R meets ArcGIS

What I find most interesting is that the uniformally distribution of points, which is supposed to reflect “on the ground” homogeneity (or close to it), is that it actually maps out spatial patterns particularly at course resolution. This variation among the different scales of analysis for the uniform distribution (green maps) is an example of modifiable areal unit problem (MAUP). The MAUP occurs when individual point data is aggregated into set areas. In this example the set areas change with the resolution. We can see that in the 3x3, 5x5 and even the 7x7 images there seems to be a higher concentration of points on the left of the map. When the resolution of area is increased to 10x10, that relationship goes away and we start to see the uniform distribution that was meant all along.

For the normal distribution map/plot, the lower resolutions seem to show the concentration of points in the center (or up and right of center) but points still seem to be distributed throughout the entire frame. As the resolution increases, the actual concentration of points becomes smaller.

The MAUP is closely related to the ecological fallacy in that as scales of analysis change, so do the conclusions that we might draw from them. If we think of the example normal distribution as locations of saplings produced from a single tree, we would expect to see a concentration of trees around the original. As stated above, the coarser resolutions show a wider distribution of saplings. However the apple, indeed, does not fall far from the tree, and the finer resolutions how the clustering better.

 

R Code for creating data sets

setwd("/Users/Erin/R_work/ArcGIS")

#generate 2 sets of 250 numbers between 0 and 1000 from a uniform distribution;
x=runif(250,0,1000)
y=runif(250,0,1000)
#puts the two sets together and saves as a .csv file
uniform250 = round(cbind(x,y),0)
write.csv(uniform250,file="uniform250.csv")
 
#generates 2 sets of 250 numbers from a normal distribution with a mean of 100 and variance of 100
x1=rnorm(250,100,100)
y1=rnorm(250,100,100)
#puts the two sets together and saves as a .csv file
normal250 = round(cbind(x1,y1),0)
write.csv(normal250,file="normal250.csv")

##creates a 2 row, 3 column image that contains the scatter plots of both the normal and uniform distribution of the 2 sets of 250 numbers. Then plots the histogram of all created number sets.
par(mfrow=c(2,3))
for(i in 1:6){
plot(x,y,xlim=c(0,999),ylim=c(0,999))
hist(x)
hist(y)
plot(x1,y1,xlim=c(-199,299),ylim=c(-199,299))
hist(x1)

hist(y1)}