, Volume 84, Issue 1, pp 19–40 | Cite as

On the Identifiability of Diagnostic Classification Models

  • Guanhua Fang
  • Jingchen LiuEmail author
  • Zhiliang Ying


This paper establishes fundamental results for statistical analysis based on diagnostic classification models (DCMs). The results are developed at a high level of generality and are applicable to essentially all diagnostic classification models. In particular, we establish identifiability results for various modeling parameters, notably item response probabilities, attribute distribution, and Q-matrix-induced partial information structure. These results are stated under a general setting of latent class models. Through a nonparametric Bayes approach, we construct an estimator that can be shown to be consistent when the identifiability conditions are satisfied. Simulation results show that these estimators perform well under various model settings. We also apply the proposed method to a dataset from the National Epidemiological Survey on Alcohol and Related Conditions (NESARC).


identifiability diagnostic classification models Dirichlet allocation 



This research is supported in part by NSF IIS-1633360 and SES-1826540.

Supplementary material

11336_2018_9658_MOESM1_ESM.pdf (214 kb)
Supplementary material 1 (pdf 213 KB)
11336_2018_9658_MOESM2_ESM.rdata (5 kb)
Supplementary material 2 (Rdata 4 KB)
11336_2018_9658_MOESM3_ESM.r (5 kb)
Supplementary material 3 (R 4 KB)


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Copyright information

© The Psychometric Society 2019

Authors and Affiliations

  1. 1.Columbia UniversityNew YorkUSA

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