Geographically weighted redundancy analysis

Redundancy Analysis (RDA) is a conventional ordination technique to identify key relationships between multiple response and explanatory variables. It is routinely used both in the physical sciences and the social sciences, but for spatial processes, RDA is often applied without full consideration of spatial effects. Such naive applications can be problematic in terms of the interpretation of the RDA outputs and the understanding of the study process - leading to poor decision making. In this respect, RDA can be used to explore: (i) spatial autocorrelation, (ii) spatial heterogeneity with regard to data relationships, or (iii) both spatial effects (i) and (ii). In this study, the focus is on spatial heterogeneity, where RDA is novelly set within a geographically weighted (GW) framework where localised RDAs can be calibrated at any spatial location to form a GWRDA. This spatial setting of RDA entails non-stationary structures in the multivariate dataset can be identified and investigated across space. The proposed GWRDA algorithm is given with key calibration and diagnostic tools and evaluated both through a simulation experiment and an empirical case study. A route map for future refinements and developments of GWRDA is given.