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opening of a supermarket is interpreted as an “innovation”, and the model
formalizes a diffusion process along the urban hierarchy. The application in the case
of Sweden between 1927 and 1976 reveals the main role of the size of the city and
the absence of role of the distance to the company headquarter. It also shows the
existence of an avoidance strategy for the supermarkets coming from a cooperative
chain when a competition strategy predominates for the others.
The approach which consists of modeling change, eventually allows the trends to
be extended by reasoning “everything else being equal” ( ceteris paribus ) by
identifying, the average law describing the change depending on the overall
structure of associations between variables. Two points do however warrant
attention:
- For some phenomena, explanatory factors vary over space. To remedy this
problem, some authors have developed specific statistics models. The
“geographically weighted regression” [GWR, FOR 02] is thus a regression method
that allows us to take into account the localizations of the entities and their local
spatial dependency. In such a model, the regression parameters vary in space, which
can improve the quality of the model.
- The model enables us to identify where the change is more likely to happen but
it does not allow us to identify when this change will take place. These approaches
are therefore instead related to descriptive approaches, which allow us to progress
with the understanding of the spatial organization of change.
3.3. Understanding the evolution of a spatial system's entities
The question of the follow-up of spatial entities generally arises when the latter
make sense, and the analysis will generate a reflection on the dynamics of the
system that they compose. In a first example, time is formalized through a given
variable for a series of dates. The concern is about representing the demographic and
economic trajectories of cities and the evolution of each city is considered
independently from those of the others. The objective is to characterize the diversity
of trajectories from a clustering that allows the shape of these trajectories to be
categorized. In the second example, the question is to identify the evolution of
employment centers in a metropolitan area between two dates, both in terms of
existence and spatial boundaries. Spatial interactions enable the changes to be
identified. In this example, the method consists of building a priori types of change
and performing a classification of employment centers following the rules hence
defined. The third example is about modeling the land cover change in a perspective
of planning urban sprawl. Two models are coupled: a model where the status of an
entity depends on its previous state and a model where it also depends on the states
of neighboring entities.
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