Residual Maximum Likelihood

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A Residual Maximum Likelihood is a maximum likelihood estimation that uses the likelihood function of a transformed dataset.



mixed model]]s. In contrast to the earlier maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters.

The idea underlying REML estimation was put forward by M. S. Bartlett in 1937. The first description of the approach applied to estimating components of variance in unbalanced data was by Desmond Patterson and Robin Thompson of the University of Edinburgh in 1971, although they did not use the term REML. A review of the early literature was given by Harville.

REML estimation is available in a number of general-purpose statistical software packages, including Genstat (the REML directive), SAS (the MIXED procedure), SPSS (the MIXED command), Stata (the mixed command), JMP (statistical software), and R (especially the lme4 and older nlme packages), as well as in more specialist packages such as MLwiN, HLM, ASReml, Statistical Parametric Mapping and CropStat.

REML estimation is implemented in Surfstat a Matlab toolbox for the statistical analysis of univariate and multivariate surface and volume.


  • (Oehlert, 2014) ⇒ Oehlert, G. W. (2014). A few words about REML.
    • REML is actually a way to estimate variance components. Once we have estimated variance components, we then assume that the estimated components are “correct” (that is, equal to their estimated values) and compute generalized least squares estimates of the fixed effects parameters. GLS is a version of least squares that allows us to account for covariances among the responses, such as might be present in a mixed effects model. Sometimes we get the same estimates using GLS that we would get using ordinary least squares, but not always. The variances we compute for our fixed effects can also differ between ordinary least squares and GLS. Butdon’t worry, all the GLS stuff will be done internally to lmer or lme. REML works by first getting regression residuals for the observations modeled by the fixed effects portion of the model, ignoring at this point any variance components (...)