Specification of multiscale space-time varying coefficient GAMs

Abstract

This paper demonstrates an approach to the application of generalized additive models (GAMs) with space-time smooths to model coefficient processes that vary over space and time. The approach is to create and evaluate multiple GAMs, each with the predictor variables specified in different ways. It emphasizes the need to determine the nature of the space-time dependencies present in the data relationships rather than to assume them, based on the perceived data generating process, especially if this is unknown. The approach is explored using simulated coefficient data with known space-time dependencies. The GAMs are compared with multiscale geographically and temporally weighted regression (MGTWR) models and are shown to have marginally weaker predictive performance and to be marginally better at coefficient recovery. The inferential costs of misspecifying the target-to-predictor variable relationships in the GAMs is quantified both for individual variable main effects and interacting misspecifications. The approach is then applied to an empirical case study of NDVI (as a proxy for forest productivity) informed by precipitation and temperature in the Chaco dry rainforest of South America. The best GAM is determined and its space-time varying coefficient estimates are investigated. The methods and results are discussed and several areas of further work and enhancements to the stgam R package used to undertake this analysis are identified.