Question

New to R, and I have a long-ish question:

I have a shapefile/map, and I’m aiming to calculate a certain index for every polygon in that map, based on attributes of that polygon and each polygon that neighbors it.

I have an adjacency matrix — which I think is the same as a “1st-order queen contiguity weights matrix”, although I’m not sure — that describes which polygons border which other polygons, e.g.,

POLYID A B C D E  
    A  0 0 1 0 1  
    B  0 0 1 0 0    
    C  1 1 0 1 0     
    D  0 0 1 0 1     
    E  1 0 0 1 0

The above indicates, for instance, that polygons ‘C’ and ‘E’ adjoin polygon ‘A’; polygon ‘B’ adjoins only polygon ‘C’, etc.

The attribute table I have has one polygon per row:

POLYID TOT L10K 10_15K 15_20K ...  
     A 500   24     30     77 ...

---

Where TOT, L10K, etc. are the variables I use to calculate an index.

There are 525 polygons/rows in my data, so I’d like to use the adjacency matrix to determine which rows’ attributes to incorporate into the calculation of the index of interest. For now, I can calculate the index when I subset the rows that correspond to one ‘bundle’ of neighboring polygons, and then use a loop (if it’s of interest, I’m calculating the Centile Gap Index, a measure of local income segregation). E.g., subsetting the ‘neighborhood’ of the Detroit City Schools:

Detroit <- UNSD00[c(142,150,164,221,226,236,295,327,157,177,178,364,233,373,418,424,449,451,487),]

Then record the marginal column proportions and a running total:

catprops <- vector()
for(i in 4:19)
{
  catprops[(i-3)]<-sum(Detroit[,i])/sum(Detroit[,3])
}
catprops <- as.data.frame(catprops)
catprops[,2]<-cumsum(catprops[,1])

Columns 4:19 are the necessary ones in the attribute table.

Then I use the following code to calculate the index — note that the loop has “i in 1:19” because the Detroit subset has 19 polygons.

cgidistsum <- 0
for(i in 1:19)
{  
   pranks <- vector()
   for(j in 4:19)
    {
      if (Detroit[i,j]==0)
        pranks <- append(pranks,0)
      else if (j == 4)
      pranks <- append(pranks,seq(0,catprops[1,2],by=catprops[1,2]/Detroit[i,j]))
      else 
        pranks <- append(pranks,seq(catprops[j-4,2],catprops[j-3,2],by=catprops[j-3,1]/Detroit[i,j]))
    }
  distpranks <- vector()
  distpranks<-abs(pranks-median(pranks))
  cgidistsum <- cgidistsum + sum(distpranks)
  }
cgi <- (.25-(cgidistsum/sum(Detroit[,3])))/.25

My apologies if I’ve provided more information than is necessary. I would really like to exploit the adjacency matrix in order to calculate the CGI for each ‘bundle’ of these rows.

If you happen to know how I could started with this, that would be great.

and my apologies for any novice mistakes, I’m new to R!

EDIT:

I’ve since figured out how to approach this, but for the sake of problem clarity and in response to one question asked in the comments, let me say that a polygon’s neighborhood is the union of itself and every polygon it is adjacent to. In the example I gave above, for polygon ‘A’, that would be the union of polygon’s ‘A’, ‘C’, and ‘E’

Answer 1

This is what I ended up doing, although it doesn’t appear to be as elegant as @agstudy ‘s:

for(k in 1:nrow(adjacency00))
 {
  positions <- grep(1,adjacency00[k,])-1
  nghbrd <- UNSD00[c(positions,k),]

etc., thereby creating a frame of adjacent polygons on which to conduct subsequent calculations