. As the CBLIM is equivalent to the Multiple Strategy DINA, these results transfer to a whole class of cognitive diagnostic models (Heller, Stefanutti, Robusto, and Anselmi, 2013). It will be demonstrated how the mentioned identifiability issues can be addressed in practical applications by using the R package pks. References: Heller, J., Stefanutti, L., Robusto, E., and Anselmi, P. (2013). Cognitive diagnostic models and knowledge space theory: the non-missing link. Manuscript submitted for publication.