Models for polytomous data

In the first two chapters of this volume, models for binary or dichotomous variables have been discussed. However, in a wide range of psychological and sociological applications it is very common to have data that are polytomous or multicategorical. For instance, the response scale in the verbal aggression data set (see Chapters 1 and 2) originally consisted of three categories (“yes,” “perhaps,” “no”), but it was dichotomized to illustrate the application of models for binary data. In aptitude testing, the response is often classified into one of several categories (e.g., wrong, partially correct, fully correct). In attitude research, frequent use is made of rating scales with more than two categories (e.g., “strongly agree,” “agree,” “disagree,” “strongly disagree”). Other examples are multiple-choice items, for which each separate choice option represents another category. In a typical discrete choice experiment, the subject is faced with a choice between several options (e.g., several brands of a product in a marketing study).