This study proposes and evaluates a diagnostic classification model framework for multiple‐choice items. Models in the proposed framework have a two‐level nested structure which allows for binary scoring (for correctness) and polytomous scoring (for distractors) at the same time. One advantage of these models is that they can provide distractor information while maintaining the statistical properties of the correct response option. We evaluated parameter recovery through a simulation study using Hamiltonian Monte Carlo algorithms in Stan. We also discussed three approaches to implementing the proposed modelling framework for different purposes and testing scenarios. We illustrated those approaches and compared them with a binary model and a traditional nominal model through an operational study.

中文翻译：

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多项选择项的嵌套诊断分类模型

本研究提出并评估了多项选择项目的诊断分类模型框架。所提出框架中的模型具有两级嵌套结构，允许同时进行二元评分（为了正确性）和多分评分（为了干扰项）。这些模型的一个优点是它们可以提供干扰信息，同时保持正确响应选项的统计特性。我们通过在 Stan 中使用 Hamiltonian Monte Carlo 算法的模拟研究来评估参数恢复。我们还讨论了为不同目的和测试场景实施建议的建模框架的三种方法。我们举例说明了这些方法，并通过操作研究将它们与二元模型和传统名义模型进行了比较。