Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing
Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing
复制标题
DOI：
10.1007/s11336-022-09845-x
复制
发表时间：
2022-03
期刊：
影响因子：
3
通讯作者：
F. Liu;Xiaojing Wang;R. Hancock;Ming-Hui Chen
中科院分区：
文献类型：
--
作者：
F. Liu;Xiaojing Wang;R. Hancock;Ming-Hui Chen
计算机化评估提供了丰富的多维数据，包括试验的准确性和反应时间（RT）的措施。建模这类数据的一个关键问题是如何将RT数据，例如，在项目反应理论（IRT）模型的能力估计的援助。为了解决这个问题，我们提出了一个联合模型，包括一个双参数IRT模型的二分法项目反应数据，一个对数正态模型的连续RT数据，和相应的纸笔分数的正常模型。然后，我们重新制定和重新参数化的模型，以捕捉模型参数之间的关系，以促进先验规范，并使贝叶斯计算更有效。在此基础上，提出了几种新的基于偏差信息准则（DIC）分解的伪边缘似然对数（LPML）模型评价准则。所提出的标准可以量化的多维数据的一个部分的其他部分的拟合的改善。最后，我们已经进行了几个模拟研究，以检查所提出的模型评估标准的实证表现，并说明了这些标准的应用程序使用一个真实的数据集从计算机化的教育评估程序。
Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.