Theory of self-learning $Q$-matrix

TL;DR

This paper develops a mathematical framework for cognitive assessment, providing conditions under which the attributes associated with test items can be reliably learned from data.

Contribution

It introduces a theoretical model for self-learning Q-matrices and establishes conditions for attribute identifiability from data.

Findings

Sufficient conditions for attribute learnability are derived.

A formal framework for cognitive test analysis is proposed.

Theoretical guarantees for attribute identification are provided.

Abstract

Cognitive assessment is a growing area in psychological and educational measurement, where tests are given to assess mastery/deficiency of attributes or skills. A key issue is the correct identification of attributes associated with items in a test. In this paper, we set up a mathematical framework under which theoretical properties may be discussed. We establish sufficient conditions to ensure that the attributes required by each item are learnable from the data.