Multilevel models are the regression models for the multilevel or clustered data where units i are nested in the clusters j, for example a cross-sectional study where students are nested in schools or the longitudinal studies where measurement occasions are nested in subjects. In multilevel data responses are expected to be dependent or correlated even after the conditioning on observed covariates. Such dependence should be taken into account to ensure the valid statistical inference.
Multilevel regression models comprise random effects with the normal distributions to induce dependence among units belonging in the cluster. The simplest multilevel model is the linear random intercept model The multilevel generalized linear models or the generalized linear mixed models are multilevel models where random effects are introduced in linear predictor of generalized linear models. Additionally to linear models for the continuous responses, such type of models include, for instance, the logistic random effects models for dichotomous, ordinal and nominal responses and the log-linear random effects models for counts.
Multilevel models can also be specified for the higher-level data where units are nested in clusters which are nested in the superclusters. An instance of such a design would be measurement occasions nested in subjects which are nested in communities. Other terms sometimes used for the multilevel models include mixed models, random effects models hierarchical models, and random coeffiencnt models.