Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying Cognitive Diagnosis Models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. I will present a Bayesian formulation for CDMs with attribute hierarchy, and propose an efficient Metropolis within Gibbs algorithm to estimate the underlying hierarchy through transitive reductions of directed acyclic graphs (DAGs). Simulation studies demonstrated our method can estimate the whole graph or a subgraph of the underlying structure across various conditions. Applications to educational data indicate the potential of learning and validating hierarchical structures through the proposed method.