Concept: Logistic Regression

Introduction

The logistic regression model has become, in many fields, the standard method of data analysis concerned with describing the relationship between a response variable and one or more explanatory variables where the response variable follows a binomial distribution. Logistic regression is used to model the probability p of occurrence of a binary or dichotomous outcome. Binary-valued covariates are usually given arbitrary numerical coding such as zero for one possible outcome and one for the other possible outcome. Linear regression models may not be used when the outcome is binary valued because the probability of being modeled must lie between zero and one. Ordinary linear regression does not guarantee these limits. Dichotomous data may be analyzed using a logistic function where the logit transformation of p is used as the independent variable.

General Model

If x ₁ , . . . , x _k are a collection of independent variables and y is a binomial outcome variable with probability of success = p , then the multiple logistic regression model is given by:

logit(p) = ln(p/1- p) = a + b ₁ x ₁ + . . . + b _k x _k

where a, b ₁ , . . . , b _k are parameters.