Multilevel model

Multilevel models are known by several names: hierarchical linear models, generalized linear mixed models, nested models, mixed models (in biostatistics), random coefficient or random-effects models (in econometrics), random parameter models, and split-plot designs. They are statistical models with model parameters arranged in a hierarchical structure. For example, in educational research it may be necessary to assess the performance of schools teaching reading by one method against schools teaching reading by a different method. It would be a mistake to analyse the data as though the pupils were simple random samples from the population of pupils taught by a particular method. Pupils are taught in classes, which are in schools. The performance of pupils within the same class will be correlated, as will the performance of pupils within the same school. These correlations must be represented in the analysis for correct inference to be drawn from the experiment.

In statistics, multilevel models are used when some variable under study varies at more than one level. These models can be seen as generalizations of linear models, although they can also extend non-linear models. Although not a new idea, they have been much more popular following the growth of computing power and availability of software.

Uses of multilevel models

Multilevel models have been used in education, to estimate separately the variance between pupils within the same school, and the variance between schools. In psychological applications, the multiple levels are comprised of items in an instrument, individuals, and families. Different covariables may be relevant on different levels. They can be used for longitudinal studies, as with growth studies, to separate changes within one individual and differences between individuals.

Software

• HLM
• SAS's PROC MIXED function
• MLwiN
• aML
• R's lme4 package (Free - Open Source)