Glossary

Logistic Transformation (Logit)

The logistic transformation (logit) maps a probability p ∈ (0, 1) to the log-odds: log(p / (1 − p)). This maps a bounded quantity to the entire real line, enabling linear modelling of binary outcomes.

Definition

Why It Matters

Binary outcomes — yes/no, success/failure, default/repay — are ubiquitous in research and business, but probabilities are constrained between 0 and 1, making linear models inappropriate. The logit transformation removes this constraint, allowing analysts to model the log-odds of an event as a linear function of predictors. This makes logistic regression the standard tool for predicting loan defaults, diagnosing diseases, classifying emails as spam, and any situation where the outcome is dichotomous. The resulting coefficients are interpretable as changes in log-odds, and exponentiating them yields odds ratios — a widely understood effect-size measure in medical and social-science research.

Example

A bank wants to predict whether a loan applicant will default. Using logistic regression, the logit of the default probability is modelled as a linear function of credit score, debt-to-income ratio, and employment status. A coefficient of 0.05 on credit score means that each additional point on the credit score increases the log-odds of non-default by 0.05, corresponding to an odds ratio of approximately 1.05.

Related Terms

Software Notes

SPSS: Analyze > Regression > Binary Logistic; select dependent variable and covariates
R: glm(y ~ x1 + x2, family = binomial, data = df) for logistic regression
Stata: logit y x1 x2 for logistic regression; logistic y x1 x2 to display odds ratios directly