  Multilevel models (mixed-effect models or hierarchical linear models) are now
a standard approach to analysing clustered and longitudinal data in the social,
behavioural and medical sciences. This review article focuses on multilevel
linear regression models for continuous responses (outcomes or dependent
variables). These models can be viewed as an extension of conventional linear
regression models to account for and learn from the clustering in the data.
Common clustered applications include studies of school effects on student
achievement, hospital effects on patient health, and neighbourhood effects on
respondent attitudes. In all these examples, multilevel models allow one to
study how the regression relationships vary across clusters, to identify those
cluster characteristics which predict such variation, to disentangle social
processes operating at different levels of analysis, and to make
cluster-specific predictions. Common longitudinal applications include studies
of growth curves of individual height and weight and developmental trajectories
of individual behaviours. In these examples, multilevel models allow one to
describe and explain variation in growth rates and to simultaneously explore
predictors of both of intra- and inter-individual variation. This article
introduces and illustrates this powerful class of model. We start by focusing
on the most commonly applied two-level random-intercept and -slope models. We
illustrate through two detailed examples how these models can be applied to
both clustered and longitudinal data and in both observational and experimental
settings. We then review more flexible three-level, cross-classified, multiple
membership and multivariate response models. We end by recommending a range of
further reading on all these topics.
