Binomial regression

In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of ⁠${\displaystyle n}$⁠ independent Bernoulli trials, where each trial has probability of success ⁠${\displaystyle p}$⁠.^[1] In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables.

Binomial regression is closely related to binary regression: a binary regression can be considered a binomial regression with ${\displaystyle n=1}$, or a regression on ungrouped binary data, while a binomial regression can be considered a regression on grouped binary data (see comparison).^[2] Binomial regression models are essentially the same as binary choice models, one type of discrete choice model: the primary difference is in the theoretical motivation (see comparison). In machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.