Marginal Log-Linear Parameterization

In this chapter, marginal log-linear parameters are defined, which generalize log-linear parameters. Log-linear parameterizations were used earlier to conveniently define and parameterize log-linear models that applied no-higher-order association restrictions to the joint distributions of the variables which, in the case of graphical models, turned out to be conditional independences or Markov properties. The main motivation behind introducing marginal log-linear parameterizations is to define marginal log-linear models, which apply no-higher-order associations in marginals of the table. Such models include Markov models associated with DAGs. Thus, the parameterizations to be introduced provide an easy definition and parameterizations of DAG models, but are also useful in many other statistical problems.