Using GAMs to understand whether and how processes vary over space and time

This paper an informed approach for constructing varying coefficient regression models using Generalized Additive Models (GAMs) with Gaussian Process (GP) smooths. Using a house price data over 13 years for a local case study, it investigates different model forms in order to determine the most probable model given the data. It determines the presence of any space-time dependencies between the target and each predictor variable is present, and if so their nature (ie whether they are independent or interact). It does this to avoid assumptions about the nature of spatial and / or temporal dependencies, in contrast to many existing approaches for space-time regressions which implicitly include baked in assumptions assumptions about the presence of these. The analysis uses tools in the stgam R package to undertake the analysis and to extract the varying coefficients from the model and a number of areas of further work are identified.