seg (version 0.4-1)

seg: Index of Dissimilarity

Description

Calculates the index of dissimilarity proposed by Duncan and Duncan (1955). If nb is given, the index is adjusted to reflect the spatial distribution of population.

Usage

seg(data, nb)

Arguments

data

a numeric matrix or data frame with two columns that represent mutually exclusive population groups (e.g., Asians and non-Asians). If more than two columns are given, only the first two will be used for computing the index.

nb

an optional matrix object describing the intensity of interaction between geographic units.

Value

• A single numeric value between 0 and 1, indicating the degree of segregation; 0 for no segregation, and 1 for complete segregation.

Details

nb must be a square matrix (i.e., one that has the same number of rows and columns) but does not have to be symmetric. If nb is not specified, seg calculates the traditional index of dissimilarity proposed by Duncan and Duncan (1955). If nb is a rook-based contiguity matrix standardised by the total number of neighbours, the index is adjusted as described in Morrill (1991). See the example code below and nb2mat in spdep for more information regarding how to construct such a matrix. For Wong's D(w) and D(s), see https://sites.google.com/site/hongseongyun/seg. Note that the sum of all elements in nb should equal one.

References

Duncan, O. D., & Duncan, B. (1955). A methodological analysis of segregation indexes. American Sociological Review, 20, 210-217. Morrill, R. L. (1991). On the measure of geographic segregation. Geography Research Forum, 11, 25-36. Wong, D. W. S. (1993). Spatial indices of segregation. Urban Studies, 30, 559-572.

See Also

spseg, nb2mat

Examples

if (require(spdep)) { # package 'spdep' is required

  # uses the idealised landscapes in 'segdata'
  data(segdata)
  grd <- GridTopology(cellcentre.offset=c(0.5,0.5),
                      cellsize=c(1,1), cells.dim=c(10,10))
  grd.sp <- as.SpatialPolygons.GridTopology(grd)
  grd.nb <- nb2mat(poly2nb(grd.sp, queen = FALSE), style = "B")
  grd.nb <- grd.nb / sum(grd.nb)

  d <- numeric(); m <- numeric()
  for (i in 1:8) {
    idx <- 2 * i
    d <- append(d, seg(segdata[,(idx-1):idx]))
    m <- append(m, seg(segdata[,(idx-1):idx], grd.nb))
    full <- segdata[,(idx-1)] == 100
    half <- segdata[,(idx-1)] == 50
    plot(grd.sp)
    plot(grd.sp[full,], col = "Black", add = TRUE)
    if (any(half))
      plot(grd.sp[half,], col = "Grey", add = TRUE)
    text(5, 11.5, labels = paste("D = ", round(d[i], 2), 
                                 ", D(adj) = ", round(m[i], 2), sep = ""))
  }
}