Correlated observations (within centers, families, subjects,...) are common
in epidemiology. Even when one is only interested in the modeling of means
according to risk factors, it is also necessary to model the variance-cova
riance matrix of the observations in order to make correct inferences on th
e parameters of interest. All the more so when the aim of the survey is the
measurement of these correlations or of the variance of the random effects
from which they are assumed to originate. We discuss, within the framework
of the linear and of the logistic models, the implications of two choices
for the modeling of covariances. The mixed model shows the unobserved eleme
nts responsible for the similarity between certain observations. In a longi
tudinal survey, for instance, one can use a random effect, specific to each
subject expressing how much a subject's trajectory is translated as compar
ed to what is expected according to its characteristics (age, sex,...). The
marginal approach leads To modeling separately the means and the covarianc
e matrix of the observations. The distinction between these two approaches
is important for non linear models, in particular the logistic one. We insi
st on rite interconnection between a mixed model formulation and a marginal
one, as well as on the implication of the choice in terms of the parameter
s' interpretation.