Binomial regression is closely related to binary regression: if the response is a binary variable (two possible outcomes), then it can be considered as a binomial distribution with formula_1 trial by considering one of the outcomes as "success" and the other as "failure", counting the outcomes as either 1 or 0: counting a success as 1 success out of 1 trial, and counting a failure as 0 successes out of 1 trial. 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.