create density raster and extract sum by polygon feature

Question

I have a polygon (zones) and a set of coordinates (points). I'd like to create a spatial kernal density raster for the entire polygon and extract the sum of the density by zone. Points outside of the polygon should be discarded.

library(raster)
library(tidyverse)
library(sf)
library(spatstat)
library(maptools)

load(url("https://www.dropbox.com/s/iv1s5butsx2v01r/example.RData?dl=1"))
# alternatively, links to gists for each object
# https://gist.github.com/ericpgreen/d80665d22dfa1c05607e75b8d2163b84
# https://gist.github.com/ericpgreen/7f4d3cee3eb5efed5486f7f713306e96

ggplot() +
  geom_sf(data = zones) +
  geom_sf(data = points) +
  theme_minimal()

I tried converting to ppp with {spatstat} and then using density(), but I'm confused by the units in the result. I believe the problem is related to the units of the map, but I'm not sure how to proceed.

Update

Here's the code to reproduce the density map I created:

zones_owin <- as.owin(as_Spatial(zones))
pts <- st_coordinates(points)
p <- ppp(pts[,1], pts[,2], window=zones_owin, unitname=c("metre","metres"))
ds <- density(p) 
r <- raster(ds)
plot(r)

Answer 1

I'm not sure if this answers all of your question, but should be a good start. Clarify in a comment or in your question should you need a different type of output.

It removes all points that are not inside one of the 'zone' polygons, counts them by zone and plots the zones colored by the number of points that fall within.

library(raster)
library(tidyverse)
library(sf)
#> Linking to GEOS 3.6.2, GDAL 2.2.3, PROJ 4.9.3
library(spatstat)

library(maptools)
#> Checking rgeos availability: TRUE

load(url("https://www.dropbox.com/s/iv1s5butsx2v01r/example.RData?dl=1"))
# alternatively, links to gists for each object
# https://gist.github.com/ericpgreen/d80665d22dfa1c05607e75b8d2163b84
# https://gist.github.com/ericpgreen/7f4d3cee3eb5efed5486f7f713306e96

p1 <- ggplot() +
  geom_sf(data = zones) +
  geom_sf(data = points) +
  theme_minimal()

#Remove points outside of zones
points_inside <- st_intersection(points, zones)
#> although coordinates are longitude/latitude, st_intersection assumes that they are planar
#> Warning: attribute variables are assumed to be spatially constant throughout all
#> geometries
nrow(points)
#> [1] 308
nrow(points_inside)
#> [1] 201

p2 <- ggplot() + 
  geom_sf(data = zones) + 
  geom_sf(data = points_inside)

points_per_zone <- st_join(zones, points_inside) %>%
  count(LocationID.x)
#> although coordinates are longitude/latitude, st_intersects assumes that they are planar

p3 <- ggplot() + 
  geom_sf(data = points_per_zone, 
          aes(fill = n)) + 
  scale_fill_viridis_c(option = 'C')

points_per_zone
#> Simple feature collection with 4 features and 2 fields
#> geometry type:  POLYGON
#> dimension:      XY
#> bbox:           xmin: 34.0401 ymin: -1.076718 xmax: 34.17818 ymax: -0.9755066
#> epsg (SRID):    4326
#> proj4string:    +proj=longlat +ellps=WGS84 +no_defs
#> # A tibble: 4 x 3
#>   LocationID.x     n                                                    geometry
#> *        <dbl> <int>                                               <POLYGON [°]>
#> 1           10   129 ((34.08018 -0.9755066, 34.0803 -0.9757393, 34.08046 -0.975…
#> 2           20    19 ((34.05622 -0.9959458, 34.05642 -0.9960835, 34.05665 -0.99…
#> 3           30    29 ((34.12994 -1.026372, 34.12994 -1.026512, 34.12988 -1.0266…
#> 4           40    24 ((34.11962 -1.001829, 34.11956 -1.002018, 34.11966 -1.0020…

cowplot::plot_grid(p1, p2, p3, nrow = 2, ncol = 2)

It seems I underestimated the difficulty of your problem. Is something like the plot below (& underlying data) what you're looking for?

It uses raster with ~50x50 grid, raster::focal with a window of 9x9 using the mean to interpolate the data.

Answer 2

Units are difficult when you work directly with geographic coordinates (lon, lat). If possible you should convert to planar coordinates (which is a requirement for spatstat) and proceed from there. The planar coordinates would typically be in units of meters, but I guess it depends on the specific projection and underlying ellipsoid etc. You can see this answer for how to project to planar coordinates with sf and export to spatstat format using maptools. Note: You have to manually choose a sensible projection (you can use http://epsg.io to find one) and you have to project both the polygon and the points.

Once everything is in spatstat format you can use density.ppp to do kernel smoothing. The resulting grid values (object of class im) are intensities of points, i.e., number of points per square unit (e.g. square meter). If you want to aggregate over some region you can use integral.im(..., domain = ...) to get the expected number of points in this region for a point process model with the given intensity.