Generalised geographically weighted regression

The function implements generalised geographically weighted regression approach to exploring spatial non-stationarity for given global bandwidth and chosen weighting scheme.

ggwr(formula, data = list(), coords, bandwidth, gweight = gwr.Gauss,
 adapt = NULL, fit.points, family = gaussian, longlat = NULL, type = 
c("working", "deviance", "pearson", "response"))

Arguments

formula

regression model formula as in glm

data

model data frame as in glm, or may be a SpatialPointsDataFrame or SpatialPolygonsDataFrame object as defined in package sp

coords

matrix of coordinates of points representing the spatial positions of the observations

bandwidth

bandwidth used in the weighting function, possibly calculated by ggwr.sel

gweight

geographical weighting function, at present gwr.Gauss() default, or gwr.gauss(), the previous default or gwr.bisquare()

adapt

either NULL (default) or a proportion between 0 and 1 of observations to include in weighting scheme (k-nearest neighbours)

fit.points

an object containing the coordinates of fit points; often an object from package sp; if missing, the coordinates given through the data argument object, or the coords argument are used

family

a description of the error distribution and link function to be used in the model, see glm

longlat

TRUE if point coordinates are longitude-latitude decimal degrees, in which case distances are measured in kilometers; if x is a SpatialPoints object, the value is taken from the object itself

type

the type of residuals which should be returned. The alternatives are: "working" (default), "pearson", "deviance" and "response"

Value

A list of class “gwr”:

SDF

a SpatialPointsDataFrame (may be gridded) or SpatialPolygonsDataFrame object (see package "sp") with fit.points, weights, GWR coefficient estimates, dispersion if a "quasi"-family is used, and the residuals of type "type" in its "data" slot.

lhat

Leung et al. L matrix, here set to NA

lm

GLM global regression on the same model formula.

bandwidth

the bandwidth used.

this.call

the function call used.

References

Fotheringham, A.S., Brunsdon, C., and Charlton, M.E., 2002, Geographically Weighted Regression, Chichester: Wiley; http://gwr.nuim.ie/

Author

Roger Bivand Roger.Bivand@nhh.no

Note

The use of GWR on GLM is only at the initial proof of concept stage, nothing should be treated as an accepted method at this stage.

See also

ggwr.sel, gwr

Examples

if (require(sf)) {
xx <- as(st_read(system.file("shapes/sids.shp", package="spData")[1]), "Spatial")
bw <- 144.4813
if (FALSE) {
bw <- ggwr.sel(SID74 ~ I(NWBIR74/BIR74) + offset(log(BIR74)), data=xx,
  family=poisson(), longlat=TRUE)
}
nc <- ggwr(SID74 ~ I(NWBIR74/BIR74) + offset(log(BIR74)), data=xx,
  family=poisson(), longlat=TRUE, bandwidth=bw)
nc
if (FALSE) {
nc <- ggwr(SID74 ~ I(NWBIR74/10000) + offset(log(BIR74)), data=xx,
  family=poisson(), longlat=TRUE, bandwidth=bw)
nc
nc <- ggwr(SID74 ~ I(NWBIR74/10000) + offset(log(BIR74)), data=xx,
  family=quasipoisson(), longlat=TRUE, bandwidth=bw)
nc
}
}
#> Loading required package: sf
#> Linking to GEOS 3.12.0beta1, GDAL 3.7.0, PROJ 9.2.1; sf_use_s2() is TRUE
#> Reading layer `sids' from data source 
#>   `/home/rsb/lib/r_libs/spData/shapes/sids.shp' using driver `ESRI Shapefile'
#> Simple feature collection with 100 features and 22 fields
#> Geometry type: MULTIPOLYGON
#> Dimension:     XY
#> Bounding box:  xmin: -84.32385 ymin: 33.88199 xmax: -75.45698 ymax: 36.58965
#> CRS:           NA