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Going Deep in Diagnostic Modeling: Deep Cognitive Diagnostic Models (DeepCDMs).

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We introduce Deep Cognitive Diagnostic Models (DeepCDMs), a novel approach enhancing educational measurement. DeepCDMs offer improved identifiability, parsimony, and interpretability for diagnosing cognitive skills.

Keywords:
Bayesian inferenceBayesian networkDeepCDMQ-matrixcognitive diagnostic modeldeep generative modeldeep learningdirected graphical modelidentifiability

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Area of Science:

  • Educational Measurement and Psychometrics
  • Machine Learning
  • Artificial Intelligence

Background:

  • Cognitive Diagnostic Models (CDMs) are widely used in educational and psychological measurement for discrete latent variable modeling.
  • Existing CDMs face challenges in identifiability, parsimony, and interpretability, particularly in complex diagnostic scenarios.
  • Deep generative modeling offers potential advantages for capturing intricate data structures and improving model properties.

Purpose of the Study:

  • To propose a new family of Deep Cognitive Diagnostic Models (DeepCDMs) by integrating deep generative modeling with CDM principles.
  • To address limitations of traditional CDMs by enhancing identifiability, parsimony, and interpretability in cognitive diagnosis.
  • To develop theoretically sound and practically applicable methods for deep discrete diagnostic modeling.

Main Methods:

  • Introduced DeepCDMs, a novel class of models leveraging deep generative architectures for cognitive diagnosis.
  • Established mathematical conditions for the identifiability of DeepCDMs, including unique parameter and Q-matrix identification at all depths.
  • Developed Bayesian formulations and efficient Gibbs sampling algorithms for parameter estimation in the confirmatory setting with known Q-matrices.

Main Results:

  • Demonstrated that DeepCDMs are entirely identifiable, even in exploratory settings, uniquely determining parameters and Q-matrices.
  • Showcased the statistical parsimony of DeepCDMs, enabling expressive data modeling with fewer parameters due to model depth.
  • Highlighted the practical interpretability of DeepCDMs, with a deep architecture facilitating multi-granularity skill diagnosis from coarse to fine.

Conclusions:

  • DeepCDMs represent a significant advancement in cognitive diagnostic modeling, offering enhanced identifiability, parsimony, and interpretability.
  • The proposed methodology provides a robust framework for deep discrete diagnostic modeling with transparent identifiability conditions.
  • Empirical evidence from simulations and application to TIMSS 2019 data confirms the utility and effectiveness of DeepCDMs.