Diagnostic classification models in educational measurement describe ability in a knowledge domain as a composite of specific binary skills called “cognitive attributes,” each of which an examinee may or may not have mastered. Attribute Hierarchy Models (AHMs) account for the possibility that attributes are dependent by imposing a hierarchical structure such that mastery of one or more attributes is a prerequisite of mastering one or more other attributes. Thus, the number of meaningfully defined attribute combinations is reduced, so that constructing a complete Q-matrix may be challenging. (The Q-matrix of a cognitively diagnostic test documents which attributes are required for solving which item; the Q-matrix is said to be complete if it guarantees the identifiability of all realizable proficiency classes among examinees.) For structured Q-matrices (i.e., the item attribute profiles are restricted to reflect the hierarchy postulated to underlie the attributes), the conditions of completeness have been established. However, sometimes, a structured Q-matrix cannot be assembled because the items of the test in question have attribute profiles that do not conform to the prerequisite structure imposed by the postulated attribute hierarchy. A Q-matrix composed of such items is called “unstructured.” In this article, the completeness conditions of unstructured Q-matrices for the DINA model are presented. Specifically, there exists an entire range of Q-matrices that are all complete for DINA-AHMs. Thus, the theoretical results presented here can be combined with extant insights about Q-completeness for models without attribute hierarchies into a unified framework on the completeness of Q-matrices for the DINA model.

教育测量中的诊断分类模型将知识领域的能力描述为称为“认知属性”的特定二元技能的组合，考生可能已掌握或未掌握每种技能。属性层次模型（AHM）通过施加一种层次结构来说明属性依赖的可能性，这样一个或多个属性的掌握是掌握一个或多个其他属性的先决条件。因此，减少了有意义定义的属性组合的数量，因此构造一个完整的Q矩阵可能具有挑战性。（认知诊断测试的Q矩阵记录了解决哪个项目所需的属性;如果Q矩阵能够确保考生中所有可实现的熟练程度等级的可识别性，则可以说是完整的。）对于结构化的Q矩阵（即，限制项目属性概要文件以反映假定为属性基础的层次结构），已经建立了完整性条件。但是，有时，无法组装结构化的Q矩阵，因为所讨论的测试项目的属性配置文件与假定的属性层次结构强加的先决条件结构不符。由此类项目组成的Q矩阵称为“非结构化”。本文介绍了DINA模型的非结构化Q矩阵的完备性条件。具体来说，存在一个完整的Q矩阵范围，这些矩阵对于DINA-AHM都是完整的。因此，