Restricted maximum likelihood
- Restricted maximum likelihood
In statistics, restricted (or residual) maximum likelihood (REML) is a method for fitting linear mixed models. In contrast to conventional maximum likelihood estimation, REML can produce unbiased estimates of variance and covariance parameters. [Baker, Bob. [http://homepage.usask.ca/~rjb609/stats4.html Estimating variances and covariances] ]
The method was first described by Patterson and Thompson [cite journal |last=Patterson |first=HD |coauthors= Thompson, R|year= 1971
title=Recovery of inter-block information when block sizes are unequal
journal=Biometrika |volume=58 |issue=3 |pages=545–554|doi=10.1093/biomet/58.3.545 .] , although they did not use the term REML. A review of the early literature was given by Harville. [cite journal |last=Harville|first=David A.|year= 1977
title=Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems
journal=Journal of the American Statistical Association
volume=72 |issue=358 |pages=320–338|url=http://links.jstor.org/sici?sici=0162-1459%28197706%2972%3A358%3C320%3AMLATVC%3E2.0.CO%3B2-9
doi=10.2307/2286796]
REML estimation is available in a number of general-purpose statistical software packages, including Genstat (the REML directive), SAS (the MIXED procedure), Stata (the xtmixed command), and R (the nlme package) ,as well as in more specialist packages such as MLwiN and ASReml.
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