Spatially Varying Coefficient Regression with GAM Gaussian Process splines: GAM(e)-on

Abstract

Abstract. This paper describes initial work exploring GAM Gaussian Process (GP) splines parameterised by observation location, as a geographical varying coefficient model. Similar to GWR, this approach accommodates process spatial heterogeneity and generates spatially distributed, local coefficient estimates. These can be mapped to indicate the nature of the heterogeneity. The paper investigates the effect of the smoothing parameters used in the splines and how they alter the nature of the modelled heterogeneity. It optimises these in the GAM GP and the tuned model has subtle but important differences with the initial model. This has impacts on the nature of the process understanding (inference) that can be extracted from the model. This in turn suggest the need examine the underlying semantics of the resultant models in relation to the scale of process suggested by the smoothing parameters. A number of areas of further work are identified.