8: Multinomial Logistic Regression Models

Overview Section

In this lesson, we generalize the binomial logistic model to accommodate responses of more than two categories. This allows us to handle the relationships we saw earlier with \(I \times J\) tables as well as relationships involving ordinal response and quantitative predictors. To interpret odds in these situations, we can either specify a baseline response category much like the baseline references we've been using for predictors, or, if categories are ordinal, we'll be able to work with a cumulative odds, which is based on the cumulative probability of falling in a particular category or smaller, as we saw in Lesson 4.

Upon completion of this lesson, you should be able to:

  Objective 8.1

Generalize the logistic regression model to accommodate categorical responses of more than two levels and interpret the parameters accordingly.

  Objective 8.2

Explain the proportional odds assumption and use the multinomial logistic regression model to measure evidence against it. Assess the relative importance of multiple predictors in the context of multinomial logistic regression.

  Objective 8.3

Assess the relative importance of multiple predictors when fitting a logistic regression model.

 Lesson 8 Code Files

Data File: housing.dat

R Files

SAS Files