Geoscience Reference
In-Depth Information
use a spatial autoregressive model, while the estimation of total household share
uses a spatial error model.
The spatial autoregressive model used in the estimation of gay and lesbian
household tract share includes a spatially lagged dependent variable as an addi-
tional covariate:
Ws
n
i
,
j
,
t
þ
1
þ ʵ
i
s
i, j, t
þ
1
¼ α þ ʲ
s
i, k, t
þ ʳ
X
i, t
þ
Z
i
þ ˁ
ð
:
Þ
19
2
where W is a row-standardized matrix which expresses the neighbor relationship
between any two tracts
i
and
n
, and
measures the strength of the association
between household share in tract
i
and its neighbors. Spatial autoregressive models
are commonly used when the outcome of interest exhibits a diffusion or contagion
process, such as households being attracted to those areas with similar households.
The model of total household tract share is estimated using a spatial error, or
“nuisance”, model, in which the error terms of neighboring tracts are spatially
interacted. The spatial error model is expressed as:
ˁ
ʵ
n
i
þ ʼ
i
s
i, j, t
þ
1
¼ α þ ʲ
s
i, k, t
þ ʳ
X
i, t
þ
Z
i
þ ʵ
i
, where
ʵ
i
¼ ʻ
W
ð
19
:
3
Þ
where W is again a row-standardized matrix which expresses the neighbor relation-
ship between any two tracts
i
and
n
, and
measures the intensity of the relationship
between the errors terms in tract
i
and
n
. The spatial error model indicates that the
source of the spatial dependence is non-substantive, possibly the result of the
clustering of unmeasured or unobserved neighborhood features.
In all of the models estimated here, the neighbor weight matrix used is a queen
contiguity matrix, in which tracts which share any common point are considered
neighbors.
14
We estimate both the spatial autoregressive and the spatial error
models via maximum likelihood. All analyses are carried out using the
spdep
package in R.
Table
19.3
shows the results of these estimations. The table shows regressions of
the census tract's 2009 share of the central city's gay population, by gender, on the
characteristics of the tract for large central cities in the nation. There are also
separate regional estimates for these cities, as grouped into four regions.
15
In
order to assess how the effects of various neighborhood characteristics differ for
ʻ
14
In this case, the W matrix is block diagonal, with the main diagonal blocks equal to the queen
contiguity matrix within each city. The off-diagonal blocks are composed of zero matrices.
15
Cities are assigned to regions according to Census Bureau definitions, except for Baltimore and
Washington (in the South Census region, but assigned here to the Northeast); the cities in each
region are displayed in Tables
19.1
and
19.2
.
