Geoscience Reference
In-Depth Information
3.1.2.
Different ways to take time and space into account to analyze spatio-
temporal processes
Statistical analyses relate to a data table, describing a statistical population
(rows) according to a certain number of characteristics (columns). The population is
composed of homogeneous statistical individuals from a semantic point of view. The
notion of a statistical individual corresponds to the concept of an object developed in
Chapter 1. It is the basic constituent of the studied set and it is in this sense regarded
as indivisible: the students of an academy, the shops of a city, the plots of a forest
but also the cities of more than 10,000 inhabitants of a country, etc. In its most
generic form, a statistical table describes a set of individuals by a certain number of
variables (also called characteristics or attributes). When it comes to describeing a
spatial phenomenon in time, it is necessary to identify these two dimensions, the
spatial and the temporal ones, in the data. Further in the text, we give detail about
the different manners to formalize time and space in this type of table.
3.1.2.1.
From the statistical table to the geographical information matrix: “support”
space and “active” space
With the explosion of observation means and the easy access to individual data,
the questions relating to spatial configurations and processes linked to human
activities rely on data constructed from observations of increasingly finer spatial
resolution, going as far as to the located person. Further in the chapter, the presented
methods are more specifically applied to tables of geographical information.
Berry's matrix of geographical information is a particular case of a table of data
where the statistical individuals are places (or geolocalized object). It is initially by
this specific status of individuals that space intervenes in the analysis. The spatial
dimension is, however, not explicit: everything happens as if the places were a
statistical population without structure while what is happening in a given place is
precisely not independent of what is happening in neighboring places
3
[TOB 70]. A
simple regression between the population and the average income of the
municipalities of a region, for example, does not give any
a priori
role to space. The
spatial structure may be identified
a posteriori
, by mapping for example the
residuals of such a regression. In this case, we will qualify the space as “support” .
Only the issues related to the spatial variability (heterogeneity of a row) of the
phenomena being studied can be processed and not those related to the spatial
ordering of the spatial units involved. Figure 3.2 illustrates the difference between
statistical heterogeneity and spatial heterogeneity.
3 According to Tobler, “Everything is related to everything else, but near things are more
related than distant things”.
