Skip to main content
Log in

A direct derivation of the REML likelihood function

  • Notes
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

The original derivation of the widely cited form of the REML likelihood function for mixed linear models is difficult and indirect. This paper derives it directly using familiar operations with matrices and determinants.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Demidenko, E. (2004). Mixed Models: Theory and Applications. John Wiley & Sons.

  2. Harville, D.A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61: 383–385.

    Article  MATH  MathSciNet  Google Scholar 

  3. Harville, D.A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association 72: 320–338.

    Article  MATH  MathSciNet  Google Scholar 

  4. Jennrich, R.I., and Schluchter, M.D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42:805–820.

    Article  MATH  MathSciNet  Google Scholar 

  5. Laird, N. (2004). Analysis of Longitudinal and Cluster-Correlated Data. NSFCBMS Regional Conference Series in Probability and Statistics, Volume 8, Beachwood, Ohio: Institute of Mathematical Statistics.

    Google Scholar 

  6. LaMotte, L.R. (1970). A class of estimators of variance components. Technical Report No. 10, Department of Statistics, University of Kentucky, Lexington, KY.

    Google Scholar 

  7. Littell, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D. (1996). SAS System for Mixed Models, Cary, NC: SAS Institute Inc.

    Google Scholar 

  8. Searle, S.R. (1979): Notes on variance component estimation. A detailed account of maximum likelihood and kindred methodology. Technical Report BU-673-M, Biometrics Unit, Cornell University, Ithaca, New York.

    Google Scholar 

  9. Searle, S.R., Casella, G., and McCulloch, C.E. (1992). Variance Components. John Wiley & Sons.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

LaMotte, L.R. A direct derivation of the REML likelihood function. Statistical Papers 48, 321–327 (2007). https://doi.org/10.1007/s00362-006-0335-6

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00362-006-0335-6

Key words

Navigation