Skip to main content

Linear Mixed-Effects Models: Basic Concepts and Examples

  • Chapter

Part of the Statistics and Computing book series

Abstract

Many common statistical models can be expressed as linear models that incorporate both fixed effects, which are parameters associated with an entire population or with certain repeatable levels of experimental factors, and random effects, which are associated with individual experimental units drawn at random from a population. A model with both fixed effects and random effects is called a mixed-effects model.

This is a preview of subscription content, access via your institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Chambers, J. M. and Hastie, T. J. (eds) (1992). Statistical Models in S, Chapman & Hall, New York.

    MATH  Google Scholar 

  • Devore, J. L. (2000). Probability and Statistics for Engineering and the Sciences, 5th ed., Wadsworth, Belmont, CA.

    Google Scholar 

  • Goldstein, H. (1995). Multilevel Statistical Models, Halstead Press, New York.

    Google Scholar 

  • Lindley, D. and Smith, A. (1972). Bayes estimates for the linear model, Journal of the Royal Statistical Society, Ser. B 34: 1–41.

    MATH  MathSciNet  Google Scholar 

  • Milliken, G. A. and Johnson, D. E. (1992). Analysis of Messy Data. Volume 1: Designed Experiments, Chapman & Hall, London.

    Google Scholar 

  • Potthoff, R. F. and Roy, S. N. (1964). A generalized multivariate analysis of variance model useful especially for growth curve problems,;; Biometrika 51: 313–326.

    MATH  MathSciNet  Google Scholar 

  • Sakamoto, Y., Ishiguro, M. and Kitagawa, G. (1986). Akaike Information Criterion Statistics, Reidel, Dordrecht, Holland.

    MATH  Google Scholar 

  • Schwarz, G. (1978). Estimating the dimension of a model, Annals of Statistics 6: 461–464.

    MATH  CrossRef  MathSciNet  Google Scholar 

  • Venables, W. N. and Ripley, B. D. (1999). Modern Applied Statistics with S-PLUS, 3rd ed., Springer-Verlag, New York.

    MATH  Google Scholar 

Download references

Rights and permissions

Reprints and Permissions

Copyright information

© 2000 Springer Verlag New York, LLC

About this chapter

Cite this chapter

(2000). Linear Mixed-Effects Models: Basic Concepts and Examples. In: Mixed-Effects Models in Sand S-PLUS. Statistics and Computing. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-0318-1_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4419-0318-1_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4419-0317-4

  • Online ISBN: 978-1-4419-0318-1

  • eBook Packages: Springer Book Archive