Marginal log-linear parameters for graphical Markov models
Robin J. Evans, Thomas S. Richardson
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2013 · Volume 75 · Issue 4
Abstract
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.
Keywords
Acyclic directed mixed graph, Discrete graphical model, Marginal log-linear parameter, Parsimonious modelling, Variation independence
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