Hyper-local geographically weighted regression: extending GWR through local model selection and local bandwidth optimization

Abstract: Geographically weighted regression (GWR) is an inherently exploratory technique for examining process non-stationarity in data relationships. This paper develops and applies a hyper-local GWR which extends such investigations further. The hyper-local GWR simultaneously optimizes both local model selection (which covariates to include in each local regression) and local kernel bandwidth specification (how much data should be included locally). These are evaluated using a measure of model fit. By allowing models and bandwidths to vary locally, it extends the ’whole map model’ and ’constant bandwidth calibration’ under standard GWR. It provides an alternative and complementary interpretation of localized regression. The method is illustrated using a case study modeling soil total nitrogen (STN) and soil total phosphorus (STP) from data collected at 689 locations in a watershed in Northern China. The analysis compares linear regression, standard GWR and hyper-local GWR models of STN and STP and highlights the different locations at which covariates are identified as significant predictors of STN and STP by the different GWR approaches and the spatial variation in optimal bandwidths. The hyper-local GWR results indicate that the STN relationship processes are more non-stationary and localized than found via a standard application of GWR. By contrast, the results for STP are more confirmatory (i.e. similar) between the two GWR approaches providing extra assurance to the nature of the moderate non-stationary relationships observed. The overall benefits of hyper-local GWR are discussed, particularly in the context of the original investigative aims of standard GWR. Some areas of further work are suggested.