  We study the problem of ignorability in likelihood-based inference from
incomplete categorical data. Two versions of the coarsened at random assumption
(car) are distinguished, their compatibility with the parameter distinctness
assumption is investigated and several conditions for ignorability that do not
require an extra parameter distinctness assumption are established. It is shown
that car assumptions have quite different implications depending on whether the
underlying complete-data model is saturated or parametric. In the latter case,
car assumptions can become inconsistent with observed data.
