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Journal of Dairy Science Vol. 76 No. 8 2320-2324
© 1993 by American Dairy Science Association ®
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A Simple Argument Showing How to Derive Restricted Maximum Likelihood

J. L. Foulley 1

1 National Institute for Agricultural Research, Quantitative and Applied Genetics Unit, 78352 Jouy-en-Josas Cedex, France

This paper presents a pedagogical argument to explain to quantitative geneticists how REML can be derived from maximum likelihood for estimation of variance components. The argument is first developed for N independent normal observations with mean µ and variance sigma and is afterward extended to a general linear mixed model structure, y sim N(Xß,V). The argument is taken from expectation-maximization theory and consists of replacement of a quadratic in µ or ß by its conditional expectation given the observed data and the variance components.

Key Words: variance components • mixed model • restricted maximum likelihood • expectation-maximization

Submitted on November 9, 1992
Accepted on March 19, 1993






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