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

Area of Science:

• Educational Measurement and Psychometrics
• Statistical Modeling
• Cognitive Science

Background:

• Cognitive diagnostic models (CDMs) traditionally analyze categorical data to assess skill mastery.
• Modern assessments include diverse response types (e.g., response times, counts), necessitating new modeling approaches.
• The identifiability and estimability of CDMs for these novel 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 theoretical identifiability of these general-response CDMs.
• To develop an efficient estimation algorithm for a broad class of these models.

Main Methods:

• Development of a generalized cognitive diagnostic modeling framework with minimal assumptions.
• Mathematical proof of identifiability under conditions analogous to traditional CDMs.
• Implementation of an Expectation-Maximization (EM) algorithm for parameter estimation.

Main Results:

• Identifiability of general-response CDMs is established under novel theoretical conditions.
• The proposed EM algorithm efficiently estimates parameters for exponential family-based general-response CDMs.
• Simulation studies confirm the identifiability theory and demonstrate superior performance of the estimation algorithms.

Conclusions:

• A new paradigm for identifiable general-response cognitive diagnostic models is established.
• The proposed framework and algorithms extend CDMs to a wider range of educational assessment data.
• The methodology is validated through simulations and application to real-world response time data.