A review of methods for analyzing test data with local dependence structures

An item response theory perspective

Abstract

Local independence is a fundamental assumption of item response theory (IRT), allowing the factorization of the joint distribution of responses. However, it’s often violated in real-world data due to model misspecification, environmental factors, structural dependencies, and shared factors within clusters, leading to local dependence (LD). Traditional LD diagnostics, such as Yen’s Q₃ and contingency table independence tests, have improved with resampling, and novel indices have emerged. Existing IRT models, which typically address dependencies through less interpretable parameters, have been extended to simultaneously handle person and item dependencies and represent complex structures while preserving interpretability via nuisance dimension projection and copula functions. This study reviews recent LD diagnostics and modeling improvements, highlighting key practical considerations and suggesting future research directions.