Geographically Weighted Poisson Regression

Installation

You can install the package from GitHub.

install.packages("remotes") # if you have not installed "remotes" package
remotes::install_github("hoxo-m/gwpr")

Example

set.seed(123)
df <- lctools::random.test.data(10, 10, 2, "poisson")
head(df)
#>   dep      vars X Y
#> 1   5 0.2387260 1 1
#> 2   9 0.9623589 1 2
#> 3   6 0.6013657 1 3
#> 4  10 0.5150297 1 4
#> 5  11 0.4025733 1 5
#> 6   3 0.8802465 1 6

library(gwpr)
df_coord <- df[c("X", "Y")]
params <- gwpr(df, dep ~ vars, df_coord,
               kernel = "gaussian", bandwidth = 1)

library(ggplot2)
df_gg <- cbind(params, df_coord)
ggplot(df_gg, aes(X, Y)) + geom_raster(aes(fill = vars)) +
  scale_fill_gradient2()

Change bandwidth

params_bw2 <- gwpr(df, dep ~ vars, df_coord,
                   kernel = "gaussian", bandwidth = 2)
params_bw3 <- gwpr(df, dep ~ vars, df_coord,
                   kernel = "gaussian", bandwidth = 3)

df_gg_bw2 <- cbind(params_bw2, df_coord)
df_gg_bw3 <- cbind(params_bw3, df_coord)

p1 <- ggplot(df_gg, aes(X, Y)) + geom_raster(aes(fill = vars)) +
  scale_fill_gradient2() + ggtitle("bandwidth = 1")
p2 <- ggplot(df_gg_bw2, aes(X, Y)) + geom_raster(aes(fill = vars)) +
  scale_fill_gradient2() + ggtitle("bandwidth = 2")
p3 <- ggplot(df_gg_bw3, aes(X, Y)) + geom_raster(aes(fill = vars)) +
  scale_fill_gradient2() + ggtitle("bandwidth = 3")

cowplot::plot_grid(p1, p2, p3)

References

• Nakaya, Tomoki & Fotheringham, Alexander & Brunsdon, Chris & Charlton, Martin. (2005). Geographically Weighted Poisson Regression for Disease Association Mapping. Statistics in medicine. 24. 2695-717. 10.1002/sim.2129.

Related Work

• spgwr: Geographically Weighted Regression
  • 
  • ggwr(): Generalised geographically weighted regression
  • Fotheringham, A.S., Brunsdon, C., and Charlton, M.E., 2002, Geographically Weighted Regression, Chichester: Wiley; http://gwr.nuim.ie/
• GWmodel: Geographically-Weighted Models
  • 
  • ggwr.basic(): Generalised GWR models with Poisson and Binomial options
  • Nakaya, T., A. S. Fotheringham, C. Brunsdon & M. Charlton (2005) Geographically weighted Poisson regression for disease association mapping. Statistics in Medicine, 24, 2695-2717.
  • Nakaya, T., M. Charlton, S. Fotheringham & C. Brunsdon. 2009. How to use SGWRWIN (GWR4.0). Maynooth, Ireland: National Centre for Geocomputation.
  • Fotheringham S, Brunsdon, C, and Charlton, M (2002), Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, Chichester: Wiley.
• lctools: Local Correlation, Spatial Inequalities, Geographically Weighted Regression and Other Tools
  • 
  • gw.glm(): Generalised Geographically Weighted Regression (GGWR)
  • Kalogirou, S. (2003) The Statistical Analysis and Modelling of Internal Migration Flows within England and Wales, PhD Thesis, School of Geography, Politics and Sociology, University of Newcastle upon Tyne, UK. http://gisc.gr/?mdocs-file=1245&mdocs-url=false
  • Kalogirou, S. (2016) Destination Choice of Athenians: an application of geographically weighted versions of standard and zero inflated Poisson spatial interaction models, Geographical Analysis, 48(2),pp. 191-230. DOI: 10.1111/gean.12092 http://onlinelibrary.wiley.com/doi/10.1111/gean.12092/abstract