Večeřová Šárka, Komárek Arnošt, Bruyneel Luk, Lesaffre Emmanuel
Department of Probability and Mathematical Statistics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic.
Leuven Institute for Healthcare Policy, University of Leuven, Leuven, Belgium.
J Appl Stat. 2020 Apr 15;48(5):943-960. doi: 10.1080/02664763.2020.1748179. eCollection 2021.
Increasingly complex models are being fit to data these days. This is especially the case for Bayesian modelling making use of Markov chain Monte Carlo methods. Tailored model diagnostics are usually lacking behind. This is also the case for Bayesian mediation models. In this paper, we developed a method for the detection of influential observations for a popular mediation model and its extensions in a Bayesian context. Detection of influential observations is based on the case-deletion principle. Importance sampling with weights which take advantage of the dependence structure in hierarchical models is utilized in order to identify the part of the model which is influenced most. We make use of the variance of log importance sampling weights as the measure of influence. It is demonstrated that this approach is useful when interest lies in the impact of individual observations on a subset of model parameters. The method is illustrated on a three-level data set from the field of nursing research, which was previously used to fit a mediation model of patient satisfaction with care. We focused on influential cases on both the second and the third level of the data.
如今，越来越复杂的模型正被用于拟合数据。对于利用马尔可夫链蒙特卡罗方法的贝叶斯建模而言，情况尤其如此。量身定制的模型诊断通常滞后。贝叶斯中介模型亦是如此。在本文中，我们开发了一种方法，用于在贝叶斯背景下检测一种流行的中介模型及其扩展模型中的有影响观测值。有影响观测值的检测基于删除案例原则。利用分层模型中的依赖结构的加权重要性抽样被用于识别模型中受影响最大的部分。我们将对数重要性抽样权重的方差用作影响的度量。结果表明，当关注个体观测值对模型参数子集的影响时，这种方法是有用的。该方法在护理研究领域的一个三级数据集上进行了说明，该数据集先前被用于拟合患者护理满意度的中介模型。我们关注数据第二和第三层级上的有影响案例。
