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Marginal log-linear parameters for graphical Markov models.

ABSTRACT: Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a subclass of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.

SUBMITTER: Evans RJ

PROVIDER: S-EPMC3754910 | biostudies-literature | 2013 Sep

REPOSITORIES: biostudies-literature

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Marginal log-linear parameters for graphical Markov models.

Evans Robin J RJ Richardson Thomas S TS

Journal of the Royal Statistical Society. Series B, Statistical methodology 20130901 4

Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a subclass of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first des ...[more]

PMID: 23997643

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