We propose a novel nonparametric Bayesian IRT model in this paper by introducing the clustering effect at question level and further assume heterogeneity at examinee level under each question cluster, characterized by the mixture of Binomial distributions. The main contribution of this work is threefold: (1) We demonstrate that the model is identifiable. (2) The clustering effect can be captured asymptotically and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a root n rate (up to a log term). (3) We present a tractable sampling 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 an English assessment data. This data analysis example nicely illustrates how our model can be used by test makers to distinguish different types of students and aid in the design of future tests.

翻译：在本文中,我们提出一个新的非参数性巴伊西亚光学和光学研究模型,办法是在问题层面引入集束效应,并在每个问题组下进一步假设受检查层的异质性,其特点是Binomial分布的混合,这项工作的主要贡献是三重:(1) 我们证明该模型是可以辨认的。(2) 集群效应可以不时地捕捉,衡量受检查者在解决某些问题上的熟练程度的利害参数可以按根速(直到一个日志术语)估算。(3) 我们提出一种可移植的抽样算法,以便从我们提议的模型中获得有效的后方样本。我们通过一系列模拟来评估我们的模型,并将其应用到英国的评估数据中。这一数据分析实例很好地说明了我们的模型如何被测试者用来区分不同类型的学生,并协助设计今后的测试。