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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Bibliographic Details
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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Summary: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.
ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12020