choosing pixel size for kernel density estimate map (density.ppp) in r

I have a shapefile of polygons and a shapefile of points that are distributed within the polygons. I've created kernel density estimate (KDE) maps for each polygon based on the points it contains using the density.ppp function from the spatstat package. I now wish to create different kde's with different pixel sizes in order to chose the one that best suits my model. I tried using the eps argument in the as.mask function, but that only changed the pixel size of the window and not of the kernel map itself so the results did not change. after going throw the entire manual of the density.ppp function, all I was able to find that looked related was the pixellate.ppp function from the spatstat.geom package, but i'm not sure how to use it with the density.ppp.

Any suggestion how to change the pixel size of the kde's?

library(sf)
library(spatstat)

buffer <- st_read("gis/layers/buffers.shp")
pbb<- st_read("gis/layers/points_by_buffer.shp")

for (p in 1:10) {
 if(p %in% pbb$field_id) {
   
   poly123 <- pbb[pbb$field_id == p,]
   
   C <- as.owin(buffer$geometry[p])

   W<- as.mask(C, eps = 100)

   point<- ppp(poly123$X,poly123$Y, window = W)

   sigma <- bw.diggle(point)
   
   d <- density.ppp(point, kernel = "gaussian", sigma=sigma, positive = TRUE, at="pixels", )
   plot(d) 
}

Solution

Three different things:

resolution: the spacing between the grid points at which the density will be calculated.
bandwidth: the amount of smoothing that will be applied to the input data.
unit of length: the physical unit of length (e.g. metre, kilometre); the units in which the spatial coordinates are given; the density values are expressed using the same units (density is the number of points per square unit).

If you change the resolution (which you can do using the arguments eps or dimyx in the call to density.ppp), the values of density will not change very much; you are just changing the spacing of the locations where the density is calculated.

If you change the bandwidth (which you can do by using the arguments sigma and adjust in the call to density.ppp), the values of density will change substantially. When you increase the bandwidth, each data point is effectively spread over a greater distance, and the density estimate becomes smoother and flatter.

If you change the unit of length, everything will change by a scale factor. The values of density are "number of points per unit area". If the density value is 3, this means we expect to see an average of 3 points per square unit. Here the 'unit' is the unit of length in which the spatial coordinates are expressed. If the original point coordinates are expressed in metres, then the density values are 'number of points per square metre'. If you want to change this, there are two ways:

rescale the input data (recommended): for example if the original data coordinates are in metres, you could convert them to kilometres by dividing the coordinates by 1000. We recommend using the function rescale.ppp to do this: Xnew <- rescale(Xold, 1000). You can declare the name of the unit of length using the function unitname (as in unitname(Xnew) <- "km"), or using rescale.ppp (as in Xnew <- rescale(Xold, 1000, "km")). After rescaling the point pattern, you invoke density.ppp (as in Dnew <- density(Xnew, ...) with the bandwidth expressed in kilometres) and the resulting density values are expressed in points per square km.
rescale the result (not recommended): if your coordinates were in metres and you decide later that you wanted to know the density expressed in points per square kilometre, then you could just apply the scaling factor to the image (by typing Dnew <- D * 1000^2 where D is the original density image) and also rescaling the spatial coordinates of the image (by typing Dnew <- rescale(Dnew, 1000, "km")). We don't recommend this because it is easy to mess up.

See the spatstat book for further information.