Report of DFG project no. NO 1505/2-1 - On a generalization of the local independence assumption in item response theory

The assumption of local independence (LI) postulates that, conditional on the value of some latent trait, there is no association between the answers to items in psychological or educational tests. Although violations of LI threaten model validity and bias parameter estimates, a general framework encompassing the different notions of local dependence (LD) is lacking.\ Based on a generalization of LI suggested by Noventa et al. (2019), which combines the latent trait approach of Item Response Theory (IRT) with the set-theoretic approach of Knowledge Space Theory (KST), this project aimed at understanding if an integrated KST-IRT approach provided a way to systematize the different forms and approaches to LD that can be found in literature. The results show that IRT, KST, and Cognitive Diagnostic Assessment (CDA) models can be derived within a unified framework for assessment that postulates two primitives (the notion of structure and the notion of process) and two operations (factorization and reparametrization). Such a unified framework has several advantages. First, it allows to systematize and organize in a taxonomy KST, IRT, and CDA models, thus providing more general modeling techniques and a deeper understanding of model assumptions. Second, it allows to systematize many different approaches to LD. Third, it allows to distinguish between `deterministic' and `probabilistic' forms of `item invasiveness’ (i.e., dependence between items that is not due to unmodeled latent constructs), thus allowing the choice of different modeling mechanisms for problems with different substantive assumptions. Fourth, it allows generalizing and transferring of techniques from polytomous items to collections of dichotomous ones, thus simultaneously providing new approaches to the modeling of LD, a justification to the traditional use of polytomous IRT models to capture the distribution of the sum-score of dependent items, an alternative item-based approach to testlets, and confirmation that the disordered threshold controversy should not be considered a controversy at all. Finally, but not less relevant, it allows to provide closed-form estimators for the parameters of several dichotomous and polytomous IRT models.