Posterior Predictive Assessment for Item Response Theory Models: A Proposal Based on the Hellinger Distance

Bayesian posterior predictive assessment has received considerable attention for investigating specific aspects of fit of item response theory models. In fact, this approach is easy to apply within Markov chain Monte Carlo estimation, it is flexible and free from distributional assumptions. In its classical implementation, the method is based on graphical analysis and the estimation of posterior predictive p-values to investigate the degree to which observed data are expected under the model, given a discrepancy measure. In this work, we propose to quantify the distance between the realized and the predictive distributions of the discrepancy measure based on the Hellinger distance. The results show that this measure is able to provide clear recommendations about the investigated aspects of model fit.