Abstract

In the social, behavioural, educational, economic, and biomedical sciences, data are often collected in ways that introduce dependencies in the observations to be compared. For example, the same respondents are interviewed at several occasions, several members of networks or groups are interviewed within the same survey, or, within families, both children and parents are investigated. Statistical methods that take the dependencies in the data into account must then be used, e.g., when observations at time one and time two are compared in longitudinal studies. At present, researchers almost automatically turn to multi-level models or to GEE estimation to deal with these dependencies. Despite the enormous potential and applicability of these recent developments, they require restrictive assumptions on the nature of the dependencies in the data. The marginal models of this talk provide another way of dealing with these dependencies, without the need for such assumptions, and can be used to answer research questions directly at the intended marginal level. The maximum likelihood method, with its attractive statistical properties, is used for fitting the models.

In the talk I will also spend time on some interesting mathematical problems that arise in marginal modelling. These relate to smoothness of the manifold of probability distributions satisfying a marginal model, and the linear independence of a set of marginal parameters. This is important for the applicability of standard asymptotic theory, and for the calculation of the correct number of degrees of freedom for a model.

This talk is based on a recent book by the authors in the Springer series Statistics for the Social Sciences, see www.cmm.st

Joint work with Marcel Croon and Jacques Hagenaars