Glossary Entry

Generalized Linear Mixed Model

A GLM whose linear predictor contains random effects, giving hierarchical versions of logistic and Poisson regression; its likelihood involves an integral with no closed form, so fitting relies on approximations.

Models Statistics

Also called: GLMM, GLMMs, generalized linear mixed models, hierarchical logistic regression, mixed logistic regression

Seed source: Ben Bolker, GLMM FAQ

A generalized linear mixed model composes the GLM recipe with random effects: the linear predictor gains group-specific offsets drawn from a shared distribution, and the link function and outcome distribution stay as they were. Hierarchical logistic regression, churn modeled across markets with a random intercept per market, is the canonical example.

Two things distinguish GLMMs from their linear cousins. Computationally, integrating the random effects out of a non-Gaussian likelihood has no closed form, so fitting uses the Laplace approximation, adaptive quadrature, or MCMC. Interpretively, the coefficients are conditional (within-group) effects, and the population-averaged effect is systematically flatter because averaging shifted S-curves flattens them; which of the two a study reports is a recurring source of cross-study confusion.