Geoscience Reference
In-Depth Information
the previous section, regression analysis has been used on two occasions. The first
time it allowed us to give a account of a spatial organization, with the spatial
regression describing the variations of the population density (log) as a function of
the distance to the center (Clark's model). The second served to describe a
hierarchical organization, with the regression expressing the variations in population
(log) as a function of the rank (log) (model of the rank-size rule). In these two
examples, the models, simple linear regressions, are used to summarize the structure
with the help of the slope of the regression line.
In the context of a more classical use, that is to say in an “explanatory” model, a
statistical model can be constructed (multiple regression for example) at several
dates and we can compare the structures highlighted by each of them through the
respective roles of the explanatory variables. In this case, the interpretation of
change is rather qualitative, even if, as in the previous cases, the trajectories of
parameters whose value and significance are evolving over time can be built.
Statistical models can also be used to “explain”
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change more directly. In this
case, time can be summarized in the variable “to explain” which is then an
evaluation of the change of the phenomenon of interest (entities' population
variation between two dates, change in land use, for example). This type of model
makes it possible to formalize the generic framework proposed by Durand-Dastes
[DUR 90] to describe and explain the differentiated evolution of places (for example
a set of municipalities). He proposed three categories of variables referring each one
to an explanatory domain:
1) The ecological variables that refer to the economic, social, and physical
profile of these “municipalities” taken as the statistical individuals.
2) The historical variables that refer to both the past trajectory and time-stamped
events.
3)The spatial variables that characterize the relative position of the
municipalities, their accessibility, their neighborhood, etc.
Furthermore, in a predictive context, the question underlying the construction of
an “explanatory” model of change can be derived with regard to the three
components: where will change take place, how much change will occur and when
will this change take place? On the other hand, this type of model raises the question
of the capacity of a statistical model to integrate the spatial variability of the causes
of change.
7 We have chosen to put the term “explanation” in between quotation marks when it refers to
statistical terminology. In Chapter 4, we will discuss the different meanings of the explanation
with a spatial analysis approach.
