  We outline a framework for multiple imputation of nonignorable item
nonresponse when the marginal distributions of some of the variables with
missing values are known. In particular, our framework ensures that (i) the
completed datasets result in design-based estimates of totals that are
plausible, given the margins, and (ii) the completed datasets maintain
associations across variables as posited in the imputation models. To do so, we
propose an additive nonignorable model for nonresponse, coupled with a
rejection sampling step. The rejection sampling step favors completed datasets
that result in design-based estimates that are plausible given the known
margins. We illustrate the framework using simulations with stratified
sampling.
