Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model

Yamaguchi, Kazuhiro; Okada, Kensuke

doi:10.1007/s11336-020-09739-w

Cited by 21 publications

(62 citation statements)

References 44 publications

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“…To open the box, a complete data Fisher information matrix can be made available, and the observed Fisher information matrix can be estimated to adjust the complete data matrix (Meng & Rubin, 1991) in mixture models. In addition, DCMs are fundamentally the sub-models of general mixture models (Gu & Xu, 2019;Rupp & Templin, 2008;Yamaguchi, 2020;Yamaguchi & Okada, 2020, 2021Yamaguchi & Templin, in press). Moreover, the complete data Fisher information matrix is easier to derive than the observed data Fisher information matrix (Meng & Rubin, 1991).…”

Section: Standard Errors In Diagnostic Classification Modelsmentioning

confidence: 99%

“…To reveal the relationship between the boundary problem and irregular SEs estimates, a mixture formulation of the saturated DCM (e.g., Gu & Xu, 2019;Yamaguchi & Okada, 2021) is employed, and the priors are set in the second section. Furthermore, an EM algorithm for the MAP estimator of the saturated DCM is developed in a mixture model manner in the same section.…”

Section: Standard Errors In Diagnostic Classification Modelsmentioning

confidence: 99%

“…This Q-matrix generates a systematic parameter equality constraint and is represented as a G-matrix (e.g., de la Torre, 2009a;Yamaguchi, 2020;Yamaguchi and Okada, 2021). The Gmatrix is defined for each item, and its size is 2 ∑ × 2 because item can only distinguish 2 ∑ attribute mastery patterns.…”

Section: Item Response Functionmentioning

confidence: 99%

“…The Gmatrix is defined for each item, and its size is 2 ∑ × 2 because item can only distinguish 2 ∑ attribute mastery patterns. For example, let us assume that there are three attributes in a test and that an item measures the first and second attributes, implying that = (1,1,0) ⊤ , as shown in Table 1 (Yamaguchi & Okada, 2021). The G-matrix is colored gray in Table 1.…”

Section: Item Response Functionmentioning

confidence: 99%

“…An example of G-matrix for = (1,1,0) ⊤ shown in Yamaguchi & Okada (2021) Attribute mastery pattern (l) 1 2 3 4 5 6 7 8 Attr. 1 0 1 0 0 1 1 0 1…”

Section: Item Response Functionmentioning

confidence: 99%

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On the Boundary Problems in Diagnostic Classification Models

Yamaguchi¹

2021

Preprint

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In diagnostic classification models, parameter estimation sometimes provides estimates that stick to the boundaries of the parameter space, which is called the boundary problem, and it may lead to extreme values of standard errors. However, the relationship between the boundary problem and irregular standard errors has not been analytically explored. In addition, prior research has not shown how maximum a posteriori estimates avoid the boundary problem and affect the standard errors of estimates. To analyze these relationships, the expectation-maximization algorithm for maximum a posteriori estimates and a complete data Fisher information matrix are explicitly derived for a mixture formulation of saturated diagnostic classification models. Theoretical considerations show that the emptiness of attribute mastery patterns causes both the boundary problem and the inaccurate standard error estimates. Furthermore, unfortunate boundary problem without emptiness causes shorter standard errors. A simulation study shows that the maximum a posteriori method prevents boundary problems and improves standard error estimates more than maximum likelihood estimates do. The effect is sometimes radical, and the results show that the maximum a posteriori method is more appropriate than the maximum likelihood method.

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Section: Standard Errors In Diagnostic Classification Modelsmentioning

confidence: 99%

Section: Standard Errors In Diagnostic Classification Modelsmentioning

confidence: 99%

Section: Item Response Functionmentioning

confidence: 99%

Section: Item Response Functionmentioning

confidence: 99%

“…An example of G-matrix for = (1,1,0) ⊤ shown in Yamaguchi & Okada (2021) Attribute mastery pattern (l) 1 2 3 4 5 6 7 8 Attr. 1 0 1 0 0 1 1 0 1…”

Section: Item Response Functionmentioning

confidence: 99%

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On the Boundary Problems in Diagnostic Classification Models

Yamaguchi¹

2021

Preprint

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A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

Yamaguchi

Templin

2021

J Classif

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Diagnostic classification models (DCMs) are restricted latent class models with a set of crossclass 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.

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

Yamaguchi

Templin

2022

Psychometrika

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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.

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Variational Bayes Inference Algorithm for the Saturated Diagnostic Classification Model

Cited by 21 publications

References 44 publications

On the Boundary Problems in Diagnostic Classification Models

On the Boundary Problems in Diagnostic Classification Models

A Gibbs Sampling Algorithm with Monotonicity Constraints for Diagnostic Classification Models

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

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