  Item response theory (IRT) is a popular modeling paradigm for measuring
subject latent traits and item properties according to discrete responses in
tests or questionnaires. There are very limited discussions on heterogeneity
pattern detection for both items and individuals. In this paper, we introduce a
nonparametric Bayesian approach for clustering items and individuals
simultaneously under the Rasch model. Specifically, our proposed method is
based on the mixture of finite mixtures (MFM) model. MFM obtains the number of
clusters and the clustering configurations for both items and individuals
simultaneously. The performance of parameters estimation and parameters
clustering under the MFM Rasch model is evaluated by simulation studies, and a
real date set is applied to illustrate the MFM Rasch modeling.
