Binary Models for Marginal Independence

TL;DR

This paper introduces a new class of binary graphical models that effectively capture marginal independence in contingency tables, extending traditional log-linear models to accommodate these hypotheses.

Contribution

It proposes a novel framework for modeling marginal independence in binary data using bi-directed graphs, with simple parameterization and an efficient estimation algorithm.

Findings

Models can be parameterized simply

Maximum likelihood estimation is feasible with an adapted algorithm

Models can incorporate symmetry restrictions

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 taken is graphical and draws on analogies to multivariate Gaussian models for marginal independence. For the graphical model representation we use bi-directed 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 using a version of the Iterated Conditional Fitting algorithm. Finally we consider combining these models with symmetry restrictions.