GLM (Generalized Linear Model)

Family of regression models for non-normal responses (binary, counts, proportions) — link function plus exponential-family distribution.

Also known as: Generalized Linear Model, GLMs

Generalized Linear Models (Nelder & Wedderburn, 1972) extend classical linear regression to responses that are not continuous and normally distributed. They combine three building blocks:

Random component — distribution of Y from the exponential family (Normal, Binomial, Poisson, Gamma, …)
Systematic component — linear predictor $η = β_{0} + \sum β_{j} X_{j}$
Link function — connects the expected value to the linear predictor: $g (μ) = η$

g (E [Y ∣ X]) = β_{0} + β_{1} X_{1} + \dots + β_{p} X_{p}

Logistic regression — Binomial + logit link
Poisson regression — Poisson + log link
Negative binomial regression — NegBin + log link
Gamma regression — Gamma + log link (positive, skewed Y)

Used in

In the Algorithm Lab

Sources

Nelder, J. A. & Wedderburn, R. W. M. — Generalized Linear Models, Journal of the Royal Statistical Society A, 135(3), 1972
McCullagh, P. & Nelder, J. A. — Generalized Linear Models, 2nd Edition, Chapman & Hall
Fahrmeir, L. et al. — Regression: Models, Methods and Applications, 2nd Edition, Springer

GLM (Generalized Linear Model)

See also

Used in

In the Algorithm Lab

Sources