Bayesian inference for dynamic <i>Q</i> matrices and attribute trajectories in hidden Markov diagnostic classification models

Hidden Markov diagnostic classification models capture how students' cognitive attributes evolve over time. This paper introduces a Bayesian Markov chain Monte Carlo algorithm for diagnostic classification models that jointly estimates time-varying Q matrices, latent attributes, item parameters, attribute class proportions and transition matrices across multiple occasions. Using the R package hmdcm developed for this study, Monte Carlo simulations demonstrate accurate parameter recovery, and an empirical probability-concept assessment confirmed the algorithm's ability to trace attribute trajectories, supporting its value for longitudinal diagnostic classification in both research and instructional practice.

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Publication Details

Journal
British Journal of Mathematical and Statistical Psychology
Published
2026-01-20
DOI
https://doi.org/10.1111/bmsp.70028
Primary Topic
Psychometric Methodologies and Testing
Type
article
Field-Weighted Citation Impact
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article

Bayesian inference for dynamic Q matrices and attribute trajectories in hidden Markov diagnostic classification models

Chen‐Wei Liu
British Journal of Mathematical and Statistical Psychology
Psychometric Methodologies and Testing
article

Bayesian inference for dynamic Q matrices and attribute trajectories in hidden Markov diagnostic classification models

Chen‐Wei Liu
article en

Abstract

Hidden Markov diagnostic classification models capture how students' cognitive attributes evolve over time. This paper introduces a Bayesian Markov chain Monte Carlo algorithm for diagnostic classification models that jointly estimates time-varying Q matrices, latent attributes, item parameters, attribute class proportions and transition matrices across multiple occasions. Using the R package hmdcm developed for this study, Monte Carlo simulations demonstrate accurate parameter recovery, and an empirical probability-concept assessment confirmed the algorithm's ability to trace attribute trajectories, supporting its value for longitudinal diagnostic classification in both research and instructional practice.

British Journal of Mathematical and Statistical Psychology
National Taiwan Normal University (TW)
Quality Education
Openalex Percentile: Top 84%
Psychometric Methodologies and Testing
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