Using Diagnostic Classification Models to Validate Attribute Hierarchies and Evaluate Model Fit in Bayesian Networks

Abstract

We investigate the relationship between Bayesian inference networks (BayesNets) and diagnostic classification models (DCMs). Specifically, we demonstrate and empirically examine the equivalency of parameterizations between BayesNets and DCMs. Then, we propose a model-comparison framework for testing the model fit of BayesNets, in which we show how BayesNets are nested within the saturated DCM structural models. Additionally, we show when attributes feature a linear hierarchy, the Hierarchical DCM is nested within both BayesNets and saturated DCMs. The usefulness of proposed framework and model-fit testing strategy was supported by the results of analyzing both simulated and empirical data.

Keywords:

• Diagnostic classification models
• Bayesian inference networks
• model fit
• attribute hierarchy

Article information

Conflict of Interest Disclosures: Each author signed a form for disclosure of potential conflicts of interest. No authors reported any financial or other conflicts of interest in relation to the work described.

Ethical Principles: The authors affirm having followed professional ethical guidelines in preparing this work. These guidelines include obtaining informed consent from human participants, maintaining ethical treatment and respect for the rights of human or animal participants, and ensuring the privacy of participants and their data, such as ensuring that individual participants cannot be identified in reported results or from publicly available original or archival data.

Funding: This work was supported by Grants DUE-1544481 and DRL-1813760 from the National Science Foundation.

Role of the Funders/Sponsors: None of the funders or sponsors of this research had any role in the design and conduct of the study; collection, management, analysis, and interpretation of data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.

Acknowledgments: The authors would like to thank the Associate Editor and two reviewers for their comments on prior versions of this manuscript. The ideas and opinions expressed herein are those of the authors alone, and endorsement by the authors’ institutions or the National Science Foundation is not intended and should not be inferred.