New developments in the evaluation of goodness of fit for multidimensional IRT models based on posterior predictive assessment: Results from the INVALSI data

The issue of model fit assessment is crucial within the framework of item response theory (IRT) models. To overcome the limitations of classical tools which are affected by the problem of sparse data, Bayesian posterior predictive model checking (PPMC) was recently introduced. The purposes of this study are: a) to examine the feasibility of the PPMC method in practice when investigating multidimensionality in IRT models; b) to propose the Hellinger distance within PPMC to be used as a goodness of fit tool. These methods are applied to the INVALSI Italian test data of grade 5. The results support the existence of a predominant general ability without excluding the presence of specific subdimensions.