Exploring spatial point patterns - Spatial Data Analysis: An Introduction for GIS Users - page 87

Figure 7.2 Dispersed point pattern (PP2).
if the points are dispersed, this suggests that events are likely to occur as far away as
possible from other events. h is chapter introduces a variety of ways for assessing and
characterizing spatial point patterns. A set of points that also have values attached to
them is called a marked point pattern, but the concern in this chapter is with points
that have no attached attribute data. While much of the early development of
approaches was in an ecological context, applications areas are now extensive. Typical
applications of point pattern analysis include the exploration of clustering in disease
events (an interesting study by Openshaw et al. (1993) notes that cases of some forms
of cancer tend to cluster while others do not) and clustering in particular species of
tree (relevant references appear at the end of the chapter).
Point pattern analysis can be divided into two sets of approaches: those that deal
with i rst-order ef ects and those that deal with second-order ef ects. First-order ef ects
are referred to in terms of intensity—that is, the mean number of events per unit area
at a given location. Second-order ef ects, or spatial dependence, refer to the relation-
ship between paired events in the study region (Bailey and Gatrell, 1995). So, the i rst
refers to the number of events in an area while the second refers to structure in the
point pattern. As an example of the latter, if the number of events in areas separated by
a i xed distance is consistently similar for all locations and similarity in the number of
events in two areas decreases as distance between these locations increases then there
is spatial dependence in the point pattern at a variety of scales. First-order ef ects are
considered in Section 7.3, while second-order ef ects are the subject of Section 7.4.
First- and second-order ef ects are a function of spatial scale. In the former case the
mean intensity may change smoothly from place to place over a large area. In the latter
case, features with a i ner scale are the concern (Bailey and Gatrell, 1995). In practical
terms, it is ot en dii cult to separate i rst- and second-order ef ects (O'Sullivan and
Unwin, 2002). h is chapter does not delve further into the particular problem of dis-
tinguishing between the two, but simply presents a set of tools for the analysis of point
patterns and provides some pointers for their use.
Before proceeding, it is worth making one comment of note. If, for example, a point
pattern represents disease events, there may be clusters of events in some places sim-
ply because there are more people in an area, for example an urban area. If we want
to explore spatial clustering, it is necessary to account for the total population, ot en