ABSTRACT
In general, categorical data models relate to c o u n t d a ta corresponding to the classification of sampling units into g ro u p s or c a te g o r ie s either on a qualitative or some quantitative basis. These categories may be defined by the essentially discrete nature of the phenomenon under study (see Ex ample 1.2.2 dealing with the OAB blood classification model) or, often for practical reasons, by the grouping of the values of an essentially continuous underlying distribution (for example, shoe sizes: 5, 5 | , 6, 6^, etc., corre sponding to half-open intervals for the actual length of a foot). Even in the qualitative case there is often an implicit ordering in the categories result ing in o rd e re d ca teg o rica l d a ta (viz., ratings: excellent, very good, good, fair and poor, for a research proposal under review). Except in some of the most simple cases, exact statistical analysis for categorical data models may not be available in a unified, simple form. Hence, asym ptotic methods are im portant in this context. They not only provide a unified coverage of statistical methodology appropriate for large sample sizes but also sug gest suitable modifications which may often be appropriate for moderate to small sample sizes. This chapter is devoted to the study of this related asymptotic theory.
