  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.
