I have read in the abstract of this paper that:
"The maximum likelihood (ML) procedure of Hartley aud Rao is modified by adapting a transformation from Patterson and Thompson which partitions the likelihood render normality into two parts, one being free of the fixed effects. Maximizing this part yields what are called restricted maximum likelihood (REML) estimators."
I also read in the abstract of this paper that REML:
"takes into account the loss in degrees of freedom resulting from estimating fixed effects."
Sadly I don't have access to the full text of those papers (and probably would not understand if I did).
Also, what are the advantages of REML vs. ML? Under what circumstances may REML be preferred over ML (or vice versa) when fitting a mixed effects model? Please give an explanation suitable for someone with a high-school (or just beyond) mathematics background!