Multinomial Response Models 6.1 the Nature of Multinomial Data 6.1.1 the Contraceptive Use Data

We now turn our attention to regression models for the analysis of categorical dependent variables with more than two response categories. Several of the models that we will study may be considered generalizations of logistic regression analysis to polychotomous data. We first consider models that may be used with purely qualitative or nominal data, and then move on to models for ordinal data, where the response categories are ordered. Let me start by introducing a simple dataset that will be used to illustrate the multinomial distribution and multinomial response models. Table 6.1 was reconstructed from weighted percents found in Table 4.7 of the final report of the Demographic and Health Survey conducted in El Salvador in 1985 (FESAL-1985). The table shows 3165 currently married women classified by age, grouped in five-year intervals, and current use of contraception, classified as sterilization, other methods, and no method. A fairly standard approach to the analysis of data of this type could treat the two variables as responses and proceed to investigate the question of independence. For these data the hypothesis of independence is soundly rejected, with a likelihood ratio χ 2 of 521.1 on 12 d.f.