September 2021 Partial-mastery cognitive diagnosis models
Zhuoran Shang, Elena A. Erosheva, Gongjun Xu
Author Affiliations +
Ann. Appl. Stat. 15(3): 1529-1555 (September 2021). DOI: 10.1214/21-AOAS1439


Cognitive diagnosis models (CDMs) are a family of discrete latent attribute models that serve as statistical basis in educational and psychological cognitive diagnosis assessments. CDMs aim to achieve fine-grained inference on individuals’ latent attributes, based on their observed responses to a set of designed diagnostic items. In the literature CDMs usually assume that items require mastery of specific latent attributes and that each attribute is either fully mastered or not mastered by a given subject. We propose a new class of models, partial mastery CDMs (PM-CDMs), that generalizes CDMs by allowing for partial mastery levels for each attribute of interest. We demonstrate that PM-CDMs can be represented as restricted latent class models. Relying on the latent class representation, we propose a Bayesian approach for estimation. We present simulation studies to demonstrate parameter recovery, to investigate the impact of model misspecification with respect to partial mastery and to develop diagnostic tools that could be used by practitioners to decide between CDMs and PM-CDMs. We use two examples of real test data—the fraction subtraction and the English tests—to demonstrate that employing PM-CDMs not only improves model fit, compared to CDMs, but also can make substantial difference in conclusions about attribute mastery. We conclude that PM-CDMs can lead to more effective remediation programs by providing detailed individual-level information about skills learned and skills that need to study.

Funding Statement

This research is partially supported by NSF Grants CAREER SES-1846747, SES-1659328 and DMS-1712717 and IES grant R305D160010.


The authors thank the Editors, an Associate Editor and two anonymous referees for their constructive comments. Elena Erosheva would like to acknowledge that this research has partly taken place while she was a visiting professor at the Laboratorie J. A. Dieudonné, Université Côte d‘Azur, CNRS, Nice, France.


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Zhuoran Shang. Elena A. Erosheva. Gongjun Xu. "Partial-mastery cognitive diagnosis models." Ann. Appl. Stat. 15 (3) 1529 - 1555, September 2021.


Received: 1 April 2020; Revised: 1 December 2020; Published: September 2021
First available in Project Euclid: 23 September 2021

MathSciNet: MR4316660
zbMATH: 1478.62343
Digital Object Identifier: 10.1214/21-AOAS1439

Keywords: cognitive diagnosis , mixed membership models , restricted latent class models

Rights: Copyright © 2021 Institute of Mathematical Statistics


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Vol.15 • No. 3 • September 2021
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