Identifiability of Hierarchical Latent Attribute Models

Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models that attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients an HLAM include binary structural matrix directed acyclic graph specifying hierarchical constraints on the configurations attributes. These components encode practitioners' design information carry important scientific meanings. Despite popularity HLAMs, fundamental identifiability issue remains unaddressed. existence attribute hierarchy leads to degenerate parameter space, potentially unknown further complicates problem. This paper addresses this identifying structure model parameters underlying HLAM. We develop sufficient necessary conditions. results directly sharply characterize different impacts cast by types graph. proposed conditions not only provide insights into diagnostic test designs under hierarchy, but also serve as tools assess validity estimated