Application des modèles hiérarchiques en démographie

Abstract EN

Following to the other social sciences, demography is increasingly using hierarchical models.

Indeed, the standard regression models, called "Uni-level", assume that the individual observations are independent of each other conditionally to the variables Xi introduced in the model.

This hypothesis may lead to erroneous statistical inferences in the presence of a dependence of observations in which the resorts remain unobserved through the variables collected in the survey (Goldstein, 1995; Sjniders and Bosker, 1999).

Unobserved heterogeneity can be linked to the sample design of a survey (in particular clusters) or to the sharing of contextual, spatial and / or family influences by members of the same group.

If unobserved heterogeneity in modeling is to be taken into account in order to obtain an unbiased estimate of the parameters of a model, it may also be of interest in itself, by offering the possibility of decomposing the total variability of a phenomenon between a compositional effect (level 1 people’s profile) and a context effect (residual variance between level 2 units after compositional effects were controlled).

Using two different application examples, the purpose of this paper is to demonstrate the contribution of hierarchical methods in demography: - Either to correct the estimation of the parameters of a model of the dependence problem of observations and thus limit the risk of erroneous inference (applied here to the case of the influence of early parental death on the trajectory of children in Burundi); - Or to measure the share of contextual effects and composition effects in the total variability of a phenomenon (applied here to cantonal mortality in metropolitan France from the 1980s).

Through these two examples, we are interested in two methods where the dependence of the observations in the groups is an endogenous element to the model (the correlation between the observations is explicit in the model and influences the estimates of the parameters through the introduction of a new factor in the series of linear predictors): multilevel models (or random effects model, conditional or mixed model) and fixed-effect models.

Moreover, and taking into consideration the nature of the variables modeled: binary in the study of the influence of early parental death on the schooling of children (never having attended school) and quantitative in the case of the analysis of the territorial variability of mortality (mortality rate), we apply logistic models in the first case and linear models in the second case.