Lu Jing, Wang Chun, Zhang Jiwei, Tao Jian
Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, China.
College of Education, University of Washington, Seattle, Washington, USA.
Br J Math Stat Psychol. 2020 May;73(2):261-288. doi: 10.1111/bmsp.12175. Epub 2019 Aug 6.
Many educational and psychological assessments focus on multidimensional latent traits that often have a hierarchical structure to provide both overall-level information and fine-grained diagnostic information. A test will usually have either separate time limits for each subtest or an overall time limit for administrative convenience and test fairness. In order to complete the items within the allocated time, examinees frequently adopt different test-taking behaviours during the test, such as solution behaviour and rapid guessing behaviour. In this paper we propose a new mixture model for responses and response times with a hierarchical ability structure, which incorporates auxiliary information from other subtests and the correlation structure of the abilities to detect rapid guessing behaviour. A Markov chain Monte Carlo method is proposed for model estimation. Simulation studies reveal that all model parameters could be recovered well, and the parameter estimates had smaller absolute bias and mean squared error than the mixture unidimensional item response theory (UIRT) model. Moreover, the true positive rate of detecting rapid guessing behaviour is also higher than when using the mixture UIRT model separately for each subscale, whereas the false detection rate is much lower than the mixture UIRT model. The deviance information criterion and the logarithm of the pseudo-marginal likelihood are employed to evaluate the model fit. Finally, a real data analysis is presented to demonstrate the practical value of the proposed model.
许多教育和心理评估关注的是多维潜在特质，这些特质通常具有层次结构，以提供总体水平信息和细粒度的诊断信息。为了便于管理和保证测试公平性，一项测试通常会对每个子测试设置单独的时间限制，或者设置一个总体时间限制。为了在规定时间内完成题目，考生在测试过程中经常会采取不同的应试行为，比如解题行为和快速猜测行为。在本文中，我们提出了一种新的针对作答和作答时间的混合模型，该模型具有层次化的能力结构，它整合了来自其他子测试的辅助信息以及能力的相关结构，以检测快速猜测行为。我们提出了一种马尔可夫链蒙特卡罗方法用于模型估计。模拟研究表明，所有模型参数都能很好地恢复，并且参数估计的绝对偏差和均方误差比混合单维项目反应理论（UIRT）模型更小。此外，检测快速猜测行为的真阳性率也高于对每个子量表分别使用混合UIRT模型时的情况，而误检率则远低于混合UIRT模型。我们使用偏差信息准则和伪边际似然对数来评估模型拟合度。最后，通过实际数据分析来证明所提出模型的实用价值。
