In particular, REML is used as a method for fitting linear mixed models.
[2] The idea underlying REML estimation was put forward by M. S. Bartlett in 1937.
[1][3] The first description of the approach applied to estimating components of variance in unbalanced data was by Desmond Patterson and Robin Thompson[1][4] of the University of Edinburgh in 1971, although they did not use the term REML.
[5] 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, BLUPF90, wombat, Statistical Parametric Mapping and CropStat.
REML estimation is implemented in Surfstat, a Matlab toolbox for the statistical analysis of univariate and multivariate surface and volumetric neuroimaging data using linear mixed effects models and random field theory,[6][7] but more generally in the fitlme package for modeling linear mixed effects models in a domain-general way.