Marginal conditional independence models with application to graphical modeling
نویسندگان
چکیده
Conditional independence models are defined 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 defined by Bergsma and Rudas (2002a). Such models are smooth, which implies the applicability of standard asymptotic theory and simplifies interpretation. Furthermore, we give a marginal loglinear parameterization and a minimal specification of the models in the subclass, which implies the applicability of standard methods to compute maximum likelihood estimates and simplifies 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.
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