论文标题
精密教育：评估数据中的贝叶斯非参数方法和考生异质性
Precision education: A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data
论文作者
论文摘要
我们在本文中提出了一种新型的非参数贝叶斯IRT模型，通过在问题水平引入聚类效应，并在每个问题群集下在考生水平上进一步假设异质性，其特征是二项式分布的混合物。这项工作的主要贡献是三倍：（1）我们证明该模型是可识别的。 （2）可以渐近地捕获聚类效应，并且可以以根n速率（最多的日志项）来估算考生解决某些问题的能力的感兴趣参数。 （3）我们提出了一种可访问的采样算法，以从我们提出的模型中获得有效的后验样品。我们通过一系列模拟评估我们的模型，并将其应用于英语评估数据。该数据分析示例很好地说明了测试制造商如何使用我们的模型来区分不同类型的学生并帮助设计未来的测试。
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.
