An MCMC Algorithm for Estimating the Q-matrix in a Bayesian Framework
An MCMC Algorithm for Estimating the Q-matrix in a Bayesian Framework
复制标题
贝叶斯框架中估计 Q 矩阵的 MCMC 算法
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Matthew S. Johnson
中科院分区：
文献类型：
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作者：
Mengta Chung;Matthew S. Johnson
本研究的目的是发展一个估计Q矩阵的MCMC算法。该算法以DINA模型为基础，从估计相关属性入手。使用饱和模型和二进制十进制转换，该算法将可能的属性模式转换为多项分布。沿着属性模式的可能性，使用Gamma分布构造的Dirichlet分布被用作从后验中采样的先验。利用反变换抽样方法生成考生的相关属性。给出了采样猜想和滑移参数的封闭形式后验，导出了Q矩阵的采样分布。一个重新标记算法，占潜在的标签切换。给出了DINA模型中属性相关数据的模拟方法。三个仿真研究进行评估的算法的性能。使用ECPE数据进行实证研究。该算法使用定制的R代码实现。
The purpose of this research is to develop an MCMC algorithm for estimating the Q-matrix. Based on the DINA model, the algorithm starts with estimating correlated attributes. Using a saturated model and a binary decimal conversion, the algorithm transforms possible attribute patterns to a Multinomial distribution. Along with the likelihood of an attribute pattern, a Dirichlet distribution, constructed using Gamma distributions, is used as the prior to sample from the posterior. Correlated attributes of examinees are generated using inverse transform sampling. Closed form posteriors for sampling guess and slip parameters are found. A distribution for sampling the Q-matrix is derived. A relabeling algorithm that accounts for potential label switching is presented. A method for simulating data with correlated attributes for the DINA model is offered. Three simulation studies are conducted to evaluate the performance of the algorithm. An empirical study using the ECPE data is performed. The algorithm is implemented using customized R codes.