Posterior Predictive Assessment of IRT Models via the Hellinger Distance: A Simulation Study

Fit assessment of item response theory models is a crucial issue. In recent years, posterior predictive model checking has become a popular tool for investigating overall model fit and potential misfit due to specific items. Different approaches rely on graphical analysis, posterior predictive p-values, the relative entropy and, more recently, the Hellinger distance. In this study, we focus on the performance of the Hellinger distance in the case multidimensional data are analyzed with a unidimensional approach. In particular, we consider the case of three latent dimensions. A simulation study is conducted to show the effectiveness of the method. Finally, the results of an empirical application to potential three-dimensional data are discussed.