Applied Logistic Regression, 3rd Edition

Chapter 8: Logistic Regression Models for Multinomial and Ordinal Outcomes

8.1 The Multinomial Logistic Regression Model

8.1.1 Introduction to the Model and Estimation of Model Parameters

In the previous chapters we focused on the use of the logistic regression model when the outcome variable is dichotomous or binary. This model can be easily modified to handle the case where the outcome variable is nominal with more than two levels. For example, consider a study of choice of a health plan from among three plans offered to the employees of a large corporation. The outcome variable has three levels indicating which plan, A, B or C is chosen. Possible covariates might include gender, age, income, family size, and others. The goal is to estimate the probability of choosing each of the three plans as well as to estimate the odds of plan choice as a function of the covariates and to express the results in terms of odds ratios for choice of different plans. McFadden (1974) proposed a modification of the logistic regression model and called it a discrete choice model. As a result, the model frequently goes by that name in the business and econometric literature while it is called the multinomial, polychotomous, or polytomous logistic regression model in the health and life sciences. We use the term multinomial in this text.

It would be possible to use an outcome variable with any number of levels to illustrate the extension of the model and methods. However, the details are most easily ...