On a generalization of the local independence assumption in item response theory

• Applicant: Stefano Noventa, Ph.D.
• Subject Area: General, Cognitive and Mathematical Psychology
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 450766602

Local independence (LI) is a fundamental assumption of Item Response Theory (IRT) and captures the idea that, conditional on the value of some latent variable (e.g., ability), there is no association between a series of manifest variables (e.g., answers to items in psychological or educational tests). In practice, however, several effects (e.g., fatigue, changes in format, dependence between items) can substantially violate LI. This threatens model validity, invalidates the likelihood, and results in problematic estimates of the parameters and false substantial inferences. Research on the topic has been extensive, yet violations of LI remain an open problem with blurred boundaries. In an attempt to disentangle the concepts involved, a generalization of LI based on Knowledge Space Theory (KST) was recently suggested. This integrated KST-IRT approach accounts indeed for `invasive' relations between items while retaining the usual characterization of LI. The combinatorial and set-theoretic approach of KST is used to identify the partial order representing the relation between the items and to obtain a generalized class of likelihoods that accounts for both response and trait dependence. Furthermore, the KST-IRT approach allows generalizing and transferring of techniques from polytomous items to collections of dichotomous ones, thus providing a further approach to the modeling of local dependence and an alternative item-based approach to testlets. The present project aims at investigating whether the KST-IRT approach can be used to formally systematize and investigate the different forms of local dependence and the different - and often unlinked - approaches that can be found in literature. Additionally, a new perspective will be provided on the modelling and testing of local dependence, polytomous items, and testlets based on bringing together different definitions and approaches that originated in the fields of Psychometrics and Mathematical Psychology. From an applied perspective, the project aims at implementing estimation procedures for the KST-IRT models in the open source R framework. The present project will deliver both techniques and software that are expected to have an impact on the interpretation and application of local independence in assessment models. For this purpose, a postdoctoral researcher is required to support the PI in developing the project and in strengthening the collaborative network of the newly founded Methods Center of the University of Tübingen. In particular, the Postdoc and the PI will collaborate with experienced Psychometricians and Mathematical Psychologists from the University of Tubingen and the University of Padova (Italy).

• DFG Programme: Research Grants