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Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm

Published online by Cambridge University Press:  01 January 2025

Kazuhiro Yamaguchi Open the ORCID record for Kazuhiro Yamaguchi [Opens in a new window]  and
Jonathan Templin Open the ORCID record for Jonathan Templin [Opens in a new window]
Kazuhiro Yamaguchi*
Affiliation:
University Of Tsukuba
Jonathan Templin
Affiliation:
The University Of Iowa
*
Correspondence should be made to Kazuhiro Yamaguchi, Division of Psychology, Faculty of Human Sciences, University of Tsukuba, Institutes of Human Sciences A314, 1-1-1 Tennodai, Tsukuba, Ibaraki 3050006, Japan. Email: yamaguchi.kazuhir.ft@u.tsukuba.ac.jp
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Abstract

This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. A second simulation showed the collapsed Gibbs sampling algorithm was computationally more efficient than another MCMC sampling algorithm, implemented by JAGS. In an analysis of real data, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

Keywords

diagnostic classification modelsMarkov chain Monte Carlo methodGibbs samplingBayesian inference
Type
Theory and Methods
Information
Psychometrika , Volume 87 , Issue 4 , December 2022 , pp. 1390 - 1421
Copyright
Copyright © 2022 The Author(s) under exclusive licence to The Psychometric Society

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Footnotes

Supplementary Information The online version contains supplementary material available at https://doi.org/10.1007/S0033312300005512a.

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