Kwon Sunbeom, Zhang Susu, Köhn Hans Friedrich, Zhang Bo
University of Illinois, Urbana-Champaign, Urbana, Illinois, USA.
Br J Math Stat Psychol. 2025 Feb;78(1):225-257. doi: 10.1111/bmsp.12357. Epub 2024 Oct 10.
Bayesian analysis relies heavily on the Markov chain Monte Carlo (MCMC) algorithm to obtain random samples from posterior distributions. In this study, we compare the performance of MCMC stopping rules and provide a guideline for determining the termination point of the MCMC algorithm in latent variable models. In simulation studies, we examine the performance of four different MCMC stopping rules: potential scale reduction factor (PSRF), fixed-width stopping rule, Geweke's diagnostic, and effective sample size. Specifically, we evaluate these stopping rules in the context of the DINA model and the bifactor item response theory model, two commonly used latent variable models in educational and psychological measurement. Our simulation study findings suggest that single-chain approaches outperform multiple-chain approaches in terms of item parameter accuracy. However, when it comes to person parameter estimates, the effect of stopping rules diminishes. We caution against relying solely on the univariate PSRF, which is the most popular method, as it may terminate the algorithm prematurely and produce biased item parameter estimates if the cut-off value is not chosen carefully. Our research offers guidance to practitioners on choosing suitable stopping rules to improve the precision of the MCMC algorithm in models involving latent variables.
贝叶斯分析严重依赖马尔可夫链蒙特卡罗（MCMC）算法从后验分布中获取随机样本。在本研究中，我们比较了MCMC停止规则的性能，并为确定潜在变量模型中MCMC算法的终止点提供了指导方针。在模拟研究中，我们考察了四种不同的MCMC停止规则的性能：潜在尺度缩减因子（PSRF）、固定宽度停止规则、盖韦克诊断法和有效样本量。具体而言，我们在DINA模型和双因素项目反应理论模型（教育和心理测量中常用的两种潜在变量模型）的背景下评估这些停止规则。我们的模拟研究结果表明，在项目参数准确性方面，单链方法优于多链方法。然而，在人员参数估计方面，停止规则的影响会减弱。我们提醒不要仅依赖最常用的单变量PSRF，因为如果截断值选择不当，它可能会过早终止算法并产生有偏差的项目参数估计。我们的研究为从业者在涉及潜在变量的模型中选择合适的停止规则以提高MCMC算法的精度提供了指导。
