Generalized Additive Spatial Smoothing (GASS): A Multiscale Regression Framework for Modeling Neighborhood Effects Across Spatial Supports

A new technique called generalized additive spatial smoothing (GASS) is introduced for modeling neighborhood effects within a regression framework. GASS has a number of desirable features, namely that it provides a data-driven mechanism for endogenously selecting neighborhoods based on a spatial scale hyperparameter. By allowing different scale hyperparameters to be selected for different relationships in the model, the technique is inherently multiscale and allows neighborhoods to vary by relationship. In addition, GASS includes a measure of uncertainty associated with each scale hyperparameter. These characteristics make it attractive for modeling phenomena where proximity might be an important aspect of a process, especially when a clear definition of proximity is not immediately available. Through multiscale data-driven spatial smoothing, GASS conducts a form of change of support and therefore also facilitates the incorporation of data from diverse sources. Finally, the technique is flexible and can be adapted and expanded with relative ease because it builds on generalized additive modeling. After providing an overview of the methodology, including a modified backfitting algorithm for calibration, a simulation experiment is described and an empirical example modeling bike-share usage is presented. The simulation results indicate that GASS can generally produce reliable results pertaining to both the regression coefficients and scale hyperparameters, and the results from the empirical example demonstrate that the GASS approach provides a better model fit and captures relationships that might otherwise be obfuscated. Overall, these results highlight the potential of the GASS framework and the importance of measuring multiscale neighborhood effects.

本文提出了一种名为广义可加空间平滑（Generalized Additive Spatial Smoothing, GASS）的新技术，用于在回归框架内对邻域效应进行建模。GASS具备多项优良特性：其一，它提供了一种数据驱动的机制，可基于空间尺度超参数内生性地选取邻域。通过允许为模型中的不同关系选取不同的尺度超参数，该技术本质上具备多尺度特性，且可使邻域随关系类型的不同而变化。此外，GASS还包含了与每个尺度超参数相关联的不确定性度量指标。这些特性使其在建模那些以邻近性为关键过程维度的现象时极具吸引力，尤其是在无法直接明确定义邻近性的场景下。通过多尺度数据驱动的空间平滑操作，GASS实现了一种支持域变换形式，因此也便于整合来自不同来源的数据。最后，由于该技术基于广义可加模型（Generalized Additive Modeling, GAM）构建，因此具备良好的灵活性，可相对轻松地进行适配与扩展。在对该方法（包括用于校准的改进反向拟合算法）进行概述之后，本文描述了一项仿真实验，并给出了一个以共享单车使用量为建模对象的实证案例。仿真结果表明，GASS通常能够在回归系数与尺度超参数两方面生成可靠的结果；而实证案例的结果则显示，GASS方法可实现更优的模型拟合度，且能捕捉到否则可能被掩盖的关系。总体而言，上述结果凸显了GASS框架的应用潜力，以及度量多尺度邻域效应的重要性。