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

2021 ◽  
Author(s):  
Kazuhiro Yamaguchi ◽  
Jonathan Templin
Keyword(s):  
Gibbs Sampling ◽  
Diagnostic Classification ◽  
Classification Models ◽  
Sampling Algorithm ◽  
Diagnostic Classification Models ◽  
Monotonicity Constraints ◽  
Gibbs Sampling Algorithm

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

2020 ◽  
Author(s):  
Kazuhiro Yamaguchi ◽  
Jonathan Templin
Keyword(s):  
Gibbs Sampling ◽  
Estimation Method ◽  
Latent Class Models ◽  
Diagnostic Classification ◽  
Accurate Estimation ◽  
Model Parameters ◽  
Classification Models ◽  
Diagnostic Classification Models ◽  
International Student Assessment ◽  
Monotonicity Constraints

Diagnostic classification models (DCM) 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. An analysis of the 2000 Programme for International Student Assessment reading assessment data using this algorithm was also conducted.

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

2020 ◽  
Author(s):  
Kazuhiro Yamaguchi ◽  
Jonathan Templin
Keyword(s):  
Gibbs Sampling ◽  
Estimation Method ◽  
Real Data ◽  
Classification Model ◽  
Diagnostic Classification ◽  
Model Parameters ◽  
Sampling Algorithm ◽  
Diagnostic Classification Models ◽  
Gibbs Sampling Algorithm ◽  
Collapsed Gibbs Sampling

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. In a real data analysis, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

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