A computationally efficient Gibbs sampler based on data-augmentation strategy for estimating the reparameterized DINA model

Abstract

With the increasing demand for precise test feedback, cognitive diagnosis models (CDMs) have attracted more and more attention for fine classification of students with regard to their ability to master given skills. The aim of this paper is to use a highly effective Gibbs algorithm based on auxiliary variables (GAAV) to estimate the deterministic input noisy “and” gate (DINA) model that is widely used for cognitive diagnosis. The applicability of the algorithm to other CDMs is also discussed. Unlike the Metropolis–Hastings algorithm, this new algorithm does not require repeated adjustment of the turning parameters to achieve an appropriate acceptance probability, and it also overcomes the dependence of the traditional Gibbs sampling algorithm on the conjugate prior distribution. Four simulation studies are conducted, and a detailed analysis of fraction subtraction test data is carried out to further illustrate the proposed methodology.

Keywords:

• Bayesian inference
• Cognitive diagnosis
• Gibbs algorithm based on auxiliary variable
• Metropolis-Hastings algorithm
• Potential scale reduction factor
• Reparameterized DINA model

Acknowledgments

The authors are greatly indebted to the Editor, Associate Editor and reviewer for their valuable comments and suggestions. This research was supported by Jilin Province Education Science “14th Five-Year Plan” 2022 Annual General Project + Data-Supported Dynamic Education Quality Monitoring and Evaluation Research–Taking the Evaluation of Jilin Province Students’ Mathematics Academic Ability Growth as an Example + Project Approval Number GH22415.

Additional information

Funding

The authors are greatly indebted to the Editor, Associate Editor and reviewer for their valuable comments and suggestions. This research was supported by Jilin Province Education Science “14th Five-Year Plan” 2022 Annual General Project + Data-Supported Dynamic Education Quality Monitoring and Evaluation Research–Taking the Evaluation of Jilin Province Students’ Mathematics Academic Ability Growth as an Example + Project Approval Number GH22415.