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in school results at the level of individuals or the differences in health between a set
of cities. In the first case, some “explanatory” variables relate to the pupils' level
(parents' social class, sex, for example) and others to the level of the school (social
profile, private/public sector, number of pupils, for example) which constitutes the
context in which the pupils evolve [FRA 14a]. In the second case, on the one hand,
there are variables characterizing the cities (size, average incomes, economical
dynamics, pollution) and on the other, variables characterizing the region in which
the city is located (climatic region, social ambiance, for example) [ASC 13]. The
multilevel statistical models enable us to assess the respective effects of these
different variables referring to different levels, by reasoning
all things being equal
,
on the differentials in terms of academic results or population's health. Such models
allow us to draw conclusions on the effect of a pupil's parents' social class on
his/her results at the high school “brevet”, all things equal with regard to the social
profile of the school where he/she performs his/her schooling, and
vice versa
. Thus,
a multilevel model allows us to refine the description of the phenomenon of interest.
- In a multi-agent model, the interactions between the entities considered as
elementary are formalized (the students in the first example used above and the
cities in the second example) and the interest is in the configuration which emerges
at a higher organization level. It concerns, in the first case, the manner of
concentration of pupils with a certain social profile in some schools, and in the
second case, the manner of the spatial configuration of cities according to their
populations' health status. The MAS approach is inherently dynamic and multilevel.
Indeed, the rules on the interactions between the elementary entities operate at each
time step and we can follow the evolution of the configurations that
emerge
over
time from these interactions at the higher level of organization through the
representation of appropriate indicators. The underlying hypothesis is that the
structures observable at a macrogeographical level (spatial segregation in the case of
Schelling's model, a rank-size organization in the case of models of the SimPop
type, Figure 4.5) emerge from a set of interactions operating at a basic level. The
principle is
bottom-up
, the interactions between agents “generating” the structures
observed at the higher level, but without the obtained structure being desired or even
perceived at the elementary level. The focus is on the plausibility of the
configuration which has emerged and which can be characterized from statistical
indicators (hierarchical organization, spatial organization, etc.). It is at this higher
level that the simulation results will be compared with the observed values, and not
at a one-to-one basis as in statistics. Having developed a MAS model with the
objective of understanding the redistribution of three categories of Israeli
populations (Jewish, Arab Christian and Arab Muslim) in the district of Yaffo
between 1955 and 1995 (old Arab city, today a Southern suburb of Tel Aviv),
Benenson
et al.
4
[BEN 02] use this approach to compare the simulated and observed
4 This example is developed in section 4.3.3.
