Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix
Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix
复制标题
认知诊断中的属性层次模型：潜在属性空间的可识别性和Q矩阵完整性的条件
作者：
Hans;Chia
教育研究人员认为，一个现实的看法，认知诊断模型中的属性的作用，应占的可能性，属性不是孤立的实体，但相互依存的测试性能的影响。文献中讨论了不同的方法;其中一种主张是强加一个层次结构，以便掌握一个或多个属性是掌握一个或多个其他属性的先决条件。属性的分层组织约束了潜在属性空间，使得不再定义若干熟练度类（如果属性没有分层组织，则它们存在），因为相应的属性组合不能与给定的属性层次一起发生。因此，潜在的属性空间的识别往往是困难的，特别是，如果属性的数量很大。作为一个额外的复杂性，如果假设测试项目的属性具有层次结构，则构建完整的Q矩阵可能根本不是简单的。本文研究了属性按层次组织时的潜在空间的可识别性条件和Q矩阵的完备性条件。
Educational researchers have argued that a realistic view of the role of attributes in cognitively diagnostic modeling should account for the possibility that attributes are not isolated entities, but interdependent in their effect on test performance. Different approaches have been discussed in the literature; among them the proposition to impose a hierarchical structure so that mastery of one or more attributes is a prerequisite of mastering one or more other attributes. A hierarchical organization of attributes constrains the latent attribute space such that several proficiency classes, as they exist if attributes are not hierarchically organized, are no longer defined because the corresponding attribute combinations cannot occur with the given attribute hierarchy. Hence, the identification of the latent attribute space is often difficult—especially, if the number of attributes is large. As an additional complication, constructing a complete Q-matrix may not at all be straightforward if the attributes underlying the test items are supposed to have a hierarchical structure. In this article, the conditions of identifiability of the latent space if attributes are hierarchically organized and the conditions of completeness of the Q-matrix are studied.