Binary outcomes: the logistic model, odds ratios, marginal effects, classification.
Course overview
This free course uses real Python and statsmodels in your browser. Work through the modules below with explanations, executable examples, interactive controls, and questions.
When y is 0 or 1, fitting a straight line (the Linear Probability Model) breaks down: it predicts probabilities outside [0,1], has built-in heteroskedasticity, and imposes a constant effect that cannot be globally true.
Logit and probit pass a linear index β₀+β₁x through an S-shaped link (the logistic CDF or the standard-normal CDF) to keep probabilities in (0,1). Both are fit by maximum likelihood; their coefficients differ only by a roughly constant scale factor.
A raw logit coefficient is a change in log-odds — not very intuitive. Exponentiate it to get an odds ratio (a multiplicative effect on the odds), or compute a marginal effect dP/dx (the change in probability), which is largest near p=0.5 and shrinks at the extremes.
Judge a binary model by likelihood-based fit (pseudo-R², LR test) and by classification: turn predicted probabilities into 0/1 at a threshold, build a confusion matrix, read accuracy, and trace the threshold-free ROC curve and its AUC — all with numpy, no sklearn.