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

Area of Science:

• Educational Measurement
• Psychometrics
• Machine Learning

Background:

• Cognitive Diagnostic Models (CDMs) are widely used for discrete latent variable modeling in educational and psychological assessments.
• Existing CDMs face challenges in identifiability, parsimony, and interpretability, particularly in complex diagnostic scenarios.

Purpose of the Study:

• To propose a novel family of Deep Cognitive Diagnostic Models (DeepCDMs) leveraging deep generative modeling.
• To enhance the hunting of deep discrete diagnostic information with improved model properties.

Main Methods:

• Developed DeepCDMs with a shrinking-ladder-shaped deep architecture for multi-granularity skill diagnosis.
• Established transparent identifiability conditions for various DeepCDMs, imposing constraints on the structure of latent layers.
• Proposed Bayesian formulations and efficient Gibbs sampling algorithms for estimation and computation in the confirmatory setting.

Main Results:

• DeepCDMs demonstrate mathematical identifiability, statistical parsimony, and practical interpretability.
• The models uniquely identify parameters and discrete loading structures at all depths.
• The proposed methodology effectively captures cognitive concepts and provides diagnoses from coarse to fine-grained levels.

Conclusions:

• DeepCDMs offer a powerful new framework for cognitive diagnosis in educational and psychological measurement.
• The models' properties of identifiability, parsimony, and interpretability advance the field of discrete latent variable modeling.
• The methodology's utility is validated through simulation studies and application to real-world assessment data (TIMSS 2019).