Identifiability of Hierarchical Latent Attribute Models
Identifiability of Hierarchical Latent Attribute Models
复制标题
DOI：
10.5705/ss.202021.0350
复制
发表时间：
2019-06
影响因子：
1.4
通讯作者：
Yuqi Gu;Gongjun Xu
中科院分区：
文献类型：
--
作者：
Yuqi Gu;Gongjun Xu
分层潜在属性模型（HLAM）是一种离散潜在变量模型，在教育、心理和行为科学领域越来越受到关注。 HLAM 的关键要素包括二元结构矩阵和有向无环图，指定对潜在属性配置的分层约束。这些组件编码了从业者的设计信息并具有重要的科学意义。尽管 HLAM 很受欢迎，但基本的可识别性问题仍未得到解决。属性层次图的存在导致参数空间退化，潜在未知的结构矩阵使可识别性问题进一步复杂化。本文解决了识别 HLAM 底层的整个潜在结构和模型参数的问题。我们开发充分且必要的识别条件。这些结果直接而尖锐地表征了图中不同属性类型对可识别性的不同影响。所提出的条件不仅提供了对先验属性层次结构下的诊断测试设计的见解，而且还可以作为评估估计的 HLAM 后验有效性的工具。
Hierarchical Latent Attribute Models (HLAMs) are a type of discrete latent variable models that are attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of an HLAM include a binary structural matrix and a directed acyclic graph specifying hierarchical constraints on the configurations of latent attributes. These components encode practitioners' design information and carry important scientific meanings. Despite the popularity of HLAMs, the fundamental identifiability issue remains unaddressed. The existence of the attribute hierarchy graph leads to degenerate parameter space, and the potentially unknown structural matrix further complicates the identifiability problem. This paper addresses this issue of identifying the entire latent structure and model parameters underlying an HLAM. We develop sufficient and necessary identifiability conditions. These results directly and sharply characterize the different impacts on identifiability cast by different attribute types in the graph. The proposed conditions not only provide insights into diagnostic test designs under the attribute hierarchy a priori but also serve as tools to assess the validity of an estimated HLAM a posteriori.