It is a very helpful paper to understanding multilevel IRT. The multilevel model was firstly introduced. A Bayesian procedure Markov chain Monte Carlo to estimate all parameters simultaneously is present. The model-data fit using the PPC method as well as the model comparison using the PsBF are also demonstrated. A simulation study using the multilevel empty model was carried out to assess the performance of the MCMC estimation procedure. Several multilevel IRT models were used to analysis the real data and then compared in a systematic way.
Future study:
The measurement models in the present study assume that the ability parameter is unidimensional though in generally, multiple latent traits will involved within the multilevel IRT model. Hence, it could be extended to multidimensional-multilevel IRT model.