Exploring spatial patterning in data values - Spatial Data Analysis: An Introduction for GIS Users - page 107

are similar (positive spatial autocorrelation specii cally). A key tool for the analysis
of spatial autocorrelation, the Moran's I coei cient, was introduced in Section 4.8. A
locally derived version of Moran's I is detailed in Section 8.4.1. h ere are various other
spatial autocorrelation measures that are applied widely. h ese include Geary's C ,
amongst others (see Bailey and Gatrell, 1995). Measures like Moran's I and Geary's C
are conventionally used to explore spatial autocorrelation with neighbours of observa-
tions—that is, they enable assessment of the degree to which values tend to be similar
to neighbouring values. It is also possible to explore how spatial autocorrelation varies
with the distance separating observations (e.g. we can use a geographical weighting
approach). One very useful tool for the exploration of spatial autocorrelation is the
Moran scatter plot. h e Moran scatter plot relates individual values to weighted aver-
ages of neighbouring values and the slope of a regression line i tted to the points in the
scatter plot gives global Moran's I . An application of the Moran scatter plot is detailed
in the case study in Section 8.7.1.

Local statistics

8.3

Section 4.6 introduced the idea of moving windows, whereby any statistic could be
computed locally using a subset of the data. Section 4.7 extended this idea through the
concept of geographical weights and inverse distance weighted prediction was illus-
trated. Another geographically weighted approach was demonstrated in Section 7.3.2,
which introduced kernel estimation. In the following section, the idea of locally
derived statistics is explored further, with a particular focus on local measures of spatial
autocorrelation. Section 8.5 outlines some approaches to exploring local variations in
the relationships between dif erent variables.

Local univariate measures

8.4

Standard univariate statistical measures are ot en computed within a moving window,
as demonstrated previously in Section 4.6. Such measures allow exploration of the
degree and nature of variation in summary statistics across the region of interest. For
example, a local version of the standard deviation enables assessment of the degree of
variability in the property of interest from place to place. Knowledge of such variation
is ot en crucial in interpreting spatial data. Section 10.4 explores this issue further with
a focus on raster grid data.
Geographical weighting schemes are widely used in the estimation of local statis-
tics. h e quartic kernel, illustrated in the previous chapter, includes bandwidth, t ,
which determines the degree of weighting by distance. For a small bandwidth, loca-
tions close to the centre of the window will receive most of the weight. In contrast, for
a large bandwidth, more distant locations will also receive quite large weights. A large