A0611
Title: Identifiability of hierarchical latent attribute models
Authors: Yuqi Gu - Duke University (United States)
Gongjun Xu - University of Michigan (United States) [presenting]
Abstract: Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models 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. The purpose is to address the issue of identifying the 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 provide insights into diagnostic test designs under the attribute hierarchy and serve as tools to assess the validity of an estimated HLAM.
