A nonparametric Bayesian item response modelling approach for clustering items and individuals simultaneously

Item response theory (IRT) is a popular modelling 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, which obtains the number of clusters and the clustering configurations for both items and individuals simultaneously. The performance of parameter estimation and parameter clustering under the MFM Rasch model is evaluated by simulation studies, and two real examples are applied to further illustrate the MFM Rasch modelling.