Binary Response Models and Logistic Regression

Abstract

The focus of this article is on regression models for a binary response. In most fields of application, logistic regression has become the standard method for relating a binary response to a set of covariates. In this article the main features of logistic regression are described and some aspects of interpretation of logistic regression are illustrated with an example. The logistic regression model is first introduced for the simple case where there is only a single predictor variable. This model is compared and contrasted with the classical linear regression model. Later the generalizations to more than one predictor variable are considered. A major emphasis of this article is placed on how logistic regression is used in practice and how the logistic regression coefficients should be interpreted. An example, based on data from the US General Social Survey, is used to illustrate and reinforce the main concepts. Finally, three important extensions of standard logistic regression are briefly reviewed: conditional logistic regression, exact logistic regression, and logistic regression for clustered data.