Restricted maximum likelihood
In
maximum likelihood estimation that does not base estimates on a maximum likelihood fit of all the information, but instead uses a likelihood function calculated from a transformed set of data, so that nuisance parameters have no effect.[1]
In the case of
maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters.[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. A review of the early literature was given by Harville.[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 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.[8]
References
- ^ ISBN 0-19-920613-9. (see REML)
- ^ Baker, Bob. Estimating variances and covariances (broken, original link) available at the Wayback Machine [1]
- .
- .
- JSTOR 2286796.
- ^ "Detecting sparse signals in random fields, with an application to brain mapping" (PDF).
- ^ "SurfStat". www.math.mcgill.ca.
- ^ "fitlme Documentation". www.mathworks.com.
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