Exploring spatial point patterns - Spatial Data Analysis: An Introduction for GIS Users - page 89

Figure 7.4 PP2: mean centre (large point) and standard distance (circle).

variable across the study region (as noted above, it is a clustered point pattern) while
the intensity of points in Figure 7.2 does not vary markedly from place to place, it is
a fairly regular point pattern. h e rest of this chapter will focus on methods for explor-
ing the degree to which a point pattern is clustered either globally (i.e. across the whole
study area) or locally (i.e. in regions within the whole study area).

Exploring spatial variations in point intensity

7.3

A key concern in point pattern analysis is exploration of spatial variation in point pat-
tern intensity. h e following sections explore some ways of mapping event intensity.
Such methods are used for exploring i rst-order ef ects (as dei ned in Section 7.1). h e
i rst focus is on quadrat analysis and the second focus is on a more sophisticated means
of assessing spatial variation in event intensity, kernel estimation.

7.3.1 Quadrats

A common way of exploring spatial patterning in the number of events is quadrat
analysis. At its simplest level, this entails superimposing a regular grid over the point
pattern and counting how many points fall within each grid square. h is is illustrated
in Figures 7.5 and 7.6 for the point patterns shown earlier. Clearly, varying quadrat
size will have an impact on analyses, as will aggregation at dif erent levels in other
applications (recall that Section 4.9 dealt with such ef ects). In addition, the origin of
the quadrat grid (its smallest x and y coordinates) will also inl uence the results.
In Figure 7.5 (PP1), there are several counts that are greater than 2. In contrast, in
Figure 7.6 (PP2), there are no counts greater than 2. h ese values rel ect the clustering
and regularity, respectively, in the two point patterns. h ere is a range of ways of assess-
ing the degree of clustering or regularity. One possible approach is to use a measure of
spatial autocorrelation (such as Moran's I , as dei ned in Section 4.8) to assess the degree
of spatial dependence in quadrat counts. For rook's case contiguity (see Section 4.8),
I for the quadrat counts in Figure 7.5 (with zeros placed in the empty cells) was 0.0017