[论文解读] Re-thinking Spatial Confounding in Spatial Linear Mixed Models

Kori Khan, Candace Berrett|arXiv (Cornell University)|Jan 13, 2023

Spatial and Panel Data Analysis被引用 10

一句话总结

本文整合了空间混淆文献，区分两种形式（数据生成 vs. 分析模型），并表明二者都能影响推断，通常支持传统空间模型胜过消解方法。

ABSTRACT

In the last two decades, considerable research has been devoted to a phenomenon known as spatial confounding. Spatial confounding is thought to occur when there is multicollinearity between a covariate and the random effect in a spatial regression model. This multicollinearity is considered highly problematic when the inferential goal is estimating regression coefficients and various methodologies have been proposed to attempt to alleviate it. Recently, it has become apparent that many of these methodologies are flawed, yet the field continues to expand. In this paper, we offer a novel perspective of synthesizing the work in the field of spatial confounding. We propose that at least two distinct phenomena are currently conflated with the term spatial confounding. We refer to these as the ``analysis model'' and the ``data generation'' types of spatial confounding. We show that these two issues can lead to contradicting conclusions about whether spatial confounding exists and whether methods to alleviate it will improve inference. Our results also illustrate that in most cases, traditional spatial linear mixed models do help to improve inference on regression coefficients. Drawing on the insights gained, we offer a path forward for research in spatial confounding.

研究动机与目标

• 总结空间混淆的历史发展与定义。
• 区分数据生成空间混淆与分析模型空间混淆。
• 在非空间、空间与修正后的空间模型下，理论比较回归系数的偏差。
• 用仿真研究何时传统空间模型优于调整方法。
• 提出解决空间混淆文献中矛盾的前进路径。

提出的方法

• 建立对比数据生成与分析模型的空间数据分析设定。
• 定义三种建模框架：非空间、传统空间，以及带空间随机效应的调整空间模型。
• 推导在不同混淆来源（数据生成与分析模型）下回归系数的偏差表达式。
• 使用高斯过程/马特恩协方差来表征 X 与 Z 及其相关性。
• 给出将偏差与模型选择及数据生成结构联系起来的理论结果。
• 提供仿真研究以说明何时传统空间模型可能优于替代方法。

实验结果

研究问题

• RQ1 文献中有哪些不同的空间混淆来源？
• RQ2 数据生成与分析模型视角如何对回归系数的偏差产生不同影响？
• RQ3 在何种条件下传统空间模型比调整方法提供更好的推断？
• RQ4 现有旨在缓解空间混淆的方法相对于标准空间回归模型的表现如何？

主要发现

• 空间混淆下存在两种不同现象：数据生成空间混淆与分析模型空间混淆。
• 回归系数的偏差取决于混淆来源及所选建模框架。
• 在许多情形中，传统空间回归模型可获得比旨在消除混淆的调整模型更好的推断。
• 仅针对一种空间混淆的办法可能比标准空间模型更扭曲推断。
• 综合澄清文献中的分歧结论，并为未来提供原则性路径。