Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis

Ying Liu (), Steven Andrew Culpepper () and Yuguo Chen ()
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Ying Liu: University of Illinois at Urbana-Champaign
Steven Andrew Culpepper: University of Illinois at Urbana-Champaign
Yuguo Chen: University of Illinois at Urbana-Champaign

Psychometrika, 2023, vol. 88, issue 2, No 1, 386 pages

Abstract: Abstract 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 $$\varvec{Q}$$ 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 $$\varvec{Q}$$ 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.

Keywords: cognitive diagnosis model; DINA model; generic identifiability; hidden Markov model (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11336-023-09904-x

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