Assessing Item-Level Fit for the DINA Model

Chun Wang, Zhan Shu, Zhuoran Shang, Gongjun Xu

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


This research focuses on developing item-level fit checking procedures in the context of diagnostic classification models (DCMs), and more specifically for the “Deterministic Input; Noisy ‘And’ gate” (DINA) model. Although there is a growing body of literature discussing model fit checking methods for DCM, the item-level fit analysis is not adequately discussed in literature. This study intends to take an initiative to fill in this gap. Two approaches are proposed, one stems from classical goodness-of-fit test statistics coupled with the Expectation-Maximization algorithm for model estimation, and the other is the posterior predictive model checking (PPMC) method coupled with the Markov chain Monte Carlo estimation. For both approaches, the chi-square statistic and a power-divergence index are considered, along with Stone’s method for considering uncertainty in latent attribute estimation. A simulation study with varying manipulated factors is carried out. Results show that both approaches are promising if Stone’s method is imposed, but the classical goodness-of-fit approach has a much higher detection rate (i.e., proportion of misfit items that are correctly detected) than the PPMC method.

Original languageEnglish (US)
Pages (from-to)525-538
Number of pages14
JournalApplied Psychological Measurement
Issue number7
StatePublished - Oct 7 2015

Bibliographical note

Publisher Copyright:
© 2015, © The Author(s) 2015.


  • DINA model
  • chi-square index
  • correct detection rate
  • false positive rate
  • posterior predictive model checking
  • power-divergence index


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