With dichotomous variables an n-variable analysis means 2n cells in the ensuing <>in-way table, whereas the inclusion of polytomies among the set of n variables produces more than 2n cells and less-compact marginal tables. A consequence is that even conceptually simple models may contain a surfeit of parameters corresponding to the enlarged marginal tables, thus making data interpretation somewhat more difficult. Also, the extra table cells may spread the sample too thinly to warrant the usual distributional assumptions about Y2 and X2.

This chapter is largely concerned with these and related problems arising from large unwieldy tables. It contains a description of some recent progress towards parsimonious modelling which involves the resolution of large sets of interaction parameters and takes account of the ordinal or higher-level values often attached to the levels of polytomies. Alternative strategies that are considered include the deletion of cells that are aberrant from the perspective of a simple model adequately fitting the majority of table cells, and category amalgamation and variable elimination. These latter ploys do have consequences which are discussed subsequently, though they remind us that table design is not an immutable phenomenon and that tables can be modified, not simply as a last resort to overcome the sparseness of observations and superfluity of parameters that often accompanies the analysis of polytomies, but as a means of illustrating and clarifying the meaning of interactions. The chapter is loosely organised as two halves. The first half mainly examines how simplification can be achieved via the models fitted to complex tables. The second half examines more-closely the role played by modifications to the table itself.