Geoscience Reference
In-Depth Information
The point of interest of these three examples is to simultaneously illustrate three
different types of objective and three adapted methods: in the first example, the
objective is to
describe
the types of evolution; in the second, the concern is to
build
the types of evolution and in the third, it is about
reproducing
these evolutions. In all
three examples, time is envisaged as a sequence of states (“time unfolded”). In
contrast, space does not play the same role: it is a “support” in the first example and
“active” in the two following, although in two different ways.
3.3.1.
Constructing, describing and categorizing trajectories of evolution
The first two examples make up a generic case where the challenge consists of
identifying
a posteriori
the types of changes: they are based on methods of
multidimensional data analysis that are appropriate to account for the diversity of the
developments of a set of entities, namely the clustering analysis and correspondence
analysis. The statistical individuals are clearly identified and described by
the measure of the same phenomenon at several dates. In this example, the concern
is about cities, described first by their populations at different dates (univariate
case), and then by the evolution over time of the structure of the active population in
terms of economic activity categories (multivariate case).
3.3.1.1.
Evolution of the system of European cities between 1600 and 1990
To analyze the evolution of a system of cities described by a single variable, the
methods of clustering are appropriate: in the associated statistical table, a row
represents the trajectory of the “city-entity” relative to the targeted variable. The
example that we are proposing concerns 450 European cities described by their
population at 9 dates (1600, 1700, 1800, 1850, 1950, 1960, 1970, 1980 and 1990)
[BRE 99]. It concerns an urban system with a strong growth: between 1660 and
1990, the population of the cities has been multiplied by 30 (it increased from
approximately 10 million in 1600 to 300 million in 1990). The purpose of this
longitudinal analysis is to follow up the relative position of each city in the urban
system, and to describe how the system growth is distributed between the cities. The
method used is a
hierarchical ascending cluster analysis
using the chi2 distance.
The latter is appropriate for the analysis of contingency tables, because it ensures the
distributional equivalence, that is to say that the similarities between the entities
will be calculated from the distribution profiles, the weight associated with each
category being inversely proportional to its weight in the statistical population
[BEN 80, SAN 89, LEB 06]. In this example, this means that the similarities
between the cities' trajectories will be calculated from the evolution profiles, and
that these are approached relative to the evolution of the urban system taken as a
whole.
