Minimum information entropy based q-matrix learning in DINA model

Abstract

Cognitive diagnosis models (CDMs) are of growing interest in test development and measurement of learners' performance. The DINA (deterministic input, noisy, and gate) model is one of the most widely used models in CDM. In this paper, we propose a new method and present an alternating recursive algorithm to learn Q-matrix and uncertainty variables, slip and guessing parameters, based on Boolean Matrix Factorization (BMF) and Minimized Information Entropy (MIE) respectively for the DINA model. Simulation results show that our algorithm for Q-matrix learning has fast convergence to the local optimal solutions for Q-matrix and students' knowledge states A matrix. This is especially important and applicable when the method is extended to big data.