  Model selection and assessment with incomplete data pose challenges in
addition to the ones encountered with complete data. There are two main reasons
for this. First, many models describe characteristics of the complete data, in
spite of the fact that only an incomplete subset is observed. Direct comparison
between model and data is then less than straightforward. Second, many commonly
used models are more sensitive to assumptions than in the complete-data
situation and some of their properties vanish when they are fitted to
incomplete, unbalanced data. These and other issues are brought forward using
two key examples, one of a continuous and one of a categorical nature. We argue
that model assessment ought to consist of two parts: (i) assessment of a
model's fit to the observed data and (ii) assessment of the sensitivity of
inferences to unverifiable assumptions, that is, to how a model described the
unobserved data given the observed ones.
