Scalable Bayesian Approach for the Dina Q-Matrix Estimation Combining Stochastic Optimization and Variational Inference

Motonori Oka () and Kensuke Okada
Additional contact information
Motonori Oka: The University of Tokyo
Kensuke Okada: The University of Tokyo

Psychometrika, 2023, vol. 88, issue 1, No 14, 302-331

Abstract: Abstract Diagnostic classification models offer statistical tools to inspect the fined-grained attribute of respondents’ strengths and weaknesses. However, the diagnosis accuracy deteriorates when misspecification occurs in the predefined item–attribute relationship, which is encoded into a Q-matrix. To prevent such misspecification, methodologists have recently developed several Bayesian Q-matrix estimation methods for greater estimation flexibility. However, these methods become infeasible in the case of large-scale assessments with a large number of attributes and items. In this study, we focused on the deterministic inputs, noisy “and” gate (DINA) model and proposed a new framework for the Q-matrix estimation to find the Q-matrix with the maximum marginal likelihood. Based on this framework, we developed a scalable estimation algorithm for the DINA Q-matrix by constructing an iteration algorithm that utilizes stochastic optimization and variational inference. The simulation and empirical studies reveal that the proposed method achieves high-speed computation, good accuracy, and robustness to potential misspecifications, such as initial value choices and hyperparameter settings. Thus, the proposed method can be a useful tool for estimating a Q-matrix in large-scale settings.

Keywords: Q-matrix estimation; stochastic optimization; variational inference; diagnostic classification models; deterministic inputs noisy “and” gate (DINA) model (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s11336-022-09884-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:psycho:v:88:y:2023:i:1:d:10.1007_s11336-022-09884-4

Ordering information: This journal article can be ordered from
http://www.springer. ... gy/journal/11336/PS2

DOI: 10.1007/s11336-022-09884-4

Access Statistics for this article

Psychometrika is currently edited by Irini Moustaki

More articles in Psychometrika from Springer, The Psychometric Society
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().