Geography Reference
In-Depth Information
11
14
18
10
5
12
4
16
13
20
2
1
7
9
17
3
6
19
8
15
0
10
20 km
Figure 8.2
Locations of observations listed in Table 8.1.
With reference to Table 8.1, note how the weights for large distances are propor-
tionately smaller when the bandwidth is smaller—that is, a small bandwidth gives
most inl uence to close-by observations whereas with a large bandwidth more distant
observations have proportionately larger weights. h e weighted means (or other sta-
tistics) could be calculated anywhere—at the location of an observation or anywhere
else (as for the inverse distance weighting example in Section 4.7). Fotheringham
et al.
(2002) discuss a range of geographically weighted statistics.
h e spatial scale of a process can be explored using geographical weights. For exam-
ple, by assessing the results obtained using a variety of dif erent kernel bandwidths,
it is possible to explore how much these results vary and, therefore, learn something
about dominant scales of spatial variation. If the geographically weighted mean aver-
age changes a great deal as the bandwidth is increased for small bandwidths, but then
stabilizes as the bandwidth is increased to some critical value, then we can say (with
some caveats) that most variation in the property of concern is at some scale i ner than
that represented by the bandwidth distance at which results stabilize.
h e following section shows how spatial autocorrelation measures can be computed
locally.
8.4.1
Local spatial autocorrelation
In most published applications, spatial autocorrelation is measured over the entire
study area, as was detailed in Section 4.8. However, such an approach masks any spa-
tial variation in the spatial structure of the variable of interest. For this reason, various
local measures of spatial autocorrelation have been developed. One of the most widely
used is a local variant of Moran's
I
presented by Anselin (1995). It is given by:
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