Geoscience Reference
In-Depth Information
To apply a classic multivariate analysis, it is necessary to refer to a two-
dimensional statistical table. The choice must then be made to project time (dates)
on the variables or on the individuals. This choice has implications. In the first case,
the profile of an statistical individual, here a city, will be the distribution of its active
population counted at each of the four dates in the 26 economic activity categories
(4 × 26 columns). The “average profile” corresponds to such a distribution on the
whole set of cities. The choice may be to project, on the contrary, time on cities. In
this case, each city will appear as many times as there are dates, that is four times in
this example. Figure 3.11(a) illustrates each of these two choices. If the aim is to
“follow” the categories of activity over time in the way that they differentiate the
cities, then time has to be projected on the variables. As the authors are focusing
here on the differentiations of the trajectories of cities, the most appropriate choice is
to project time on the cities (the individuals). The correspondence analysis will
therefore be carried out from a table with 4 × 737 rows and 26 columns. A time-
stamped-city is a point in a space with 26 dimensions, and a city is characterized by
the trajectory linking the four time-stamped-individuals associated. The analysis'
referential, if all the time-stamped-cities are “active” in the analysis, will be an
average city with all the dates mixed-up. It is also possible to choose a different
referent, for example the first date of the period, in order to highlight the change in
the cities' differentiation structure relative to this date in particular. Only the pieces
of information relating to the cities at this date will then have to be considered as
“active” individuals, the others being considered as “supplementary” individuals
(they will be represented but will not participate in the identification of the
differentiation structure).
In the example, the authors make the choice to read the cities' coevolution
relative to an average distribution structure of the activities over the whole period.
The first two factors resulting from the analysis summarize these differentiations
(25%). The trajectories are constructed a posteriori on the factorial map crossing the
two first factors (Figure 3.11). This process, if it applies to a relatively small number
of entities, is interesting because it simultaneously allows us to highlight the
evolution of the whole system and identify the specific characteristics. The
trajectory with the dotted line in Figure 3.11(b) represents the average evolution of
cities of this urban system, with a displacement of the specialization from industry
activities (manufacturing) toward the services, on the one hand, and of “old”
activities toward the high technology activities, on the other hand. The position of
the trajectory of each city, its length, its breaks and its different orientations, bring
forward both the diversity of changes on the economic plan and the diversity of
rhythms and steps. By crossing these trajectories with the cities' rank in the urban
hierarchy, the authors were able to bring forward the diffusion of innovation cycles
along the urban hierarchy.
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