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.
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References
Demidenko, E. (2004). Mixed Models: Theory and Applications. John Wiley & Sons.
Harville, D.A. (1974). Bayesian inference for variance components using only error contrasts. Biometrika 61: 383–385.
Harville, D.A. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association 72: 320–338.
Jennrich, R.I., and Schluchter, M.D. (1986). Unbalanced repeated-measures models with structured covariance matrices. Biometrics 42:805–820.
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.
LaMotte, L.R. (1970). A class of estimators of variance components. Technical Report No. 10, Department of Statistics, University of Kentucky, Lexington, KY.
Littell, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D. (1996). SAS System for Mixed Models, Cary, NC: SAS Institute Inc.
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.
Searle, S.R., Casella, G., and McCulloch, C.E. (1992). Variance Components. John Wiley & Sons.
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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
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DOI: https://doi.org/10.1007/s00362-006-0335-6