Statistical Refinement of the Q-Matrix in Cognitive Diagnosis

Chia-Yi Chiu

130 citations0/0 files storedApplied Psychological Measurement

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Educational Technology and Assessment

Abstract

Most methods for fitting cognitive diagnosis models to educational test data and assigning examinees to proficiency classes require the Q-matrix that associates each item in a test with the cognitive skills (attributes) needed to answer it correctly. In most cases, the Q-matrix is not known but is constructed from the (fallible) judgments of experts in the educational domain. It is widely recognized that a misspecification of the Q-matrix can negatively affect the estimation of the model parameters, which may then result in the misclassification of examinees. This article develops a Q-matrix refinement method based on the nonparametric classification method (Chiu & Douglas, in press), and comparisons of the residual sum of squares computed from the observed and the ideal item responses. The method is evaluated with three simulation studies and an application to real data. Results show that the method can identify and correct misspecified entries in the Q-matrix, thereby improving its accuracy.

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References

2001Cognitive Assessment Models with Few Assumptions, and Connections with Nonparametric Item Response Theory 2011The Generalized DINA Model Framework 2008DINA Model and Parameter Estimation: A Didactic 2004Higher-Order Latent Trait Models for Cognitive Diagnosis 2008Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables 1989Using Restricted Latent Class Models to Map the Skill Structure of Achievement Items 1999Estimating Multiple Classification Latent Class Models 2008An Empirically Based Method of Q‐Matrix Validation for the DINA Model: Development and Applications

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2017Identifying Latent Structures in Restricted Latent Class Models 2015Identifiability of Diagnostic Classification Models 2017Cognitive diagnosis modelling incorporating item response times 2017Bayesian Estimation of the DINA Q matrix 2015Bayesian Estimation of the DINA Model With Gibbs Sampling 2016

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