This two-year, $229,951 Project Grant from the National Science Foundation's Social, Behavioral, and Economic Sciences program aims to advance statistical and psychometric theory for Cognitive Diagnosis Models. Funded from September 2021 through August 2023, the University of Nevada, Reno will develop Bayesian methods for inferring attribute hierarchy structures within CDMs. Algorithms will estimate underlying skill hierarchies from data and allow statistical inference of attribute structures. This will help educators discover new insights for instructional intervention and promote efficient student learning. The University of Georgia Research Foundation, as a $229,951 sub-awardee, will assist in developing Bayesian estimation techniques for attribute hierarchies in statistical CDMs. Both awardees will collaborate on simulation studies, manuscripts, and software to document the resulting methods and disseminate findings. The grant supports advancing cognitive assessment through innovative statistical modeling.