[R-sig-Geo] Apply geographically weighted regression's model parameters to a finer spatial scale

[Nikolaos Tziokas]

I have two raster layers, one coarse resolution and one fine resolution. My
goal is to extract GWR's coefficients (intercept and slope) and apply them
to my fine resolution raster.

I can do this easily when I perform simple linear regression. For example:

library(terra)
library(sp)
# focal terra
tirs = rast("path/tirs.tif") # fine res raster
ntl = rast("path/ntl.tif") # coarse res raster
    # fill null values
tirs = focal(tirs,
             w = 9,
             fun = mean,
             na.policy = "only",
             na.rm = TRUE)

gf <- focalMat(tirs, 0.10*400, "Gauss", 11)
r_gf <- focal(tirs, w = gf, na.rm = TRUE)

r_gf = resample(r_gf, ntl, method = "bilinear")

s = c(ntl, r_gf)names(s) = c('ntl', 'r_gf')

model <- lm(formula = ntl ~ tirs, data = s)
# apply the lm coefficients to the fine res raster
lm_pred = model$coefficients[1] + model$coefficients[2] * tirs

But when I run GWR, the slope and intercept are not just two numbers (like
in linear model) but it's a range. For example, below are the results of
the GWR:
*Summary of GWR coefficient estimates*:

                Min.     1st Qu.      Median     3rd Qu.     Max.

Intercept -1632.61196   -55.79680   -15.99683    15.01596 1133.299

tirs20      -42.43020     0.43446     1.80026     3.75802   70.987


My question is how can extract GWR model parameters (intercept and slope)
and apply them to my fine resolution raster? In the end I would like to do
the same thing as I did with the linear model, that is, *GWR_intercept +
GWR_slope * fine resolution raster*.

Here is the code of GWR:

library(GWmodel)
library(raster)

block.data = read.csv(file = "path/block.data00.csv")
#create mararate df for the x & y coords
x = as.data.frame(block.data$x)
y = as.data.frame(block.data$y)
sint = as.matrix(cbind(x, y))
#convert the data to spatialPointsdf and then to spatialPixelsdf
coordinates(block.data) = c("x", "y")#gridded(block.data) <- TRUE
# specify a model equation
eq1 <- ntl ~ tirs

dist = GWmodel::gw.dist(dp.locat = sint, focus = 0, longlat = FALSE)

abw = bw.gwr(eq1,
       data = block.data,
       approach = "AIC",
       kernel = "tricube",
       adaptive = TRUE,
       p = 2,
       longlat = F,
       dMat = dist,
       parallel.method = "omp",
       parallel.arg = "omp")

ab_gwr = gwr.basic(eq1,
          data = block.data,
          bw = abw,
          kernel = "tricube",
          adaptive = TRUE,
          p = 2,
          longlat = FALSE,
          dMat = dist,
          F123.test = FALSE,
          cv = FALSE,
          parallel.method = "omp",
          parallel.arg = "omp")

ab_gwr

You can download the csv from here
<https://drive.google.com/drive/folders/1V115zpdU2-5fXssI6iWv_F6aNu4E5qA7?usp=sharing>.
The fine resolution raster I am using:

tirs = rast(ncols=407, nrows=342, nlyrs=1, xmin=509600, xmax=550300,
ymin=161800, ymax=196000, names=c('tirs'), crs='EPSG:27700')

-- 
Tziokas Nikolaos
Cartographer

Tel:(+44)07561120302
LinkedIn <http://linkedin.com/in/nikolaos-tziokas-896081130>

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