Multinomial Logit and Probit Regression

The multinomial logit and probit regression models are extensions of the standard logit and probit regression models to the case where the dependent variable has more than two categories (e.g., not just Pass - Fail, but Pass, Fail, Withdrawn), i.e., when the dependent or response variable of interest follows a multinomial distribution rather than binomial distribution. When multinomial responses contain rank-order information, they are also called ordinal multinomial responses (see ordinal multinomial distribution).
For additional details, see also the discussion of Link Functions, Probit Transformation and Regression, Logit Transformation and Regression, or the Generalized Linear Models chapter.