论文标题
具有许多属性的认知诊断模型的顺序吉布斯采样算法
Sequential Gibbs Sampling Algorithm for Cognitive Diagnosis Models with Many Attributes
论文作者
论文摘要
认知诊断模型（CDM）是有用的统计工具，可提供与干预和学习相关的丰富信息。作为估计和推断CDM的一种流行方法，马尔可夫链蒙特卡洛（MCMC）算法在实践中广泛使用。但是，当属性$ k $的数量很大时，现有的MCMC算法可能会耗时，因为在MCMC采样过程中通常需要$ O（2^k）$计算以获取每个属性配置文件的条件分布。为了克服这一计算问题，由Culpepper和Hudson（2018）激励，我们提出了一种计算有效的顺序gibbs采样方法，该方法需要$ o（k）$计算以对每个属性配置文件进行采样。我们使用仿真和真实数据示例来显示所提出的顺序吉布斯采样的良好有限样本性能及其比现有方法的优势。
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 (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.
