Department of Statistics, KLAS, School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
China Institute of Rural Education Development, Northeast Normal University, Changchun, China.
Multivariate Behav Res. 2022 Sep-Oct;57(5):840-858. doi: 10.1080/00273171.2021.1896352. Epub 2021 Mar 23.
Cognitive diagnosis models (CDMs) are useful statistical tools to provide rich information relevant for intervention and learning. As a popular approach to estimate and make inference of CDMs, the Markov chain Monte Carlo (MCMC) algorithm is widely used in practice. However, when the number of attributes, , is large, the existing MCMC algorithm may become time-consuming, due to the fact that calculations are usually needed in the process of MCMC sampling to get the conditional distribution for each attribute profile. To overcome this computational issue, motivated by Culpepper and Hudson's earlier work in 2018, we propose a computationally efficient sequential Gibbs sampling method, which needs () calculations to sample each attribute profile. We use simulation and real data examples to show the good finite-sample performance of the proposed sequential Gibbs sampling, and its advantage over existing methods.
认知诊断模型 (CDMs) 是一种有用的统计工具，可以提供与干预和学习相关的丰富信息。作为一种估计和进行 CDMs 推理的流行方法，马尔可夫链蒙特卡罗 (MCMC) 算法在实践中得到了广泛应用。然而，当属性数量, 很大时，由于在 MCMC 抽样过程中通常需要进行 计算才能得到每个属性分布的条件分布，现有的 MCMC 算法可能会变得耗时。为了解决这个计算问题，受 Culpepper 和 Hudson 在 2018 年早期工作的启发，我们提出了一种计算效率高的序贯 Gibbs 抽样方法，该方法需要进行 () 计算来对每个属性分布进行抽样。我们通过模拟和真实数据示例展示了所提出的序贯 Gibbs 抽样方法的良好有限样本性能，以及它相对于现有方法的优势。
