Binary models for marginal independence

Mathias Drton, Thomas S. Richardson

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of special structures, marginal independence hypotheses cannot be accommodated by these traditional models. Focusing on binary variables, we present a model class that provides a framework for modelling marginal independences in contingency tables. The approach that is taken is graphical and draws on analogies with multivariate Gaussian models for marginal independence. For the graphical model representation we use bidirected graphs, which are in the tradition of path diagrams. We show how the models can be parameterized in a simple fashion, and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm. Finally we consider combining these models with symmetry restrictions.

Original languageEnglish
Pages (from-to)287-309
Number of pages23
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume70
Issue number2
DOIs
StatePublished - Jan 2008
Externally publishedYes

Keywords

  • Bidirected graph
  • Covariance graph
  • Graphical Markov model
  • Iterative conditional fitting
  • Maximum likelihood estimation
  • Möbius inversion

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