The Stewart potentials of population is a spatial interaction modeling approach which aims to compute indicators based on stock values weighted by distance. These indicators have two main interests:
At the European scale, this functional semantic simplification may help to show a smoothed context-aware picture of the localized socio-economic activities.
In this vignette, we show a use case of these “potentials” on the regional GDP per capita at the European scale with three maps:
Regional Map of the Potential GDP per Capita
We compute the potentials of GDP for each spatial unit. The computed value takes into account the spatial distribution of the stock variable and return a sum weighted by distance, according a specific spatial interaction and fully customizable function.
# Create a distance matrix between units
mat <- CreateDistMatrix(knownpts = nuts3.spdf,
unknownpts = nuts3.spdf)
# Merge the data frame and the SpatialPolygonsDataFrame
nuts3.spdf@data <- nuts3.df[match(nuts3.spdf$id, nuts3.df$id),]
# Compute the potentials of population per units
# function = exponential, beta = 2, span = 75 km
poppot <- stewart(knownpts = nuts3.spdf,
unknownpts = nuts3.spdf,
matdist = mat,
varname = "pop2008",
typefct = "exponential",
beta = 2,
span = 75000,
returnclass = "sf")
## Warning: stewart(), rasterStewart(), plotStewart(), quickStewart(), isopoly(),
## mcStewart() and smoothy() are deprecated. Use 'potential' package for all
## potential-related functions.
## Warning: stewart(), rasterStewart(), plotStewart(), quickStewart(), isopoly(),
## mcStewart() and smoothy() are deprecated. Use 'potential' package for all
## potential-related functions.
# Create a data frame of potential GDP per capita
pot <- data.frame(id = nuts3.df$id,
gdpcap = gdppot$OUTPUT * 1000000 / poppot$OUTPUT,
stringsAsFactors = FALSE)
# Discretize the variable
bv2 <- c(min(pot$gdpcap), bv[2:8], max(pot$gdpcap))
# Draw the map
par <- par(mar = c(0,0,1.2,0))
# Draw the basemap
plot(nuts0.spdf, add = F, border = NA, bg = "#cdd2d4")
plot(world.spdf, col = "#f5f5f3ff", border = "#a9b3b4ff", add = TRUE)
# Map the regional potential of GDP per capita
choroLayer(spdf = nuts3.spdf, df = pot,
var = "gdpcap",
legend.pos = "topright",
breaks = bv2, col = pal,
border = NA,
legend.title.txt = "Potential\nGDP per capita",
legend.values.rnd = -2, add = TRUE)
plot(nuts0.spdf, add=T, lwd = 0.5, border = "grey30")
plot(world.spdf, col = NA, border = "#7DA9B8", add=T)
# Set a text to explicit the function parameters
text(x = 6271272, y = 3743765,
labels = "Distance function:\n- type = exponential\n- beta = 2\n- span = 75 km",
cex = 0.8, adj = 0, font = 3)
# Set a layout
layoutLayer(title = "Wealth Inequality in Europe",
sources = "Basemap: UMS RIATE, 2015 - Data: Eurostat, 2008",
author = "T. Giraud, 2015")
This map gives a smoothed picture of the spatial patterns of wealth in Europe while keeping the original spatial units as interpretive framework. Hence, the map reader can still rely on a known territorial division to develop its analyses.
Smoothed Map of the GDP per Capita
In this case, the potential GDP per capita is computed on a regular grid.
## Warning: stewart(), rasterStewart(), plotStewart(), quickStewart(), isopoly(),
## mcStewart() and smoothy() are deprecated. Use 'potential' package for all
## potential-related functions.
## Warning: stewart(), rasterStewart(), plotStewart(), quickStewart(), isopoly(),
## mcStewart() and smoothy() are deprecated. Use 'potential' package for all
## potential-related functions.
# Create the ratio variable
poppot$OUTPUT2 <- gdppot$OUTPUT * 1e6 / poppot$OUTPUT
# Create an isopleth layer
pot <- isopoly(x = poppot, var = "OUTPUT2",
breaks = bv,
mask = nuts0.spdf,
returnclass = "sf")
# Get breaks values
bv3 <- sort(c(unique(pot$min), max(pot$max)), decreasing = FALSE)
# Draw the map
par <- par(mar = c(0,0,1.2,0))
# Draw the basemap
plot(nuts0.spdf, add = F, border = NA, bg = "#cdd2d4")
plot(world.spdf, col = "#f5f5f3ff", border = "#a9b3b4ff", add = TRUE)
# Map the potential GDP per Capita
choroLayer(x = pot, var = "center",
legend.pos = "topright",
breaks = bv3, col = pal, add=T,
border = NA, lwd = 0.2,
legend.title.txt = "Potential\nGDP per capita",
legend.values.rnd = -2)
plot(nuts0.spdf, add=T, lwd = 0.5, border = "grey30")
plot(world.spdf, col = NA, border = "#7DA9B8", add=T)
# Set a text to explicit the function parameters
text(x = 6271272, y = 3743765,
labels = "Distance function:\n- type = exponential\n- beta = 2\n- span = 75 km",
cex = 0.8, adj = 0, font = 3)
# Set a layout
layoutLayer(title = "Wealth Inequality in Europe",
sources = "Basemap: UMS RIATE, 2015 - Data: Eurostat, 2008",
author = "T. Giraud, 2015")
Unlike the previous maps, this one doesn’t keep the initial territorial division to give a smoothed picture of the spatial patterns of wealth in Europe. The result is easy to read and can be considered as a bypassing of the Modifiable Areal Unit Problem (MAUP).
