Identifying influential observations in a Bayesian multi-level mediation model

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.

现如今，愈发复杂的模型被应用于数据分析之中。在采用马尔可夫链蒙特卡洛（Markov chain Monte Carlo）方法的贝叶斯建模（Bayesian modelling）领域，这一趋势尤为显著。当前，定制化的模型诊断方法往往相对滞后，贝叶斯中介模型（mediation model）领域亦未能例外。本文针对贝叶斯框架下的主流中介模型及其扩展形式，提出了一种强影响观测值检测方法。该方法基于个案删除原则开展强影响观测值的识别：我们采用借助分层模型依赖结构构建权重的重要抽样（importance sampling）方法，以定位模型中受影响程度最高的部分，并以对数重要抽样权重的方差作为影响程度的衡量指标。研究表明，当研究目标为探究单个观测值对模型参数子集的影响时，该方法具备切实的实用价值。我们采用护理研究领域的三级数据集对所提方法进行演示，该数据集此前曾被用于拟合患者护理满意度的中介模型，且我们重点关注了该数据集第二、第三层级中的强影响个案。