Model Choice and Diagnostics for Linear Mixed-Effects Models Using Statistics on Street Corners

The complexity of linear mixed-effects (LME) models means that traditional diagnostics are rendered less effective. This is due to a breakdown of asymptotic results, boundary issues, and visible patterns in residual plots that are introduced by the model fitting process. Some of these issues are well known and adjustments have been proposed. Working with LME models typically requires that the analyst keeps track of all the special circumstances that may arise. In this article, we illustrate a simpler but generally applicable approach to diagnosing LME models. We explain how to use new visual inference methods for these purposes. The approach provides a unified framework for diagnosing LME fits and for model selection. We illustrate the use of this approach on several commonly available datasets. A large-scale Amazon Turk study was used to validate the methods. R code is provided for the analyses. Supplementary materials for this article are available online.

线性混合效应模型（linear mixed-effects models, LME）的复杂性使得传统诊断方法的应用效果大打折扣。这是因为模型拟合过程中会出现渐近结果失效、边界异常以及残差图显现异常模式等情况。其中部分问题已被学界广泛认知，相关修正方案也已被提出。在实际开展线性混合效应模型相关研究时，统计分析师通常需要追踪所有可能出现的特殊情形。本文中，我们将介绍一种更为简洁但普适性更强的线性混合效应模型诊断方法，并阐释如何将新型可视化推断方法用于此类诊断任务。该方法为线性混合效应模型拟合诊断与模型选择提供了统一的分析框架。我们将在多个常用公开数据集上演示该方法的具体应用。此外，本研究还通过大规模亚马逊土耳其机器人（Amazon Turk）实验对所提方法进行了验证。本文附带的R语言代码可复现相关分析，文章的补充材料可在线获取。