A Proof of the Duality of the DINA Model and the DINO Model

Hans Friedrich Köhn, Chia Yi Chiu

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


The Deterministic Input Noisy Output “AND” gate (DINA) model and the Deterministic Input Noisy Output “OR” gate (DINO) model are two popular cognitive diagnosis models (CDMs) for educational assessment. They represent different views on how the mastery of cognitive skills and the probability of a correct item response are related. Recently, however, Liu, Xu, and Ying demonstrated that the DINO model and the DINA model share a “dual” relation. This means that one model can be expressed in terms of the other, and which of the two models is fitted to a given data set is essentially irrelevant because the results are identical. In this article, a proof of the duality of the DINA model and the DINO model is presented that is tailored to the form and parameterization of general CDMs that have become the new theoretical standard in cognitively diagnostic modeling.

Original languageEnglish (US)
Pages (from-to)171-184
Number of pages14
JournalJournal of Classification
Issue number2
StatePublished - Jul 1 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016, Classification Society of North America.


  • Cognitive diagnosis
  • DINA model
  • DINO model
  • General cognitive diagnosis models


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