Log-mean linear models for binary data

TL;DR

This paper proposes log-mean linear models for binary data, enabling straightforward specification of marginal independence and graphical models through linear constraints on a novel parameterization.

Contribution

It introduces a new class of models for binary data that simplifies the representation of marginal independence and improves upon existing parameterizations.

Findings

Marginal independence can be characterized by zeroing specific interactions.

Graphical models of marginal independence are encompassed within log-mean linear models.

The approach addresses limitations of previous parameterizations.

Abstract

This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a log-linear expansion of the mean parameter of the multivariate Bernoulli distribution. We show that marginal independence relationships between variables can be specified by setting certain log-mean linear interactions to zero and, more specifically, that graphical models of marginal independence are log-mean linear models. Our approach overcomes some drawbacks of the existing parameterizations of graphical models of marginal independence.