Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis

Research output: Contribution to journalArticlepeer-review


Hidden Markov models (HMMs) have been applied in various domains, which makes the identifiability issue of HMMs popular among researchers. Classical identifiability conditions shown in previous studies are too strong for practical analysis. In this paper, we propose generic identifiability conditions for discrete time HMMs with finite state space. Also, recent studies about cognitive diagnosis models (CDMs) applied first-order HMMs to track changes in attributes related to learning. However, the application of CDMs requires a known Q matrix to infer the underlying structure between latent attributes and items, and the identifiability constraints of the model parameters should also be specified. We propose generic identifiability constraints for our restricted HMM and then estimate the model parameters, including the Q matrix, through a Bayesian framework. We present Monte Carlo simulation results to support our conclusion and apply the developed model to a real dataset.

Original languageEnglish (US)
Pages (from-to)361-386
Number of pages26
Issue number2
StatePublished - Jun 2023


  • DINA model
  • cognitive diagnosis model
  • generic identifiability
  • hidden Markov model

ASJC Scopus subject areas

  • Applied Mathematics
  • General Psychology


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