  We consider marginal log-linear models for parameterizing distributions on
multidimensional contingency tables. These models generalize ordinary
log-linear and multivariate logistic models, besides several others. First, we
obtain some characteristic properties of marginal log-linear parameters. Then
we define collapsibility and strict collapsibility of these parameters in a
general sense. Several necessary and sufficient conditions for collapsibility
and strict collapsibility are derived based on simple functions of only the
cell probabilities, which are easily verifiable. These include results for an
arbitrary set of marginal log-linear parameters having some common effects. The
connections of strict collapsibility to various forms of independence of the
variables are explored. We analyze some real-life datasets to illustrate the
above results on collapsibility and strict collapsibility. Finally, we obtain a
result relating parameters with the same effect but different margins for an
arbitrary table, and demonstrate smoothness of marginal log-linear models under
collapsibility conditions.
