The code and data in this repository are for the GW-ELNR simulation study described in the Journal of Journal of Spatial
Information Science submission. The code is described in the file Comber_hyperlocal.R. To run the code, save the .R file locally and run it. You will need an internet connection to access the data in this repository. Note that the hyperlocal code (lines 245 to 440) will take about 40 minutes to run . You could run this, save the outputs and load these in when you are experimenting (as in lines 441 and 442). Have fun!
Please contact Lex Comber a.comber@leeds.ac.uk if you have any questions.
Alexis Comber1 and Yunqiang Wang2 Yihe Lü3 Xingchang Zhang4 Paul Harris5
Alexis Comber1, Yunqiang Wang2, Yihe Lü3, Xingchang Zhang4, and Paul Harris5
1School of Geography, University of Leeds, Leeds, UK LS2 9JT 2State Key Laboratory of Loess and Quaternary Geology, Institute of Earth Environment, Chinese Academy of Sciences, Xi'an, China\ 3State Key Laboratory of Urban and Regional Ecology, Research Center for Eco-Environmental Sciences, Chinese Academy of Sciences; Joint Center for Global Change Studies; University of Chinese Academy of Sciences, Beijing, China\ 4Institute of Soil and Water Conservation, Chinese Academy of Sciences and Ministry of Water Resources, Yangling, China\ 5Rothamsted Research, North Wyke, Okehampton, Devon, UK EX20 2SB\
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 localised 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.
This work was supported by National Natural Science Foundation of China (NSFC) and the Natural Environment Research Council (NERC) Newton Fund through the China-UK collaborative research on critical zone science (No. 41571130083 and NE/N007433/1), the NSFC (No.41530854) and UK Biotechnology and Biological Sciences Research Council grant (BBSRC BB/J004308/1). All of the analyses and mapping were undertaken in R 3.3.2 the open source statistical software. The GWR analyses used the GWmodel package, v2.0-1 \cite{gollini2015gwmodel}.