Q-matrix learning and DINA model parameter estimation

Abstract

The DINA model is one of the most widely used models in cognitive and skills diagnosis, and several algorithms have been developed for estimating the model parameters. However, since the parameter space is very large and has a mix of binary variables, even medium-sized testing is extremely challenging. To make the model practical, a fast optimization algorithm for parameter estimation is needed. In this study, we converted the deterministic Q-matrix learning problem into a Boolean matrix factorization (BMF) problem and developed a recursive algorithm to find an approximate solution while solving the uncertainty parameters analytically using maximum likelihood estimation (MLE). We proved that the MLE is equivalent to the minimum information entropy of the DINA model. Simulation results demonstrated that our proposed algorithm converges rapidly to the optimal solution under suitable initial values of skill - item association and is insensitive to the initial values of the uncertainty parameters.