5.1. Introduction

Binary logit analysis is ideal when your dependent variable has two categories, but what if it has three or more? In some cases, it may be reasonable to collapse categories so that you have only two, but that strategy inevitably involves some loss of information. In other cases, collapsing categories could seriously obscure what you’re trying to study. Suppose you want to estimate a model predicting whether newly registered voters choose to register as Democrats, Republicans, or Independents. Combining any two of these outcomes could lead to seriously misleading conclusions.

How you deal with such situations depends somewhat on the nature of the outcome variable and the goal of the analysis. If the categories of the dependent variable have an inherent ordering, the methods in the next chapter should do the job. If there’s no inherent ordering and the goal is a model in which characteristics of the outcome categories predict choice of category, then the discrete-choice model of Chapter 7 is probably what you need. In this chapter we consider models for unordered categories where the predictor variables are characteristics of the individual, and possibly the individual’s environment. For example, we could estimate a model predicting party choice of newly registered voters based on information about the voter’s age, income, and years of schooling. We might also include information about the precinct in which the voter is registering.

The model is called the multinomial logit model because the probability distribution for the outcome variable is assumed to be a multinomial rather than a binomial distribution. Because the multinomial logit model can be rather complicated to interpret when the outcome variable has many categories, I’ll begin with the relatively simple case of a three-category outcome.