Abstract：
Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings.
摘要：
诊断分类模型(DCMs)在教育和心理测量中得到了广泛的应用，尤其是形成性评估。在最近的文献中已经研究了存在testlet的DCM。基于测试的DCM的统计建模和分析的关键因素是两个潜在结构的叠加，属性配置文件和testlet效果。本文扩展了标准测试DINA（T-DINA）模型，以适应两种潜在结构之间的潜在相关性。研究了模型的可辨识性，并提出了一组充分条件。作为副产品，还建立了标准T-DINA的可识别性。所提出的模型应用于2015年国际学生评估计划的数据集。与DINA和T-DINA进行比较，表明在拟合优度方面有了实质性的改善。进行仿真以评估新方法在各种设置下的性能。
