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A logistic regression can specify each binary response conditionally on recorded past outcomes and baseline covariates. A chain rule for probabilities gives the path likelihood as the product of the conditional Bernoulli distribution masses. This permits dependence within a person's history without treating their outcomes as unconditionally independent. The model must specify the initial history and which past features enter its conditional mean.

A logistic model maps a real-valued score $\eta$ to the probability $p=(1+e^{-\eta }{)}^{-1}$, equivalently $\log (p/(1-p))=\eta$. Logistic regression takes $\eta$ to be an affine function of the predictors.

A regression for a categorical response with more than two possible outcomes, parametrizing log probability ratios relative to a baseline category by linear predictors. It preserves categories that a binary logistic regression would merge.