Bayesian Inference for Attribute Hierarchy in Cognitive Diagnosis Models

This research project will advance statistical methods for estimation and inference on attribute hierarchy within the framework of cognitive diagnosis models (CDM). CDMs have been widely applied to the field of educational assessment, psychiatric diagnosis, and other social sciences. In conjunction with diagnostic assessments, this type of model uses subjects' observed responses to specifically designed diagnostic items to determine the fine-grained classification of the underlying latent attribute patterns.

Attribute hierarchy, or the relationship among attributes, plays an important role in designing an effective diagnostic assessment. However, there is a lack of efficient statistical tools for estimating attribute hierarchy from observed data. This project will develop a series of Bayesian approaches for estimating attribute hierarchy.

The project will contribute to the newly developed interdisciplinary field that integrates artificial intelligence with psychometrics. The new methods will be useful for applied research in education and psychology, as well as other social science disciplines. The investigators will apply the new methods to educational data sets.

Graduate students will participate in the conduct of this research, and publicly available software will be developed.

This research project will develop Bayesian inference on attribute hierarchy for both static and dynamic CDM models and promote the use of CDMs in conjunction with attribute hierarchy to facilitate learning. The project will address major research questions on 1) the formulation of Bayesian framework for static and dynamic CDMs and 2) the development of methods to directly learn attribute hierarchy from the observed data in these two setups.

For static CDMs, a series of new Bayesian estimation methods will be employed to directly estimate the attribute hierarchy and explicitly enforce the permissibility of attribute patterns. Stochastic processes and irreducible transitions will be created to ensure the convergence of the proposed algorithms. The project also will consider stochastic search variable selection methods to estimate the attribute hierarchy when the CDM satisfies conjunctive assumptions.

The new methods for static CDMs will be extended to model and draw inferences on the process of learning in practice with the framework of dynamic CDMs. A set of simulation studies will be used to evaluate the new methods, and the methods will be applied to two spatial rotation learning datasets.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.