Random-Effects Models

Random-effects models are statistical models in which some of the parameters (effects) that define systematic components of the model exhibit some form of random variation. Statistical models always describe variation in observed variables in terms of systematic and unsystematic components. In fixed-effects models, the systematic effects are considered fixed or nonrandom. In random-effects models, some of these systematic effects are considered random. Models that include both fixed and random effects may be called mixed-effects models or just mixed models.

Randomness in statistical models usually arises as a result of random sampling of units in data collection. When effects can have different values for each unit that is sampled, it is natural to think of them as random effects. For example, consider observations on a variable Y ...