Binary regression
In statistics, specifically regression analysis, a binary regression estimates a relationship between one or more explanatory variables and a single output binary variable. Generally the probability of the two alternatives is modeled, instead of simply outputting a single value, as in linear regression.
Part of a series on Statistics 
Regression analysis 

Models 
Estimation 
Background 

Binary regression is usually analyzed as a special case of binomial regression, with a single outcome (), and one of the two alternatives considered as "success" and coded as 1: the value is the count of successes in 1 trial, either 0 or 1. The most common binary regression models are the logit model (logistic regression) and the probit model (probit regression).
Applications
Binary regression is principally applied either for prediction (binary classification), or for estimating the association between the explanatory variables and the output. In economics, binary regressions are used to model binary choice.
Interpretations
Binary regression models can be interpreted as latent variable models, together with a measurement model; or as probabilistic models, directly modeling the probability.
The latent variable interpretation has traditionally been used in bioassay, yielding the probit model, where normal variance and a cutoff are assumed. The latent variable interpretation is also used in item response theory (IRT).
The simplest direct probabilistic model is the logit model, which models the logodds as a linear function of the explanatory variable or variables. The logit model is "simplest" in the sense of generalized linear models (GLIM): the logodds are the natural parameter for the exponential family of the Bernoulli distribution, and thus it is the simplest to use for computations.
References
 Long, J. Scott; Freese, Jeremy (2006). "4. Models for binary outcomes: 4.1 The statistical model". Regression Models for Categorical Dependent Variables Using Stata, Second Edition. Stata Press. pp. 131–136. ISBN 9781597180115.
 Agresti, Alan (2007). "3.2 Generalized Linear Models for Binary Data". Categorical Data Analysis (2nd ed.). pp. 68–73.