Spatial Confounding: From Classical Models to Modern Applications

Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially structured data. The concept of spatial confounding has been interpreted in various ways in the literature but is broadly defined as bias in estimates arising from unmeasured spatial variation. When this spatial variation follows specific structures, standard spatial models may fail to mitigate the bias fully. This thesis provides a comprehensive review of spatial confounding, exploring its multiple definitions, classical spatial models, and recent methodological advances. We examine traditional approaches such as spatial lag model and spatial filtering, alongside modern methods like TGMRF, spectral adjustments, and machine-learning-based solutions. Additionally, the thesis addresses spatial confounding from a causal inference perspective, integrating methods like propensity score splines, generalized structural equation models, and spatial+ approaches. Through simulation studies using real and synthetic data, we evaluate the effectiveness of existing methods and bridge different conceptualizations of spatial confounding. By synthesizing recent advances, we clarify misconceptions, evaluate methodological trade-offs, and provide directions for future research.