Identifiability of Hierarchical Latent Attribute Models
This addresses a critical theoretical problem for researchers and practitioners using HLAMs in fields like education and psychology, though it is incremental as it builds on existing model frameworks.
The paper tackled the fundamental identifiability issue in Hierarchical Latent Attribute Models (HLAMs), which had been unaddressed despite their popularity in educational and psychological sciences, by developing sufficient and necessary conditions that characterize the impacts of different attribute types on identifiability.
Hierarchical Latent Attribute Models (HLAMs) are a family 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 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, but also serve as tools to assess the validity of an estimated HLAM.