University of Washington - Department of Statistics
Marginal models are defined by restrictions on certain lower dimensional marginal distributions of the joint distribution of several categorical variables. Such models are relevant when analyzing repeated measurements, including panel studies; in various forms of data fusion; and graphical models based on directed acyclic graphs are also marginal models. After reviewing these motivating examples, a formal definition will be given, as the intersection of log-affine (or log-linear) models defined on certain marginals of the contingency table. The models will be defined through a class of particular parameterizations of the joint distribution using marginal log-linear parameters for effects of certain subsets within the marginals. It will be shown that many of the desirable properties of the model (existence, standard asymptotic behavior) and of the parameters (variation independence) depend on combinatorial properties of the marginals and of the effects involved. Finally, the introductory examples will be revisited, including the parameterization of graphical models based on directed acyclic graphs.