标题： 空间垂直回归用于空间面板数据：评估佛罗伦萨第一条有轨电车线路对商业活力的影响 显示英文标题

标题： Spatial vertical regression for spatial panel data: Evaluating the effect of the Florentine tramway's first line on commercial vitality

摘要： 合成控制方法在面板数据设置中常用于评估干预措施的效果。 在许多情况下，处理组和对照组单位对应于空间单位，如地区或社区。 我们的方法解决了理解在特定位置实施的干预如何影响周围区域的挑战。 传统的合成控制应用可能在定义影响的有效区域、处理在空间上的传播范围以及效果随距离变化的差异方面遇到困难。 为了解决这些挑战，我们在贝叶斯框架内引入了空间垂直回归（SVR）。 这种创新方法使我们能够准确预测不同距离处理地点的结果，同时仔细考虑数据中固有的空间结构。 具体而言，基于合成控制方法的垂直回归框架，SVR使用高斯过程确保对处理地点不同距离区域的缺失潜在结果的插补在空间上是一致的，反映了附近区域经历相似结果并与对照区域有相似关系的预期。 这种方法特别适用于我们对佛罗伦萨第一条电车线路建设的研究。 我们研究其对当地商业景观的影响，重点关注不同距离电车站的商业普及率的变化。 显示英文摘要

摘要： Synthetic control methods are commonly used in panel data settings to evaluate the effect of an intervention. In many of these cases, the treated and control units correspond to spatial units such as regions or neighborhoods. Our approach addresses the challenge of understanding how an intervention applied at specific locations influences the surrounding area. Traditional synthetic control applications may struggle with defining the effective area of impact, the extent of treatment propagation across space, and the variation of effects with distance from the treatment sites. To address these challenges, we introduce Spatial Vertical Regression (SVR) within the Bayesian paradigm. This innovative approach allows us to accurately predict the outcomes in varying proximities to the treatment sites, while meticulously accounting for the spatial structure inherent in the data. Specifically, rooted on the vertical regression framework of the synthetic control method, SVR employs a Gaussian process to ensure that the imputation of missing potential outcomes for areas of different distance around the treatment sites is spatially coherent, reflecting the expectation that nearby areas experience similar outcomes and have similar relationships to control areas. This approach is particularly pertinent to our study on the Florentine tramway's first line construction. We study its influence on the local commercial landscape, focusing on how business prevalence varies at different distances from the tram stops.