Title: On a Generalization of Local Independence in Item Response Theory

Authors: Stefano Noventa, Andrea Spoto, Jürgen Heller, Augustin Kelava

Affiliation: University of Tübingen, Germany; University of Padova, Italy

Abstract:
Knowledge Space Theory (KST) structures can be introduced within Item Response
Theory (IRT) as a possible way to model local dependence (LD) between items.
This allows to generalize the usual characterization of local independence
without introducing new parameters and to merge the information provided by
the IRT and KST perspectives. In detail, connections are established between
the KST Simple Learning Model (SLM) and the IRT General Graded Response Model
(GRM), and between the KST Basic Local Independence model (BLIM) and IRT
models in general. As a consequence, IRT models become a subset of KST models
and both local independence assumption and IRT likelihood functions can be
generalized to account for the existence of prerequisite relations between the
items. Considerations are drawn for the modeling of both dichotomous and
polytomous items, and for their interpretation (e.g., relevance and meaning of
the parameters, definition of polytomous items as knowledge structures of
dichotomous ones, interpretation of Rasch model as a probabilistic version of
Guttman's scale).