Multinomial Regression

Abstract

This chapter examines models that generalize logistic regression to the multiple-category situation. Nominal logistic regression is based on the principle of choosing a baseline category and then simultaneously estimating separate logistic regressions for each of the other categories versus that baseline. The nominal logistic regression model requires the assumption of independence of irrelevant alternatives, an assumption that can easily be violated in discrete choice models. There is a large literature on tests for IIA and extensions and generalizations of multiple category regression models that are appropriate in the discrete choice framework. If the response variable has naturally ordered categories, it is appropriate to explore models that take that into account, as they can often provide parsimonious representations of the relationships in data. These models are generally underutilized in practice, as analysts tend to just use ordinary linear regression with the category number as the response value to analyze these data. Controlled Vocabulary Terms multinomial logistic regression