Glossary Entry

Random Effect

A group-specific coefficient treated as a draw from a shared distribution rather than a free parameter, so the model estimates the distribution's variance and shrinks each group's estimate toward the population center.

Models Statistics

Also called: random effects, random intercept, random intercepts, random slope, random slopes

Seed source: UCLA OARC, Introduction to Linear Mixed Models

A random effect gives a group its own coefficient without spending a free parameter on it: the group offsets are modeled as draws from a common distribution, usually a zero-mean Gaussian, and what the model actually estimates is that distribution’s variance. A random intercept lets groups differ in baseline; a random slope lets them differ in how strongly a predictor acts.

Because the offsets share a distribution, each group’s predicted effect is shrunk toward zero deviation by an amount that depends on its sample size, which is what distinguishes random effects from per-group dummy variables and makes them usable even for groups with a handful of observations.