Dependent Dirichlet Process Rating Model

Abstract

Typical item response theory (IRT) rating scale models assume that the rating category threshold parameters are the same over examinees. Unfortunately, such models are inappropriate for rating data that exhibit differential item functioning (DIF). The authors introduce a new Bayesian nonparametric IRT model for rating scale items, which is more appropriate for rating data that contain DIF. The model is an infinite mixture of Rasch partial credit models, with mixture distribution modeled by the local (Dependent) Dirichlet process. The model treats the rating category thresholds as the random parameters that are subject to the mixture, with (stick-breaking) mixture weights that are covariate-dependent. Thus, the model allows the rating category thresholds to differ across items and examinees, while allowing the form of the distribution for the category thresholds to vary flexibly as a function of covariates. The authors illustrate the new model through the analysis of simulated data and real data. The model demonstrated the ability to correctly identify DIF items. Moreover, the model attained better predictive-fit performance than did other commonly used IRT rating models.