Comparing spatially‐varying coefficients models for analysis of ecological data with non‐stationary and anisotropic residual dependence

Summary 1. When exploring spatially complex ecological phenomena using regression models it is often unreasonable to assume a single set of regression coefficients can capture space-varying and scaledependent relationships between covariates and the outcome variable. This is especially true when conducting analysis across large spatial domains, where there is an increased propensity for anisotropic dependence structures and non-stationarity in the underlying spatial processes. 2. Geographically weighted regression (GWR) and Bayesian spatially-varying coefficients (SVC) are the most common methods for modelling such data. This paper compares these methods for modelling data generated from non-stationary processes. The comparison highlights some strengths and limitations of each method and aims to assist those who seek appropriate methods to better understand spatially complex ecological systems. Both synthetic and ecological data sets are used to facilitate the comparison. 3. Results underscored the need for the postulated model to approximate the underlying mechanism generating the data. Further, results show GWR and SVC can produce very different regression coefficient surfaces and hence dramatically different conclusions can be drawn regarding the impact of covariates. The trade-off between the richer inferential framework of SVC models and computational demands is also discussed.