Dependent Dirichlet Process Rating Model (DDP-RM)

Typical IRT rating-scale models assume that the rating category threshold parameters are the same over examinees. However, it can be argued that many rating data sets violate this assumption. To address this practical psychometric problem, we introduce a novel, Bayesian nonparametric IRT model for rating scale items. The model is an infinite-mixture of Rasch partial credit models, based on a localized Dependent Dirichlet process (DDP). The model treats the rating thresholds as the random parameters that are subject to the mixture, and has (stick-breaking) mixture weights that are covariate-dependent. Thus, the novel model allows the rating category thresholds to vary flexibly across items and examinees, and allows the distribution of the category thresholds to vary flexibly as a function of covariates. We illustrate the new model through the analysis of a simulated data set, and through the analysis of a real rating data set that is well-known in the psychometric literature. The model is shown to have better predictive-fit performance, compared to other commonly used IRT rating models.