Multilevel modelling

Mark Tranmer, Social Statistics/CCSR.

Multilevel modelling is a quantitative statistical method to investigate variations and relationships for variables of interest, taking into account population structure and dependencies. These population structures may be hierarchical, such as pupils in classes in schools.

More complex non-hierarchal structures can also be considered, where groups overlap, or people can belong to more than one group. Major developments in multilevel modelling began in the 1980s, starting with hierarchical population structures. More recently, developments have been made for modelling realistically complex non-hierarchal structures, with improved computing and estimation methods.

Multilevel modelling is hence a flexible framework for testing sophisticated social, or other, theories. It allows us to look at individuals in context, including the way in which individuals change over time.


Examples include: exam score variations for pupils in schools, with a focus on school effectiveness and value-added analysis; variations in self-assessed health measures for individuals in households in areas; Looking at pupils’ progress over time in reading tests.

Diagram of 2 level hierachy

The figure below shows a simple 2 level hierarchy with pupils at level 1 and schools at level 2. Only a few pupils and schools are shown here for simplicity; in general there would be more pupils and schools.

For this structure we could, for example, use multilevel modelling to investigate variations in recently taken exam scores between pupils and schools, given information on pupils’ previous exam score, gender, age of school buildings, and percentage of pupils on free school meals.

chart using multilevel modelling to investigate variations in recently taken exam scores between pupils and schools

Web based resource

Further reading

  • An Introductory textbook: Snijders T & Bosker R (1999) Multilevel Analysis: An introduction to basic and advanced multilevel modelling. Sage
  • An Advanced Textbook: Goldstein (2003) Multilevel Statistical Models (3rd Edition). Edward Arnold
  • Historical Reference: Aitkin M. and Longford N. (1986). Statistical modelling issues in school effectiveness studies, JRSS (A), 149: 1-43.

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