Geography Reference
In-Depth Information
related to everything else, but near things are more related than distant things
”.
Positive spatial autocorrelation refers to patterns where nearby or neighbouring
values are more alike; while negative spatial autocorrelation refers to patterns
where nearby or neighbouring values are dissimilar. One can distinguish two
main types of spatial autocorrelation, which are global and local. While global
clustering methods are used to assess whether clustering is apparent throughout the
study region, local methods of cluster detection define the locations and extent of
clusters (Pfeiffer et al.
2008
). The null hypothesis for global clustering methods is
simply that no clustering exists (i.e. random spatial dispersion
CSR). These
techniques are collectively denoted as Exploratory Spatial Data Analysis (ESDA)
and Local Indicators of Spatial Association (LISA), which are widespread in
geosciences and GIS software.
Probably the most frequently used method for both global and local analyses of
spatial autocorrelation is Moran
s I statistics (together with e.g. Getis-Ord G and
'
Gearys
s C statistics). Moran
s I coefficient of autocorrelation is similar to
'
'
Pearson
s correlation coefficient, and quantifies the similarity of an outcome var-
iable among areas that are defined as spatially related (Moran
1950
). Moran
'
sI
'
statistic is given by:
n
X
i
X
j
W
ij
Z
i
Z
Z
Z
j
X
k
Z
k
I
¼
ð
4
Þ
X
i
X
j
W
ij
Z
2
where
Z
i
could be the residuals
(O
i
E
i
)
or standardized mortality or morbidity
ratio (SMR) of an area, and
W
ij
is a measure of the closeness of areas
i
and
j
.A
weights matrix is used to define the spatial relationships so that regions close in
space are given greater weight when calculating the statistic than those that are
distant (Moran
1950
). Local Moran
s I is used for the mapping of either similar
(cluster) or dissimilar (outlier) disease frequency values around a given observation
in the space. A comprehensive explanation of the hypothesis and theory is provided
by Anselin (
1995
) and Scott and Janikas (
2010
).
The problem with variance instability for rates or proportions, which served as
the motivation for applying smoothing techniques to maps, may also affect the
inference for Moran
'
s I test for spatial autocorrelation (Anselin
2003
). The imple-
mentation of the adjustment procedure of Assuncao and Reis (
1999
), which uses a
variable transformation based on the Empirical Bayes principle, may be one of the
solutions. This yields a new variable that has been adjusted for the potentially
biasing effects of variance instability due to differences in the size of the underlying
population at risk (Anselin
2003
).
'
