New Paradigm of Identifiable General-response Cognitive Diagnostic Models: Beyond Categorical Data

Area of Science:

• Educational Measurement
• Psychometrics
• Data Science

Background:

• Cognitive Diagnostic Models (CDMs) traditionally analyze categorical data.
• Modern assessments include diverse response types like response times and count data.
• Identifiability and estimability of CDMs for these new response types remain largely unexplored.

Purpose of the Study:

• To propose a general cognitive diagnostic modeling framework for arbitrary multivariate response types.
• To establish the identifiability of these general-response CDMs.
• To develop an efficient estimation algorithm for these models.

Main Methods:

• Developed a generalized CDM framework with minimal assumptions.
• Established identifiability using Q-matrix-based conditions.
• Proposed an Expectation-Maximization (EM) algorithm for parameter estimation.
• Conducted simulation studies across various response types.

Main Results:

• Proved that general-response CDMs are identifiable under Q-matrix conditions.
• Demonstrated the superior empirical performance of the proposed EM algorithm.
• Simulation results corroborated the theoretical identifiability findings.

Conclusions:

• A new paradigm of identifiable general-response CDMs has been established.
• The proposed framework and EM algorithm are effective for diverse response types in educational assessments.
• The methodology was successfully applied to a real-world dataset (TIMSS 2019 response times).