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.

翻译：认知诊断模型(CDM)是有用的统计工具,可以提供与干预和学习有关的丰富信息;作为估算和推断CDM的流行方法,在实践中广泛使用Markov连锁Monte Carlo(MCMC)算法;然而,当属性数量巨大(K$)时,现有的MCMC算法可能会耗时,因为MMC取样过程中通常需要O(2K)美元计算,以获得每个属性剖面的有条件分布;为了克服由Culpepper和Hudson(2018年)驱动的这一计算问题,我们提议一种计算高效的连续测序Gibbs取样方法,这需要一O(K)美元计算来抽样每个属性剖面。我们使用模拟和真实数据示例来显示拟议的按顺序采集的抽样的优劣性、其优于现有方法的优势。