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Marginal log-linear parameters for graphical Markov models

Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parameterizations under linear constraints induce a wide variety of models, including models that are defined by conditional independences. We introduce a subclass of MLL models which correspond to acycli...

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Published in:	Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2013-09, Vol.75 (4), p.743-768
Main Authors:	Evans, Robin J., Richardson, Thomas S.
Format:	Article
Language:	English
Subjects:	Acyclic directed mixed graph Conditional probabilities Degrees of freedom Directed acyclic graphs Discrete graphical model Econometric models Graphs Induced substructures Linear models Lists Marginal log-linear parameter Marginality Markov models Markovian processes Mathematical models Methodology Modelling Multivariate analysis Parameterization Parametric models Parametrization Parsimonious modelling Parsimony Random variables Statistical analysis Statistics Studies Variation independence Vertices
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container_title	Journal of the Royal Statistical Society. Series B, Statistical methodology
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creator	Evans, Robin J. Richardson, Thomas S.
description	Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parameterizations under linear constraints induce a wide variety of models, including models that are defined by conditional independences. We introduce a subclass of MLL models which correspond to acyclic directed mixed graphs under the usual global Markov property. We characterize for precisely which graphs the resulting parameterization is variation independent. The MLL approach provides the first description of acyclic directed mixed graph models in terms of a minimal list of constraints. The parameterization is also easily adapted to sparse modelling techniques, which we illustrate by using several examples of real data.
doi_str_mv	10.1111/rssb.12020
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subjects	Acyclic directed mixed graph Conditional probabilities Degrees of freedom Directed acyclic graphs Discrete graphical model Econometric models Graphs Induced substructures Linear models Lists Marginal log-linear parameter Marginality Markov models Markovian processes Mathematical models Methodology Modelling Multivariate analysis Parameterization Parametric models Parametrization Parsimonious modelling Parsimony Random variables Statistical analysis Statistics Studies Variation independence Vertices
title	Marginal log-linear parameters for graphical Markov models
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