Encapsulating Spatially Varying Relationships with a Generalized Additive Model

Abstract: This paper describes the use of Generalized Additive Models (GAMs) to create regression models whose coefficient estimates vary with geographic location—spatially varying coefficient (SVC) models. The approach uses Gaussian Process (GP) splines (smooths) for each predictor variable, which are parameterised with observation location in order to generate SVC estimates. These describe the spatially varying relationships between predictor and response variables. The proposed GAM approach was compared with Multiscale Geographically Weighted Regression (MGWR) using simulated data with complex spatial heterogeneities. The geographical GP GAM (GGP-GAM) was found to out-perform MGWR across a range of fit metrics and resulted in more accurate coefficient estimates and lower residual errors. One of the GGP-GAM models was investigated in detail to illustrate model diagnostics, checks of spline/smooth convergence and basis evaluations. A larger simulated case study was investigated to explore the trade-offs between GGP-GAM complexity (via the number of knots), performance and computational efficiency. Finally, the GGP-GAM and MGWR approaches were applied to an empirical case study. The resulting models had very similar accuracies and fits and generated subtly different spatially varying coefficient estimates. A number of areas of further work are identified.