Wolfgang Ludwig-Mayerhofer:
The Multilevel Modeling Page

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What is Multilevel Modeling?

Multilevel modeling (MM) is a family of statistical procedures that try to come to terms with influences that are located on different, well, levels. So naturally the question arises what is meant by "level".

One way to think about it is as follows: People do not live entirely on their own, but rather embedded in social units. Even though today, in a globalized world, we may say that people have relationships with other people all over the world, most people have some relationships that are more special than others. People who are linked together via special relationships frequently communicate among each other, and thus the possibility rises that the people you are linked to influence your views. So we may think about the individuals as one (the lowest) level and their network (whether it consists of people that are met in person or of people communication with whom may take place only via artifical media) as a next (higher) level.
(Note that "low" and "high" are just labels; we may well think about things the other way round. "High" just means something like "aggregate"; that is, several individuals – entities on the "low" level – are seen as agglutinated).

A second way: Opportunities structure the behaviour of individuals, and as many people select their opportunities by local proximity, the region in which a person lives may enhance or restrict his or her opportunity. For instance, if a person lives in a region with high unemployment, this may influence his or her behaviour about acceptable wage levels when looking for a new job.

A third way: Often people, be it voluntarily or not, are subject to common external influences. Take, for instance, a university professor. All the students that come to him or her are subject to her or his way of teaching. Could be that this way of teaching influences these students (even though this certainly – if sometimes fortunately – happens less frequently than we professors might desire). Again, we may think of a multitude of professors as the "higher" level units and of their many students as the "lower" level units.

For a variety of reasons, data referring to more than one level often cannot be analyzed by conventional statistical models. For instance, classical OLS regression analysis requires that residuals from individual observations are not correlated. This requirement becomes doubtful if these individual observations are subject to the same influences or are related to each other in other ways.

After so many words, this page – for the time being – does very little: It provides a few links to MM related pages, and it also provides selected references to the literature, with short comments.

Regrettably, updates of this page are quite limited:



Dear reader, the following remarks are intended to serve as a guide to the growing literature on multilevel modelling. They cover most of the textbooks and many of the "classical" papers by those statisticians who did most of the pathbreaking work.
Regrettably my overview covers only the years up to 1999 (even though I will try to stay up to date as far as textbooks are concerned)! Of course, since that time many useful new papers have appeared, but even though I take an occasional glance at some of them, I do not find the time to include them here. Please accept my apologies!

Note that the Centre for Multilevel Modeling now has a similar website that introduces you particularly to newer, and also to more specialised, books. (However, it does not treat the texts in German that are covered below).

Introductory texts (elementary and advanced) (this section is updated occasionally)

Other papers on multilevel random coefficient (or variance components) models (this section has seen very few updates since 1999)

Literature with emphasis on the "pre-random coefficients" stage in thinking about multilevel models

About the Author

This page is a process initiated and maintained by

Prof. Dr. Wolfgang Ludwig-Mayerhofer
Universität Siegen / University of Siegen
Philosophische Fakultät – Soziologie /Faculty of Arts – Sociology
57068 Siegen

Homepage at the University of Siegen

E-Mail: E-Mail
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Top of page | Last update: 25 May 2017