Extending to multi-class classification
Many problems feature more than two classes. For example, the Standard and Poor's (S&P) bond rating includes multiple classes, such as AAA, AA, A, and more like these. Corporate client accounts in a bank are categorized into good credit, past due, overdue, doubtful, or loss. Such settings require the multinomial logistic regression model, which is a generalization of the binomial logistic regression model in the multi-class classification context. Essentially, the target variable, y, can take more than two possible discrete outcomes and allows for more than two categorical values.
Assume that the target variable can take on three values, giving y ∈ {0,1, 2}. Let us choose class 0 as the pivot value or the baseline. We will model the odds of the probabilities of the other categories (classes 1 and 2) relative to this baseline. In other words, we have the following:
p(y = 1) _ p(y = 0) = e z ...
