Sequential Gibbs Sampling Algorithm for Cognitive Diagnosis Models with Many Attributes
Sequential Gibbs Sampling Algorithm for Cognitive Diagnosis Models with Many Attributes
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DOI：
10.1080/00273171.2021.1896352
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发表时间：
2021-03-02
影响因子：
3.8
通讯作者：
Xu, Gongjun
中科院分区：
文献类型：
--
作者：
Wang, Juntao;Shi, Ningzhong;Xu, Gongjun
认知诊断模型是一种有用的统计工具，可以为干预和学习提供丰富的信息。马尔可夫链蒙特卡罗(MCMC)算法作为一种流行的CDM估计和推理方法，在实际中得到了广泛的应用。然而，当属性数K较大时，现有的MCMC算法可能会变得很耗时，因为在MCMC采样过程中，通常需要O(2(K))次计算才能得到每个属性轮廓的条件分布。为了克服这一计算问题，受CulPepper和Hudson在2018年的早期工作的启发，我们提出了一种计算高效的顺序Gibbs抽样方法，该方法需要O(K)计算来对每个属性剖面进行采样。我们用仿真和实际数据例子说明了所提出的序贯Gibbs抽样的良好的有限样本性能，以及它相对于现有方法的优势。
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, K, is large, the existing MCMC algorithm may become time-consuming, due to the fact that O(2(K)) 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 O(K) 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.