Estimating the Cognitive Diagnosis $$\varvec{Q}$$ Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset

Steven Andrew Culpepper ()
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Steven Andrew Culpepper: University of Illinois at Urbana-Champaign

Psychometrika, 2019, vol. 84, issue 2, No 1, 333-357

Abstract: Abstract Cognitive diagnosis models (CDMs) are an important psychometric framework for classifying students in terms of attribute and/or skill mastery. The $$\varvec{Q}$$ Q matrix, which specifies the required attributes for each item, is central to implementing CDMs. The general unavailability of $$\varvec{Q}$$ Q 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 $$\varvec{Q}$$ Q 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 models; general diagnostic model; Bayesian; multivariate regression; variable selection; validation; spike–slab priors (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (15)

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DOI: 10.1007/s11336-018-9643-8

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