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A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models
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A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

Kazuhiro Yamaguchi and Jonathan Templin
PsyArXiv
Center for Open Science
07/31/2021
DOI: 10.31234/osf.io/undcv
url
https://doi.org/10.1007/s00357-021-09392-7View
Published (Version of record)This article has now been published in a journal and has been peer-reviewed by subject experts. This version may differ significantly from the preprint version Access restricted to faculty, staff and students
url
https://doi.org/10.31234/osf.io/undcvView
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

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Abstract

Diagnostic classification models (DCMs) are restricted latent class models with a set of cross-class equality constraints and additional monotonicity constraints on their item parameters, both of which are needed to ensure the meaning of classes and model parameters. In this paper, we develop an efficient, Gibbs sampling-based Bayesian Markov chain Monte Carlo estimation method for general DCMs with monotonicity constraints. A simulation study was conducted to evaluate parameter recovery of the algorithm which showed accurate estimation of model parameters. Moreover, the proposed algorithm was compared to a previously developed Gibbs sampling algorithm which imposed constraints on only the main effect item parameters of the log-linear cognitive diagnosis model. The newly proposed algorithm showed less bias and faster convergence. An analysis of the 2000 Programme for International Student Assessment reading assessment data using this algorithm was also conducted.
 Computer Science Bayesian probability Convergence (routing) Gibbs sampling Main effect Markov chain Monte Carlo Mathematical optimization Monotonic function Pattern recognition (psychology) Set (abstract data type)

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