Cognitive Diagnostic Models With Attribute Hierarchies: Model Estimation With a Restricted Q-Matrix Design

Dongbo Tu, Shiyu Wang, Yan Cai, Jeff Douglas, Hua Hua Chang

Research output: Contribution to journalArticlepeer-review


Attribute hierarchy is a common assumption in the educational context, where the mastery of one attribute is assumed to be a prerequisite to the mastery of another one. The attribute hierarchy can be incorporated through a restricted Q matrix that implies the specified structure. The latent class–based cognitive diagnostic models (CDMs) usually do not assume a hierarchical structure among attributes, which means all profiles of attributes are possible in a population of interest. This study investigates different estimation methods to the classification accuracy for a family of CDMs when they are combined with a restricted Q-matrix design. A simulation study is used to explain the misclassification caused by an unrestricted estimation procedure. The advantages of the restricted estimation procedure utilizing attribute hierarchies for increased classification accuracy are also further illustrated through a real data analysis on a syllogistic reasoning diagnostic assessment. This research can provide guidelines for educational and psychological researchers and practitioners when they use CDMs to analyze the data with a restricted Q-matrix design and make them be aware of the potentially contaminated classification results if ignoring attribute hierarchies.

Original languageEnglish (US)
Pages (from-to)255-271
Number of pages17
JournalApplied Psychological Measurement
Issue number4
StatePublished - Jun 1 2019


  • attribute hierarchies
  • classification accuracy
  • cognitive diagnostic models
  • restricted Q matrix

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)


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