Abstract：
Diagnostic classification models (DCMs) can be used to track the cognitive learning states of students across multiple time points or over repeated measurements. This study developed an effective variational Bayes (VB) inference method for hidden Markov longitudinal general DCMs. The simulations performed in this study verified the validity of the proposed algorithm for satisfactorily recovering true parameters. Simulation and applied data analyses were conducted to compare the proposed VB method to Markov chain Monte Carlo (MCMC) sampling. The results revealed that the parameter estimates provided by the VB method were consistent with the MCMC method with the additional benefit of a faster estimation time. The comparative simulation also indicated differences between the two methods in terms of posterior standard deviation and coverage of 95% credible intervals. Thus, with limited computational resources and time, the proposed VB method can output estimations comparable to that of MCMC.
摘要：
诊断分类模型（DCM）可用于跟踪学生跨多个时间点或重复测量的认知学习状态。这项研究开发了一种有效的变分贝叶斯（VB）推理方法，用于隐马尔可夫纵向一般DCM。在这项研究中进行的仿真验证了所提出的算法的有效性，用于令人满意地恢复真实参数。进行了模拟和应用数据分析，以将提出的VB方法与马尔可夫链蒙特卡罗（MCMC）采样进行比较。结果表明，VB方法提供的参数估计与MCMC方法一致，具有更快的估计时间。比较模拟还显示了两种方法在后验标准偏差和95%可信区间的覆盖率方面的差异。因此，有限的计算资源和时间，提出的VB方法可以输出与MCMC相当的估计。
