Log-mean linear models for binary data

Abstract

This paper introduces a novel class of models for binary data, which we call log-mean linear
\nmodels. They are specified by linear constraints on the log-mean linear parameter, defined
\nas a log-linear expansion of the mean parameter of the multivariate Bernoulli distribution. We
\nshow that marginal independence relationships between variables can be specified by setting certain
\nlog-mean linear interactions to zero and,more specifically, that graphical models of marginal
\nindependence are log-mean linear models. Our approach overcomes some drawbacks of the existing
\nparameterizations of graphical models of marginal independence.