Variational Bayesian Inference for a Q-Matrix-Free Hidden Markov Log-Linear Additive Cognitive Diagnostic Model
Hao Duan, James Tang, Matthew J. Madison, Michael E. Cotterell, Minjeong Jeon · Algorithms · 2025
Cognitive diagnostic models (CDMs) are commonly used in educational assessment to uncover the specific cognitive skills that contribute to student performance, allowing for precise identification of individual strengths and weaknesses and the design of targeted interventions. Traditional CDMs, however, depend heavily on a predefined Q-matrix that specifies the relationship between test items and underlying attributes. In this study, we introduce a hidden Markov log-linear additive cognitive diagnostic model (HM-LACDM) that does not require a Q-matrix, making it suitable for analyzing longitudinal assessment data without prior structural assumptions. To support scalable applications, we develop a variational Bayesian inference (VI) algorithm that enables efficient estimation in large datasets. Additionally, we propose a method to reconstruct the Q-matrix from estimated item-effect parameters. The effectiveness of the proposed approach is demonstrated through simulation studies.