Spatial models are used in a variety of research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in such spatial regression models is spatial confounding. This phenomenon is observed when spatially indexed covariates modeling the mean of the response are correlated with a spatial random effect included in the model, for example, as a proxy of unobserved spatial confounders. As a result, estimates for regression coefficients of the covariates can be severely biased and interpretation of these is no longer valid. Recent literature has shown that typical solutions for reducing spatial confounding can lead to misleading and counterintuitive results. In this article, we develop a computationally efficient spatial model that explicitly correlates a Gaussian random field for the covariate of interest with the Gaussian random field in the main model equation and integrates novel prior structures to reduce spatial confounding. Starting from the univariate case, we extend our prior structure also to the case of multiple spatially confounded covariates. In simulation studies, we show that our novel model flexibly detects and reduces spatial confounding in spatial datasets, and it performs better than typically used methods such as restricted spatial regression. These results are promising for any applied researcher who wishes to interpret covariate effects in spatial regression models. As a real data illustration, we study the effect of elevation and temperature on the mean of monthly precipitation in Germany.

中文翻译：

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通过显式关联高斯随机场来减轻空间混淆

空间模型用于各种研究领域，例如环境科学、流行病学或物理学。这种空间回归模型中的一个常见现象是空间混杂。当建模响应平均值的空间索引协变量与模型中包含的空间随机效应相关时，就会观察到这种现象，例如，作为未观察到的空间混杂因素的代理。因此，协变量回归系数的估计可能存在严重偏差，并且对这些的解释不再有效。最近的文献表明，减少空间混淆的典型解决方案可能会导致误导和违反直觉的结果。在本文中，我们开发了一种计算效率高的空间模型，该模型将感兴趣的协变量的高斯随机场与主模型方程中的高斯随机场明确关联起来，并整合了新的先验结构以减少空间混杂。从单变量情况开始，我们还将我们的先验结构扩展到多个空间混杂协变量的情况。在模拟研究中，我们表明我们的新模型可以灵活地检测和减少空间数据集中的空间混杂，并且它的性能优于通常使用的方法，例如受限空间回归。这些结果对于任何希望在空间回归模型中解释协变量效应的应用研究人员来说都是有希望的。作为一个真实的数据说明，我们研究了海拔和温度对德国月降水量平均值的影响。