Hypothesis Testing for Hierarchical Structures in Cognitive Diagnosis Models

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models widely used in educational, psychological and social sciences. In many applications CDMs, certain hierarchical structures among the attributes assumed by researchers to characterize their dependence structure. Specifically, directed acyclic graph is specify constraints on allowable configurations attributes. this paper, we consider important yet unaddressed problem testing existence CDMs. We first introduce concept testability CDMs present sufficient conditions. Then study asymptotic behaviors likelihood ratio test (LRT) statistic, which for nested models. Due irregularity problem, distribution LRT becomes nonstandard tends provide unsatisfactory finite sample performance under practical statistical insights such failures, propose use parametric bootstrap perform testing. also demonstrate effectiveness superiority hierarchies over non-parametric na\"ive Chi-squared through comprehensive simulations an educational assessment dataset.