Models for Binary Outcomes

Introduction

The simple or binary response (for example, success or failure) analysis models the relationship between a binary response variable and one or more explanatory variables. For a binary response variable Y, it assumes:

where p is Prob(Y=y₁) for y₁ as one of two ordered levels of Y, is the parameter vector, x is the vector of explanatory variables, and g is a function of which p is assumed to be linearly related to the explanatory variables.

The binary response model shares a common feature with a more general class of linear models that a function g=g() of the mean of the dependent variable is assumed to be linearly related to the explanatory variables. The function g(), often referred as the link function, provides the link between the random or stochastic component and the systematic or deterministic component of the response variable. For the binary response model, logistic and probit regression techniques are often employed among all others.