The Hellinger Distance within Posterior Predictive Assessment for Investigating Multidimensionality in IRT Models

Abstract

Under the Bayesian approach, posterior predictive model checking (PPMC) has become a popular tool for fit assessment of item response theory (IRT) models. In this study, we propose the use of the Hellinger distance within PPMC to quantify the distance between the realized and the predictive distribution of the model-based covariance for item pairs. Specifically, the case of multidimensional data analyzed with a unidimensional approach is taken into account. The results of the simulation study show the effectiveness of the method in detecting model misfit and the sensitivity to the trait correlations. An application to real data on tourism perceptions shows the feasibility of the method in practice and especially the capability of detecting potential misfit attributed to specific items.

Keywords:

• Posterior predictive model checking
• Hellinger distance
• MIRT models
• goodness of fit
• MCMC

Notes

1 Monte Carlo standard error in brackets.