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International Journal of Epidemiology 2000;29:158-167
© International Epidemiological Association 2000

Principles of multilevel modelling

Sander Greenland

Department of Epidemiology, UCLA School of Public Health, 22333 Swenson Drive, Topanga, CA 90290, USA.

Background Multilevel modelling, also known as hierarchical regression, generalizes ordinary regression modelling to distinguish multiple levels of information in a model. Use of multiple levels gives rise to an enormous range of statistical benefits. To aid in understanding these benefits, this article provides an elementary introduction to the conceptual basis for multilevel modelling, beginning with classical frequentist, Bayes, and empirical-Bayes techniques as special cases. The article focuses on the role of multilevel averaging (‘shrinkage’) in the reduction of estimation error, and the role of prior information in finding good averages.

Keywords Bayesian statistics, empirical-Bayes estimation, hierarchical regression, mixed models, multilevel modelling, random-coefficient regression, ridge regression, risk assessment, Stein estimation

Accepted 29 June 1999


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