Agriculture Reference
In-Depth Information
Point locations may correspond to all possible events (mapped point pattern) or
to subsets (sampled point pattern). For instance, the points could represent trees,
animal nests, earthquake epicenters, domiciles of new cases of influenza, and so
on. The points may have extra information attached to them, called marks. In this
case, we refer to the pattern as a marked spatial point pattern; otherwise it is defined
as unmarked. The marked variable could be categorical (e.g., type of agricultural
crop) or quantitative (e.g., tree diameter). Additionally, the mark may be multivar-
iate, or even more complicated.
1.4.2 Spatial Dependence
Dependence is a distinctive characteristic of spatial data. Spatial dependence
follows directly from Tobler
s(
1970
) First Law of Geography, according to which
“everything is related to everything else, but near things are more related than distant
things”.
'
Goodchild (
1992
) also defines spatial dependence as
“the propensity for nearby locations to influence each other and to possess similar
attributes”.
As a consequence, a variable will tend to have similar values in adjacent areas,
leading to spatial clusters. For example, an area cultivated with wheat may be close
to other wheat-cultivated zones.
The spatial clustered map implies that many samples of geographical data will
no longer satisfy the usual statistical assumption of independent observations.
Unfortunately, traditional statistical techniques assume that observations are inde-
pendent. As a consequence, standard estimation procedures used in geographical
studies can lead to biases and inefficient estimates. Therefore, dependence is a
phenomenon that should be properly taken into account when dealing with spatially
distributed data.
Spatial dependence or autocorrelation may also be referred to as the relationship
among values of a variable that is a result of the geographical arrangement of their
locations. It measures the similarity of objects within an area, the degree to which a
spatial phenomenon is correlated to itself in space, and the level of interdependence
between the variables (Cliff and Ord
1981
; Cressie
1993
; Haining
2003
). The
procedures used to analyze patterns of spatial autocorrelation depend on the type
of data. In this section, we will describe some well-known measures of spatial
autocorrelation, which are generated for lattice data. In particular, we describe
some statistics applicable when y is a continuous variable.
In this case, the most popular statistic for investigating spatial autocorrelation is
Global Moran
s
I
index
'
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