A Nonparametric Bayesian Item Response Modeling Approach for Clustering Items and Individuals Simultaneously

TL;DR

This paper introduces a nonparametric Bayesian method using mixture of finite mixtures to simultaneously cluster items and individuals in item response theory, enhancing heterogeneity detection in test data.

Contribution

It proposes a novel MFM-based Bayesian approach for joint clustering of items and individuals under the Rasch model, addressing a gap in heterogeneity pattern detection.

Findings

Effective parameter estimation demonstrated through simulations

Successful real data application illustrating model utility

Simultaneous clustering improves heterogeneity understanding

Abstract

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.