  Item response theory (IRT) models are widely used to obtain interpretable
inference when analyzing data from questionnaires, scaling binary responses
into continuous constructs. Typically, these models rely on a normality
assumption for the latent trait characterizing individuals in the population
under study. However, this assumption can be unrealistic and lead to biased
results. We relax the normality assumption by considering a flexible Dirichlet
Process mixture model as a nonparametric prior on the distribution of the
individual latent traits. Although this approach has been considered in the
literature before, there is a lack of comprehensive studies of such models or
general software tools. To fill this gap, we show how the NIMBLE framework for
hierarchical statistical modeling enables the use of flexible priors on the
latent trait distribution, specifically illustrating the use of Dirichlet
Process mixtures in two-parameter logistic (2PL) IRT models. We study how
different sets of constraints can lead to model identifiability and give
guidance on eliciting prior distributions. Using both simulated and real-world
data, we conduct an in-depth study of Markov chain Monte Carlo posterior
sampling efficiency for several sampling strategies. We conclude that having
access to semiparametric models can be broadly useful, as it allows inference
on the entire underlying ability distribution and its functionals, with NIMBLE
being a flexible framework for estimation of such models.
