Calculating measure of spatial segregation?

Question

There is five polygons for five different cities (see attached file in the link, it's called bound.shp). I also have a point file "points.csv" with longitude and latitude where for each point I know the proportion of people belonging to group m and group h.

I am trying to calculate the spatial segregation proposed by Reardon and O’Sullivan, “Measures of Spatial Segregation”

There is a package called "seg" which should allow us to do it. I am trying to do it but so far no success.

Here is the link to the example file: LINK. After downloading the "example". This is what I do:

setwd("~/example")
library(seg)
library(sf)
bound <- st_read("bound.shp")
points <- st_read("points.csv", options=c("X_POSSIBLE_NAMES=x","Y_POSSIBLE_NAMES=y"))
#I apply the following formula
seg::spseg(bound, points[ ,c(group_m, group_h)] , smoothing = "kernel", sigma = bandwidth)
Error: 'x' must be a numeric matrix with two columns

Can someone help me solve this issue? Or is there an alternate method which I can use?

Thanks a lot.

Answer 1

first: I do not have experience with the seg-package and it's function.

What I read from your question, is that you want to perform the spseg-function, om the points within each area?

If so, here is a possible apprach:

library(sf)
library(tidyverse)
library(seg)
library(mapview) # for quick viewing only

# read polygons, make valif to avoid probp;ems later on
areas  <- st_read("./temp/example/bound.shp") %>%
  sf::st_make_valid()
# read points and convert to sf object
points <- read.csv("./temp/example/points.csv") %>%
  sf::st_as_sf(coords = c("x", "y"), crs = 4326) %>%
  #spatial join city (use st_intersection())
  sf::st_join(areas)
# what do we have so far??
mapview::mapview(points, zcol = "city")

# get the coordinates back into a data.frame
mydata <- cbind(points, st_coordinates(points))
# drop the geometry, we do not need it anymore
st_geometry(mydata) <- NULL
# looks like...
head(mydata)
#   group_m group_h city        X        Y
# 1    8.02   84.51    2 84.02780 27.31180
# 2    8.02   84.51    2 84.02780 27.31180
# 3    8.02   84.51    2 84.02780 27.31180
# 4    5.01   84.96    2 84.04308 27.27651
# 5    5.01   84.96    2 84.04622 27.27152
# 6    5.01   84.96    2 84.04622 27.27152

# Split to a list by city
L <- split(mydata, mydata$city)

# loop over list and perform sppseg function
final <- lapply(L, function(i) spseg(x = i[, 4:5], data = i[, 1:2]))

# test for the first city
final[[1]]
# Reardon and O'Sullivan's spatial segregation measures
# 
# Dissimilarity (D)     : 0.0063 
# Relative diversity (R): -0.0088 
# Information theory (H): -0.0067 
# Exposure/Isolation (P): 
#   group_m   group_h
# group_m 0.1160976 0.8839024
# group_h 0.1157357 0.8842643
# --
#   The exposure/isolation matrix should be read horizontally.
# Read 'help(spseg)' for more details.

spplot(final[[1]], main = "Equal")

Answer 2

I don't know what exactly spseg function does but when evaluating the spseg function in the seg package documentation;

1. First argument x should be dataframe or object of class Spatial.
2. Second argument data should be matrix or dataframe.

After evaluating the Examples for spseg function, it should have been noted that the data should have the same number of rows as the id number of the Spatial object. In your sample, the id is the cities that have different polygons.

First, let's examine the bound data;

setwd("~/example")

library(seg)
library(sf)

#For the fortify function
library(ggplot2)

bound <- st_read("bound.shp")
bound <- as_Spatial(bound)

class(bound)

"SpatialPolygonsDataFrame"
attr(,"package")
"sp"

tail(fortify(bound))

Regions defined for each Polygons
         long      lat order  hole piece id group
5379 83.99410 27.17326   972 FALSE     1  5   5.1
5380 83.99583 27.17339   973 FALSE     1  5   5.1
5381 83.99705 27.17430   974 FALSE     1  5   5.1
5382 83.99792 27.17552   975 FALSE     1  5   5.1
5383 83.99810 27.17690   976 FALSE     1  5   5.1
5384 83.99812 27.17700   977 FALSE     1  5   5.1

So you have 5 id's in your SpatialPolygonsDataFrame. Now, let's read the point.csv with read.csv function since the data is required to be in matrix format for the spseg function.

points <- read.csv("c://Users/cemozen/Downloads/example/points.csv")
tail(points)

    group_m  group_h        x        y
950    4.95 78.49000 84.32887 26.81203
951    5.30 86.22167 84.27448 26.76932
952    8.68 77.85333 84.33353 26.80942
953    7.75 82.34000 84.35270 26.82850
954    7.75 82.34000 84.35270 26.82850
955    7.75 82.34000 84.35270 26.82850

In the documentation and the example within, it has been strictly stated that; the row number of the points which have two attributes (group_m and group_h in our data), should be equal to the id number (which is the cities). Maybe, you should calculate a value by using the mean for each polygon or any other statistics for each city in your data to be able to get only one value for each polygon.

On the other hand, I just would like to show that the function is working properly after feeding with a matrix that has 5 rows and 2 groups.

sample_spseg <- spseg(bound, as.matrix(points[1:5,c("group_m", "group_h")]))
print(sample_spseg)

    Reardon and O'Sullivan's spatial segregation measures

Dissimilarity (D)     : 0.0209283 
Relative diversity (R): -0.008781 
Information theory (H): -0.0066197 
Exposure/Isolation (P): 
           group_m   group_h
group_m 0.07577679 0.9242232
group_h 0.07516285 0.9248372
--
The exposure/isolation matrix should be read horizontally.
Read 'help(spseg)' for more details.