Variational Bayes inference for hidden Markov diagnostic classification models

• Published in: British journal of mathematical & statistical psychology Vol. 77; no. 1; pp. 55 - 79
• Main Authors: Yamaguchi, Kazuhiro, Martinez, Alfonso J.
• Format: Journal Article
• Language: English
• Published: England British Psychological Society 01.02.2024
• Subjects: Algorithms; Bayes Theorem; Classification; cognitive diagnostic model; Computer Simulation; diagnostic classification model; Diagnostic systems; hidden Markov model; Humans; Inference; longitudinal analysis; Markov chain Monte Carlo method; Markov Chains; Mathematical models; Monte Carlo Method; Parameter estimation; variational Bayes inference; longitudinal analysis; Markov chain Monte Carlo method; cognitive diagnostic model; hidden Markov model; diagnostic classification model; variational Bayes inference
• ISSN: 0007-1102; 2044-8317; 2044-8317
• DOI: 10.1111/bmsp.12308

Diagnostic classification models (DCMs) can be used to track the cognitive learning states of students across multiple time points or over repeated measurements. This study developed an effective variational Bayes (VB) inference method for hidden Markov longitudinal general DCMs. The simulations performed in this study verified the validity of the proposed algorithm for satisfactorily recovering true parameters. Simulation and applied data analyses were conducted to compare the proposed VB method to Markov chain Monte Carlo (MCMC) sampling. The results revealed that the parameter estimates provided by the VB method were consistent with the MCMC method with the additional benefit of a faster estimation time. The comparative simulation also indicated differences between the two methods in terms of posterior standard deviation and coverage of 95% credible intervals. Thus, with limited computational resources and time, the proposed VB method can output estimations comparable to that of MCMC.