The GWmodel R package:further topics for exploring spatial heterogeneity using geographically weighted models

In this study,we present a collection of local models,termed geographically weighted(GW)models,which can be found within the GWmodel R package.A GW model suits situations when spatial data are poorly described by the global form,and for some regions the localized fit provides a better description.The approach uses a moving window weighting technique,where a collection of local models are estimated at target locations.Commonly,model parameters or outputs are mapped so that the nature of spatial heterogeneity can be explored and assessed.In particular,we present case studies using:(i)GW summary statistics and a GW principal components analysis;(ii)advanced GW regression fits and diagnostics;(iii)associated Monte Carlo significance tests for non-stationarity;(iv)a GW discriminant analysis;and(v)enhanced kernel bandwidth selection procedures.General Election data-sets from the Republic of Ireland and US are used for demonstration.This study is designed to complement a companion GWmodel study,which focuses on basic and robust GW models.