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Mixed Models

In: Regression

Author

Listed:
  • Ludwig Fahrmeir

    (University of Munich, Department of Statistics)

  • Thomas Kneib

    (University of Göttingen, Chair of Statistics)

  • Stefan Lang

    (University of Innsbruck, Department of Statistics)

  • Brian Marx

    (Louisiana State University, Experimental Statistics)

Abstract

Mixed models extend the predictor $$\eta \,=\,\boldsymbol{x}\prime\boldsymbol{\beta }$$ of linear, generalized linear, and categorical regression models by incorporating random effects or coefficients in addition to the non-random or “fixed” effects $$\boldsymbol{\beta }$$ . Therefore, mixed models are sometimes also called random effects models, and have become quite popular for analyzing longitudinal data obtained from repeated observations on individuals or objects in longitudinal studies. A closely related situation is the analysis of clustered data, i.e., when observations are obtained from objects selected by subsampling primary sampling units (clusters or groups of objects) in cross-sectional studies. For example, clusters may be defined by hospitals, schools, or firms, where data from (possibly small) subsamples of patients, students, or clients are collected.

Suggested Citation

  • Ludwig Fahrmeir & Thomas Kneib & Stefan Lang & Brian Marx, 2013. "Mixed Models," Springer Books, in: Regression, edition 127, chapter 7, pages 349-412, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-34333-9_7
    DOI: 10.1007/978-3-642-34333-9_7
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