Title: Item response theory model fit assessment via posterior predictive checking: Two case studies
Authors: Mariagiulia Matteucci - University of Bologna (Italy) [presenting]
Stefania Mignani - University of Bologna (Italy)
Abstract: Within the framework of latent variable models, item response theory (IRT) models are used to analyze educational and psychological response data. The issue of model fit assessment is crucial especially in detecting violations to the assumption of unidimensionality and the consequent need of a multidimensional solution, where the conditional independence holds given a set of latent variables. To this aim, Bayesian posterior predictive checks may be employed when the model parameters are estimated through a Markov chain Monte Carlo algorithm. The results of a simulation study using discrepancy measures based on association or correlation among item pairs are presented. Moreover, the effectiveness of the method is shown in two different empirical applications. In the first case study, the perceived benefits and costs of residents towards the tourism industry are investigated by using a questionnaire under the assumption of a multidimensional latent structure. In the second case study, response data coming from an educational language assessment are taken into account where the examinees are scored on a single scale, even if the tests explicitly consists of two different subtests.