A SIMPLE ARGUMENT SHOWING HOW TO DERIVE RESTRICTED MAXIMUM-LIKELIHOOD

This paper presents a pedagogical argument to explain to quantitative geneticists how REML can be derived from maximum likelihood for estima tion of variance components. The argument is first developed for N ind ependent normal observations with mean mu and variance sigma2 and is a fterward extended to a general linear mixed model structure, y approxi mately N(Xbeta,V). The argument is taken from expectation-maximization theory and consists of replacement of a quadratic in mu or beta by it s conditional expectation given the observed data and the variance com ponents.