Counts item Response Models under a Bayesian perspective

Count Item Response Theory (IRT) Models identify individual latent traits and facilities of the items of tests that model the error (or success) count in several tasks over time. These types of models can be more informative than traditional dichotomous IRT models. In this talk we introduce the main models in this area and propose some new models. Additionally, under a Bayesian approach we develop residual analysis to assess model fit by introducing randomized quantile residuals for items. Data used to illustrate the method comes from 228 people who took a selective attention test. The test has 20 blocks (items), with a time limit of 15 seconds for each block. Finally, we discuss extensions and challenges for future developments in the area mainly under a Bayesian approach.