### Multinomial Logistic Regression

The multinomial (a.k.a. polytomous) logistic regression model is a simple extension of the binomial logistic regression model. They are used when the dependent variable has more than two nominal (unordered) categories.

Dummy coding of independent variables is quite common. In multinomial logistic regression the *dependent* variable is dummy coded into multiple 1/0 variables. There is a variable for all categories but one, so if there are M categories, there will be M-1 dummy variables. All but one category has its own dummy variable. Each category’s dummy variable has a value of 1 for its category and a 0 for all others. One category, the reference category, doesn’t need its own dummy variable as it is uniquely identified by all the other variables being 0.

The multinomial logistic regression then estimates a separate binary logistic regression model for each of those dummy variables. The result is [Read more…] about Logistic Regression Models for Multinomial and Ordinal Variables