Xu Xin, de la Torre Jimmy, Zhang Jiwei, Guo Jinxin, Shi Ningzhong
Key Laboratory of Applied Statistics of MOE, School of Mathematics and Statistics, Northeast Normal University, Changchun, China.
Faculty of Education, The University of Hong Kong, Pokfulam, Hong Kong.
Front Psychol. 2020 Sep 25;11:2260. doi: 10.3389/fpsyg.2020.02260. eCollection 2020.
In this paper, the slice-within-Gibbs sampler has been introduced as a method for estimating cognitive diagnosis models (CDMs). Compared with other Bayesian methods, the slice-within-Gibbs sampler can employ a wide-range of prior specifications; moreover, it can also be applied to complex CDMs with the aid of auxiliary variables, especially when applying different identifiability constraints. To evaluate its performances, two simulation studies were conducted. The first study confirmed the viability of the slice-within-Gibbs sampler in estimating CDMs, mainly including G-DINA and DINA models. The second study compared the slice-within-Gibbs sampler with other commonly used Markov Chain Monte Carlo algorithms, and the results showed that the slice-within-Gibbs sampler converged much faster than the Metropolis-Hastings algorithm and more flexible than the Gibbs sampling in choosing the distributions of priors. Finally, a fraction subtraction dataset was analyzed to illustrate the use of the slice-within-Gibbs sampler in the context of CDMs.
在本文中，已引入吉布斯抽样内切片法作为估计认知诊断模型（CDM）的一种方法。与其他贝叶斯方法相比，吉布斯抽样内切片法可以采用多种先验规范；此外，借助辅助变量，它还可应用于复杂的CDM，特别是在应用不同的可识别性约束时。为评估其性能，进行了两项模拟研究。第一项研究证实了吉布斯抽样内切片法在估计CDM方面的可行性，主要包括G-DINA和DINA模型。第二项研究将吉布斯抽样内切片法与其他常用的马尔可夫链蒙特卡罗算法进行了比较，结果表明，吉布斯抽样内切片法的收敛速度比梅特罗波利斯-黑斯廷斯算法快得多，并且在选择先验分布方面比吉布斯抽样更灵活。最后，分析了一个分数减法数据集，以说明吉布斯抽样内切片法在CDM背景下的应用。
