Title: A note on the role of projectivity in likelihood-based inference for random graph models,
Abstract: There is widespread confusion about the role of projectivity in
likelihood-based inference for random graph models. The confusion is rooted in
claims that projectivity, a form of marginalizability, may be necessary for
likelihood-based inference and consistency of maximum likelihood estimators. We
show that likelihood-based superpopulation inference is not affected by lack of
projectivity and that projectivity is not a necessary condition for consistency
of maximum likelihood estimators.