基于混合模型的贝叶斯 MH-RM 算法在多维 4PLM 中的应用。
Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM.
机构信息
Shanghai Institute of AI for Education and Department of Educational Psychology of Faculty of Education, East China Normal University, Shanghai, China.
School of Educational Science, Liaocheng University, Liaocheng, China.
出版信息
Br J Math Stat Psychol. 2023 Nov;76(3):585-604. doi: 10.1111/bmsp.12300. Epub 2023 Feb 2.
Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.
几项最近的研究都针对单维四参数逻辑模型（4PLM）的估计问题进行了探讨。尽管已经做了这些努力，但多维 4PLM（M4PLM）的问题仍然是一个挑战。Fu 等人（2021）提出了一种用于 M4PLM 的 Gibbs 抽样器，但它非常耗时。本文提出了一种基于混合建模的贝叶斯 MH-RM（MM-MH-RM）算法，用于 M4PLM 以获得最大后验（MAP）估计。在将 MM-MH-RM 算法与原始 MH-RM 算法进行比较时，两项模拟研究和一个实证示例表明，MM-MH-RM 算法具有混合建模方法的优势，可以产生更稳健的估计值，并保证收敛速度和快速计算。MM-MH-RM 算法的 MATLAB 代码可在在线附录中获得。
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