Marginal conditional independence models with application to graphical modeling
Tamás Rudas, Wicher Bergsma · 2009
Conditional independence models are deflned by a set of conditional independence restrictions and play an important role in many statistical applications, especially, but not only, graphical modeling. In this paper we identify a subclass of these models which are hierarchical marginal log-linear, as deflned by Bergsma and Rudas (2002a). Such models are smooth, which implies the applicability of standard asymptotic theory and simplifles interpretation. Furthermore, we give a marginal loglinear parameterization and a minimal speciflcation of the models in the subclass, which implies the applicability of standard methods to compute maximum likelihood estimates and simplifles the calculation of the degrees of freedom for the model. We illustrate the utility of our results by applying them to certain block recursive Markov models associated with chain graphs.