The evenness of groups across areal units (Massey and Denton 1988),
from a table of counts with one row per unit and one column per group:
Duncan's dissimilarity D = sum |x_ik / X_k - x_il / X_l| / 2 between
each pair of groups (the share of either group that would have to move
for the two to be spread alike), and for each group against the rest
the segregation index IS, Theil's entropy index H, Atkinson's index
with shape delta and the Gini index. With weights w between the
units, Morrill's (1991) adjusted D subtracts the weighted mean
absolute difference of the pair's shares between neighbouring units, so
that segregation across a boundary counts less than segregation within.
Units with no one in them are left out. That D lies between 0 and 1 is
proved in Lean: see proof("dissix").
Arguments
- x
The counts: a matrix or data frame of numbers from 0, units by groups (named columns), every group with a positive total.
- delta
Atkinson's shape, above 0 and below 1.
- w
NULL, or weights between the units (asgmoran()takes them), with a positive total.
Value
A list of class dissix: d, the matrix of D; grp, a data
frame of group, is, h, atk and gini; dm, NULL or the
matrix of Morrill's D; and delta.
References
Duncan, O. D. and Duncan, B. (1955). A methodological analysis of segregation indexes. American Sociological Review, 20(2), 210-217. doi:10.2307/2088328
Massey, D. S. and Denton, N. A. (1988). The dimensions of residential segregation. Social Forces, 67(2), 281-315. doi:10.2307/2579183
Morrill, R. L. (1991). On the measure of geographic segregation. Geography Research Forum, 11, 25-36. doi:10.64166/p1b4ca43
Examples
x <- cbind(a = c(90, 80, 10, 5, 50), b = c(10, 20, 85, 95, 50))
dissix(x)
#> dissix: dissimilarity between groups
#> a b
#> a 0.0000000 0.6284779
#> b 0.6284779 0.0000000
#> group is h atk gini
#> a 0.6284779 0.4052672 0.5217079 0.7680033
#> b 0.6284779 0.4052672 0.5217079 0.7680033
dissix(x, w = spwt(nb = list(2, c(1, 3), c(2, 4), c(3, 5), 4),
type = "contig"))$dm
#> a b
#> a 0.0000000 0.3134779
#> b 0.3134779 0.0000000