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Data-driven Q-matrix learning based on Boolean matrix factorization in cognitive diagnostic assessment.

Jianhua Xiong1,2, Zhaosheng Luo1, Guanzhong Luo1

  • 1School of Psychology, Jiangxi Normal University, Nanchang, China.

The British Journal of Mathematical and Statistical Psychology
|May 17, 2022
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Summary
This summary is machine-generated.

This study introduces a novel data-driven method for automatically generating the Q-matrix, a key component in cognitive diagnostic assessment. This approach reduces the time and effort required from domain experts, improving efficiency in educational measurement.

Keywords:
Boolean matrix factorizationDINA modelQ-matrixattribute mastery patterncognitive diagnostic assessment

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Area of Science:

  • Educational Measurement
  • Psychometrics
  • Data Science

Background:

  • Cognitive diagnostic assessment relies on attributes and the Q-matrix, typically defined by domain experts.
  • Manual definition of attributes and Q-matrix is time-consuming and challenging for experts.

Purpose of the Study:

  • To present a new data-driven approach for automatically learning the Q-matrix from response data.
  • To address the need for efficient and intelligent methods in cognitive diagnostic assessment.

Main Methods:

  • Utilized Boolean matrix factorization to decompose the response matrix.
  • Developed a statistical index and a heuristic algorithm for Q-matrix learning.
  • The response matrix was decomposed into the Boolean product of the Q-matrix and attribute mastery patterns.

Main Results:

  • Demonstrated the feasibility of the data-driven approach using simulated data under various conditions.
  • Showcased the practical utility of the proposed method with a real-world data example.

Conclusions:

  • The proposed data-driven approach offers an efficient and intelligent alternative to manual Q-matrix specification.
  • This method has significant implications for streamlining cognitive diagnostic assessment processes.