A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data
A Bayesian nonparametric approach for handling item and examinee heterogeneity in assessment data
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用于处理评估数据中的项目和考生异质性的贝叶斯非参数方法
DOI：
10.1111/bmsp.12322
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发表时间：
2024
影响因子：
2.6
通讯作者：
Hu, Guanyu
中科院分区：
文献类型：
--
作者：
Pan, Tianyu;Shen, Weining;Davis‐Stober, Clintin P.;Hu, Guanyu
我们提出了一种新的非参数贝叶斯项目反应理论模型，估计集群的问题水平，同时允许在考生水平下的每个问题集群的异质性，其特征在于由一个混合的二项分布。这项工作的主要贡献有三个方面。首先，我们提出了我们的新模型，并证明它是可识别的一组条件下。其次，我们证明了我们的模型可以正确地渐近识别问题级别的聚类，并且可以以n的速率（直到对数项）估计衡量考生解决某些问题的熟练程度的感兴趣参数。第三，我们提出了一个易于处理的采样算法，以获得有效的后验样本从我们提出的模型。与现有的方法相比，我们的模型设法揭示考生的水平在处理不同类型的问题简约的多维度，通过施加一个嵌套的聚类结构。通过一系列的模拟，以及将其应用于英语水平评估数据集所提出的模型进行评估。这个数据分析的例子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，并帮助设计未来的测试。
We propose a novel nonparametric Bayesian item response theory model that estimates clusters at the question level, while simultaneously allowing for heterogeneity at the examinee level under each question cluster, characterized by a mixture of binomial distributions. The main contribution of this work is threefold. First, we present our new model and demonstrate that it is identifiable under a set of conditions. Second, we show that our model can correctly identify question‐level clusters asymptotically, and the parameters of interest that measure the proficiency of examinees in solving certain questions can be estimated at a n rate (up to a log term). Third, we present a tractable sampling algorithm to obtain valid posterior samples from our proposed model. Compared to the existing methods, our model manages to reveal the multi‐dimensionality of the examinees' proficiency level in handling different types of questions parsimoniously by imposing a nested clustering structure. The proposed model is evaluated via a series of simulations as well as apply it to an English proficiency assessment data set. 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.