Bayesian Estimation of a Multi-Unidimensional Graded Response IRT Model

Unidimensional graded response models are useful when items are designed to measure a unified latent trait. They are limited in practical instances where the test structure is not readily available or items are not necessarily measuring the same underlying trait. To overcome the problem, this paper proposes a multi-unidimensional normal ogive graded response model under the Bayesian framework. The performance of the proposed model was evaluated using Monte Carlo simulations. It was further compared with conventional polytomous models under simulated and real test situations. The results suggest that the proposed multi-unidimensional model is more general and flexible, and offers a better way to represent test situations not realized in unidimensional models.