Multilevel models (also hierarchical linear models"), generalized linear mixed models, nested models, mixed models, random coefficient, random effects models"), random parameter models) are statistical models of parameters that vary at more than one level. These models can be seen as generalizations of linear models, although they can also extend nonlinear models. Although they are not new, they have become more popular with the growth of computing power and software availability.

For example, education research might require measuring performance in schools that use one learning method versus schools that use a different method. It would be a mistake to analyze these data thinking that students are "simple random samples" of the population of students who learn under a particular method. Students are grouped into classes (courses), which in turn are grouped into schools. The performance of students within a class is correlated, as is the performance of students within the same school. These correlations must be represented in the analysis for the correct inference obtained by the experiment.

Multilevel models have been used in education to separately estimate the variance between students in the same school, and the variance between schools. In psychological applications, the multiple levels could be questions on a questionnaire, individuals and families. Different covariates may be relevant at different levels. These models can be used in longitudinal studies, such as growth studies, to separate changes within an individual and differences between individuals.[1]​.

Multilevel models can be used to model the change over time in a variable of interest. A total change function is fitted to the entire sample and the parameters may vary. For example, in a study analyzing income growth versus age, individuals can be assumed to show positive growth over time. The intercept and slope can be allowed to vary across individuals. The simplest models assume that the effect of time is linear. Polynomial models can be specified to allow for quadratic or cubic effects in time. Non-linear models in their parameters can also be adjusted in special software. Nonlinear models might be more appropriate for representing various growth functions where asymptotes represent limits on the range of possible values. These models can also incorporate constant time or time-varying covariates as predictors.