Computational strategies and estimation performance with Bayesian semiparametric Item Response Theory models

Abstract: Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures offer a more flexible representation of the unknown distribution of the latent trait. However, the use of such models in the IRT literature has been extremely limited, in good part because of the lack of comprehensive studies and accessible software tools. This paper provides guidance for practitioners on semiparametric IRT models and their implementation. In particular, we rely on NIMBLE, a flexible software system for hierarchical models that enables the use of Dirichlet process mixtures. We highlight efficient sampling strategies for model estimation and compare inferential results under parametric and semiparametric models.