Multiscale space-time varying coefficient modeling using generalized additive models: determining model form

This paper describes an approach to multiscale space-time varying coefficient modelling using Generalized Additive Models (GAMs). This builds on GAMs that have been previously used to generate spatially varying coefficients, but now extended to the temporal domain. However, for this space-time extension, a key consideration concerns model specification - i.e. how best to specify space and time in the GAM smooths. This depends on the nature of the space-time dependencies in the predictor-to-response variable relationships for a given dataset, where a key issue is how to relax assumptions about the presence of space-time dependencies that are found. For this study, multiple competing GAMs are created, with their space-time interactions specified in different ways for each predictor variable. A final GAM is found by the lowest AIC. The proposed approach is applied to simulated data and an empirical case study, where in both cases the best fitting GAM was found to out-perform Multiscale Geographically and Temporally Weighted Regression, a popular alternative. Model specification/selection for GAMs undertaken in this way provides insights into the nature of the space-time dependencies present in the data’s relationships, including the scale of these dependencies. The overall approach is novel and several areas of further work are identified.