An exploratory Q-matrix estimation method based on sparse non-negative matrix factorization.

Area of Science:

• Educational Measurement
• Psychometrics
• Data Science

Background:

• Cognitive Diagnostic Assessment (CDA) provides detailed diagnostic information.
• The Q-matrix is fundamental to CDA, typically defined by experts or data-driven methods.
• Existing data-driven Q-matrix methods often require prior knowledge, limiting their application.

Purpose of the Study:

• To propose a novel data-driven method for estimating the number of attributes and Q-matrix elements simultaneously.
• To develop a method that does not require any prior knowledge, addressing limitations of current approaches.
• To apply the sparse non-negative matrix factorization (SNMF) method under the G-DINA model.

Main Methods:

• Developed a simultaneous estimation approach for attribute number and Q-matrix elements using Sparse Non-negative Matrix Factorization (SNMF).
• The proposed method operates under the G-DINA model without requiring initial Q-matrix, q-vectors, or attribute counts.
• Employed simulation studies to evaluate the performance and accuracy of the SNMF method.

Main Results:

• SNMF demonstrated strong performance in accurately estimating both the number of attributes and Q-matrix elements across various simulation conditions.
• The method showed good scalability and universality, suitable for complex datasets.
• Successful application illustrated using a real-world dataset.

Conclusions:

• The proposed SNMF method offers an objective, accurate, and cost-effective approach for data-driven Q-matrix estimation in CDA.
• This method effectively overcomes the need for prior knowledge, enhancing the practicality of CDA.
• Future research should explore further refinements and applications of SNMF in cognitive diagnostic assessment.