In cognitive diagnostic assessment a property of the Q-matrix, usually referred to as completeness, warrants that the cognitive attributes underlying the observed behaviour can be uniquely assessed. Characterizations of completeness were first derived under the assumption of independent attributes, and are currently under investigation for interdependent attributes. The dominant approach considers so-called attribute hierarchies, which are conceptualized through a partial order on the set of attributes. The present paper extends previously published results on this issue obtained for conjunctive attribute hierarchy models. Drawing upon results from knowledge structure theory, it provides novel sufficient and necessary conditions for completeness of the Q-matrix, not only for conjunctive models on attribute hierarchies, but also on more general attribute structures.

中文翻译：

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一般属性结构的合取模型中的完整 Q 矩阵

在认知诊断评估中，Q矩阵的属性（通常称为完整性）保证了可以唯一评估所观察行为背后的认知属性。完整性的表征首先是在独立属性的假设下得出的，目前正在研究相互依赖的属性。主要的方法考虑所谓的属性层次结构，它是通过属性集的部分顺序来概念化的。本论文扩展了先前发表的关于此问题的结果，这些结果是针对连接属性层次模型获得的。借鉴知识结构理论的结果，为Q的完备性提供了新的充要条件。-matrix，不仅适用于属性层次结构的连接模型，还适用于更一般的属性结构。