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Figure 4.3. Formalization of a problematic referring to the differences in social composition
of a set of schools following a) a statistical perspective and b) a multi-agent perspective
The relation to empirical reality differs in the two approaches, which, as we
discussed earlier, is linked to differences in the objective of the models developed in
a statistical or agent framework. In one case, relatively complete information is
available, formalized in the form of a statistical table, and the objective is to develop
a model which reproduces the observed facts in the most faithful possible manner
(the point is to obtain the best fit between model estimates and observed values). In
the other case, a set of rules is established, which allows the production of a stylized
fact 2 . In the first case, the aim is to identify and describe the regularities in the
differentiations between the statistical individuals, and also identify the variables
that are discriminant to “explain” (in the statistical sense) these differentiations. In
the other case, the objective of the model is to explore the mechanisms at the origin
of the emergence of such differentiations. In the first case, the statistical model is
calibrated from a set of observations, i.e. the values of the parameters are estimated
(the coefficients of a multiple regression, for example) by minimizing the difference
between the observed values and the values estimated by the model. The validation
step then consists of testing the model on a set of observations that had not been
2 A “stylized fact” is a simplified presentation of a recurring empirical regularity (observable
in the form of correlation, spatial configuration or hierarchical organization).
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