Random-effects model
Also known as: Random effects, Mixed-effects model
Treating groups or studies as draws from a wider population rather than as fixed.
What it means
A random-effects model is a statistical approach that treats group-level differences — across studies, schools, clusters, or repeated measures within people — as random draws from a population distribution rather than as a set of fixed, separately estimated parameters. By estimating the variance of these effects instead of a coefficient for each group, it pools information across units, shrinking noisy small-group estimates toward the overall mean and allowing generalization to units not in the sample. In meta-analysis, a random-effects model assumes the true effect varies across studies and so yields wider, more honest intervals than a fixed-effect model when studies are heterogeneous. The key contrast is with fixed-effects approaches, which condition on the observed groups and absorb all stable between-group differences but cannot generalize beyond them or estimate group-level predictors. It matters because choosing between random and fixed effects encodes substantive assumptions about heterogeneity, generalization, and what counts as the population of interest.
Examples
Pooling forty clinical trials of a drug with a random-effects model acknowledges that each trial estimates a slightly different true effect, widening the combined confidence interval accordingly.
Estimating exam gains across 300 schools, a random-effects model pulls one tiny school's freak result back toward the average and lets you say something about schools not in the sample.
A supermarket chain modelling weekly sales treats each of its 800 stores as a draw from a store population, so a quiet branch's odd week never becomes its own hard-coded parameter.