Bayesian Modeling of Local Item Dependence in IRT Testlet Data Using Antedependence Models

In educational assessments, testlet-based designs are widely used but often violate the local independence assumption of item response theory (IRT). This work proposes a flexible Bayesian approach for modeling local item dependence (LID) in testlet data, using a multivariate two-parameter probit IRT model with a structured correlation matrix defined via antedependence models. By incorporating Toeplitz structures, the model captures nuanced within-testlet dependencies. We implement an efficient posterior sampling scheme using the No-U-Turn Sampler via Stan package. A simulation study shows accurate parameter recovery and reduced bias in the presence of LID. In addition, we provide applications to real educational datasets, including large-scale assessments in Brazil, in which we show that our approach yields more interpretable and stable parameter estimates compared to standard IRT models.