Variational Bayes Inference for the DINA Model

Yamaguchi, Kazuhiro; Okada, Kensuke

doi:10.3102/1076998620911934

Cited by 26 publications

(35 citation statements)

References 49 publications

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“…In addition, the standard errors (SEs) of estimates may sometimes be inaccurate. Yamaguchi and Okada (2020) showed that the SE estimates for correct item response probability parameters, which should range from zero to one, are sometimes larger than one in the DINA model.…”

Section: Standard Errors In Diagnostic Classification Modelsmentioning

confidence: 99%

“…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%

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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%

On the Boundary Problems in Diagnostic Classification Models

Yamaguchi¹

2021

Preprint

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“…Wang et al [15] used the expectation-maximization algorithm to solve the estimated values of the parameters in the Bayesian model. Yamaguchi and Okada [16] proposed a variational Bayes inference method, which applied the iterative algorithm for optimization, for the deterministic input noisy model of cognitive diagnostic assessment. Carlon et al [17] used the stochastic gradient descent and its accelerated counterpart, which employs Nesterov's method, to solve the optimization problem in optimal experimental design.…”

Section: Introductionmentioning

confidence: 99%

Damage Evaluation of Bridge Hanger Based on Bayesian Inference: Analytical Model

Ding

Dong

Yang

et al. 2021

Advances in Materials Science and Engineering

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With the increase of the long-span bridge, the damage of the long-span bridge hanger has attracted more and more attention. Nowadays, the probability statistics method based on Bayes’ theorem is widely used for evaluating the damage of bridge, that is, Bayesian inference. In this study, the damage evaluation model of bridge hanger is established based on Bayesian inference. For the damage evaluation model, the analytical expressions for calculating the weights by finite mixture (FM) method are derived. In order to solve the complex analytical expressions in damage evaluation model, the Metropolis-Hastings (MH) sampling of Markov chain Monte Carlo (MCMC) method was used. Three case studies are adopted to demonstrate the effect of the initial value and the applicability of the proposed model. The result suggests that the proposed model can evaluate the damage of the bridge hanger.

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“…Humphreys and Titterington (2003) and White and Murphy (2014) derived a VB inference algorithm for latent class models. Furthermore, there has been recent work which has led to the development of VB inference algorithm for DCMs (Yamaguchi, 2020;Yamaguchi & Okada, 2020. In particular, Yamaguchi and Okada (2021) introduced a mixture model formulation of the DCMs and derived a VB estimation algorithm for general DCMs that extended the algorithm initially based on the DINA model (Yamaguchi & Okada, 2020) and the multiple-choice DINA model (Yamaguchi, 2020).…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, there has been recent work which has led to the development of VB inference algorithm for DCMs (Yamaguchi, 2020;Yamaguchi & Okada, 2020. In particular, Yamaguchi and Okada (2021) introduced a mixture model formulation of the DCMs and derived a VB estimation algorithm for general DCMs that extended the algorithm initially based on the DINA model (Yamaguchi & Okada, 2020) and the multiple-choice DINA model (Yamaguchi, 2020). Yamaguchi and Okada (2021) indicated the VB estimation method provided similar parameter estimates as MCMC estimation but at a much faster estimation time.…”

Section: Introductionmentioning

confidence: 99%

Variational Bayes Inference for Hidden Markov Diagnostic Classification Models

Yamaguchi¹,

Martinez²

2021

Preprint

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General diagnostic classification models (DCMs) can be used to capture individual students’ cognitive learning status. Moreover, DCMs for longitudinal data are appropriate to track students transition of cognitive elements. This study developed an effective Bayesian posterior approximation method called variational Bayesian (VB) inference method for hidden Markov type longitudinal general DCMs. Simulation study indicated the proposed algorithm could satisfactorily recover true parameters. Comparative study of the VB and previously developed Markov chain Monte Carlo (MCMC) methods was conducted in real data example. The result revealed that the VB method provided similar parameter estimates to the MCMC with faster estimation time.

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Variational Bayes Inference for the DINA Model

Cited by 26 publications

References 49 publications

On the Boundary Problems in Diagnostic Classification Models

On the Boundary Problems in Diagnostic Classification Models

Damage Evaluation of Bridge Hanger Based on Bayesian Inference: Analytical Model

Variational Bayes Inference for Hidden Markov Diagnostic Classification Models

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