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We propose a novel nonparametric Bayesian IRT model in this paper byintroducing the clustering effect at question level and further assumeheterogeneity at examinee level under each question cluster, characterized bythe mixture of Binomial distributions. The main contribution of this work isthreefold: (1) We demonstrate that the model is identifiable. (2) Theclustering effect can be captured asymptotically and the parameters of interestthat measure the proficiency of examinees in solving certain questions can beestimated at a root n rate (up to a log term). (3) We present a tractablesampling algorithm to obtain valid posterior samples from our proposed model.We evaluate our model via a series of simulations as well as apply it to anEnglish assessment data. This data analysis example nicely illustrates how ourmodel can be used by test makers to distinguish different types of students andaid in the design of future tests.

Precision education: A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data