Diagnostic Classification Models for Testlets: Methods and Theory

Xin Xu, Guanhua Fang, Jinxin Guo, Zhiliang Ying, Susu Zhang

Research output: Contribution to journalArticlepeer-review


Diagnostic classification models (DCMs) have seen wide applications in educational and psychological measurement, especially in formative assessment. DCMs in the presence of testlets have been studied in recent literature. A key ingredient in the statistical modeling and analysis of testlet-based DCMs is the superposition of two latent structures, the attribute profile and the testlet effect. This paper extends the standard testlet DINA (T-DINA) model to accommodate the potential correlation between the two latent structures. Model identifiability is studied and a set of sufficient conditions are proposed. As a byproduct, the identifiability of the standard T-DINA is also established. The proposed model is applied to a dataset from the 2015 Programme for International Student Assessment. Comparisons are made with DINA and T-DINA, showing that there is substantial improvement in terms of the goodness of fit. Simulations are conducted to assess the performance of the new method under various settings.

Original languageEnglish (US)
StateE-pub ahead of print - Mar 26 2024


  • diagnostic classification model
  • hypothesis testing
  • identifiability
  • interaction
  • model selection
  • PISA
  • Q-matrix
  • testlet DINA

ASJC Scopus subject areas

  • General Psychology
  • Applied Mathematics


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