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Estimating the Cognitive Diagnosis Q\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{Q}$$\end{document} Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset

Published online by Cambridge University Press:  01 January 2025

Steven Andrew Culpepper Open the ORCID record for Steven Andrew Culpepper [Opens in a new window]
Steven Andrew Culpepper*
Affiliation:
University of Illinois at Urbana-Champaign
*
Correspondence should be made to Steven Andrew Culpepper, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL61820, USA. Email: sculpepp@illinois.edu
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Abstract

Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The Q\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{Q}$$\end{document} matrix, which specifies the required attributes for each item, is central to implementing CDMs. The general unavailability of Q\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{Q}$$\end{document} for most content areas and datasets poses a barrier to widespread applications of CDMs, and recent research accordingly developed fully exploratory methods to estimate Q. However, current methods do not always offer clear interpretations of the uncovered skills and existing exploratory methods do not use expert knowledge to estimate Q. We consider Bayesian estimation of Q\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\varvec{Q}$$\end{document} using a prior based upon expert knowledge using a fully Bayesian formulation for a general diagnostic model. The developed method can be used to validate which of the underlying attributes are predicted by experts and to identify residual attributes that remain unexplained by expert knowledge. We report Monte Carlo evidence about the accuracy of selecting active expert-predictors and present an application using Tatsuoka’s fraction-subtraction dataset.

Keywords

exploratory cognitive diagnosis modelsgeneral diagnostic modelBayesianmultivariate regressionvariable selectionvalidationspike–slab priors
Type
Original Paper
Information
Psychometrika , Volume 84 , Issue 2 , June 2019 , pp. 333 - 357
Copyright
Copyright © 2018 The Psychometric Society

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