Bayesian Item Response Modeling in R with brms and Stan

Abstract

Item response theory (IRT) is widely applied in the human sciences to model persons' responses on a set of items measuring one or more latent constructs. While several R packages have been developed that implement IRT models, they tend to be restricted to respective pre-specified classes of models. Further, most implementations are frequentist while the availability of Bayesian methods remains comparably limited. I demonstrate how to use the R package brms together with the probabilistic programming language Stan to specify and fit a wide range of Bayesian IRT models using flexible and intuitive multilevel formula syntax. Further, item and person parameters can be related in both a linear or non-linear manner. Various distributions for categorical, ordinal, and continuous responses are supported. Users may even define their own custom response distribution for use in the presented framework. Common IRT model classes that can be specified natively in the presented framework include 1PL and 2PL logistic models optionally also containing guessing parameters, graded response and partial credit ordinal models, as well as drift diffusion models of response times coupled with binary decisions. Posterior distributions of item and person parameters can be conveniently extracted and postprocessed. Model fit can be evaluated and compared using Bayes factors and efficient cross-validation procedures.

Keywords

• item response theory
• bayesian statistics
• r
• stan
• brms