Scalable Estimation Algorithm for the DINA Q-matrix Combining Stochastic Optimization and Variational Inference.

Diagnostic classification models (DCMs) enable finer-grained inspection of the latent states of respondents' strengths and weaknesses. However, the accuracy of diagnosis deteriorates when misspecification occurs in the predefined item-attribute relationship, which is defined by a Q-matrix. To forestall misdiagnosis, several Q-matrix estimation methods have been developed in recent years; however, their scalability to large-scale assessment is extremely limited. In this study, we focus on the deterministic inputs, noisy "and" gate (DINA) model and propose a new framework for Q-matrix estimation in which the goal is to find the Q-matrix with the maximized marginal likelihood. Based on this framework, we developed a scalable estimation algorithm for the DINA Q-matrix by constructing an iteration algorithm utilizing stochastic optimization and variational inference. The simulation and empirical studies reveal that the proposed method achieves high-speed computation and good accuracy. Our method can be a useful tool for estimating a Q-matrix in large-scale settings.