Statistical Refinement of the Q-Matrix in Cognitive Diagnosis

Chia Yi Chiu

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)598-618
Number of pages21
JournalApplied Psychological Measurement
Issue number8
StatePublished - Nov 2013
Externally publishedYes


  • classification
  • cognitive diagnosis
  • Q-matrix
  • residual sum of squares
  • validity


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