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.