Sparseness occurs when the number of cells in a table is
relatively large in comparison with the sample size. It may also
occur in parts of a table which exhibits strong association: if
many cases are on the diagonal, the bottom left and top right
corners may be sparsely populated.
Sparseness is a general problem in that the properties of
and that we depend on for assessing fit are
asymptotic large sample properties: we can trust these measures
less when there is sparseness. For instance, where there are
several cells with fitted values less than about five.
General sparseness can be dealt with by collapsing the table,
or collapsing variable categories (good for localised
sparseness), or by getting more data.
Some localised sparseness is not a disaster: models can
usually cope with parts of a table which have a low probability.
and 
that we depend on for assessing fit are
asymptotic large sample properties: we can trust these measures
less when there is sparseness. For instance, where there are
several cells with fitted values less than about five.
