Marginal log-linear parameters for graphical Markov models

TL;DR

This paper introduces a subclass of marginal log-linear models for graphical Markov models, specifically for ADMGs, providing a minimal, variation-independent parametrization that facilitates sparse modeling and interpretation.

Contribution

It characterizes when MLL parametrizations for ADMGs are variation independent and offers the first minimal constraint description for these models.

Findings

Provides a minimal list of constraints for ADMG models

Characterizes graphs with variation-independent parametrizations

Demonstrates applicability to real data with sparse modeling

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 sub-class 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.