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proportion measure easily compares groups with very different sizes, allowing
standardized comparisons across cities, time periods, and groups. Also, the city
proportion measure “removes” or “standardizes” for swings in the population of a
group due to secular economic changes in things such as revealing sexual orien-
tation or migration within a city.
19.1.2 Are Gays Spatially Concentrated in Large U.S. Cities?
Table
19.1
reports the Duncan Index of Dissimilarity
5
for lesbian households and
for gay male households, relative to all households, for large U.S. cities by region in
2000 and 2010. The Duncan index is a commonly used measure of spatial segre-
gation that indicates whether there are neighborhoods (census tracts) within cities
that include relatively more gay households than other neighborhoods. The indices
show that gay men and lesbians are far less segregated than African Americans.
6
As
suggested by Castells (
1983
), lesbians are less segregated than gay men in most
cities in both years, and lesbians are becoming less segregated, as indicated by
declining segregation indices between 2000 and 2010 for all but two cities. The
Duncan Index of Dissimilarity measures one dimension of segregation, specifically
the “evenness” of the distribution of gay households within neighborhoods in the
central city. It does not, however, account for the relative spatial position, or
clustering, of the neighborhoods or census tracts with similar shares of gay
households. In cities with high values of the Index of Dissimilarity, gay households
are concentrated within specific tracts, but these highly concentrated tracts may be
distributed across the city or they may be in the same sections of the city. The global
Moran's I can be used to assess whether tracts with large (or small) shares of gay
households are also clustered in space.
7
5
The segregation index, the Duncan Index of Dissimilarity, is calculated:
2
X
iP
i
1
=
j
nP
i
j
where P
i
is the proportion of the city's gay male (lesbian) households in census tract i and nP
i
is the
proportion of the city's non-gay households in census tract i.
The index takes on values between 0 and 1, where 0 indicates no segregation (partnerships of
different sexual compositions are sorted identically across neighborhoods) and 1 indicates perfect
segregation (gay partnership households and heterosexual partnership households live in
completely different neighborhoods).
6
Madden (
2014
) reports African American segregation indices of 0.46 for 2000 and 0.44 for 2009
for these same Western metro areas, 0.55 and 0.51 respectively for the South, 0.71 and 0.67 for the
Midwest, 0.65 and 0.63 for the Northeast.
7
Moran's I is calculated as:
X
i
X
j
w
ij
XiX
!
ð
Þ
ð
Þ
Xj
X
X
i
X
j
w
ij
X
i
N
EðÞ ¼
1
N
1
I
¼
2
ð
Þ
XiX
where
X
i
is the proportion of tract
i
0
s households that are of a given type,
X
j
is the proportion of
tract
j
(
i)
0
s households that are of this same type,
X
is the mean proportion of this household type
6¼
