Within the mixed effects model world, REML has become the method of choice in order to correct for the downward bias in variance components. For years, I accepted this rationale without thinking about the potential effects this bias-correction might have on the estimator's variability.
Recently, however, I bumped into the article "On the inefficiency of the restricted maximum likelihood" (Longford, 2015), in which it is shown that "this unbiasedness is accompanied in some balanced designs by an inflation of the mean squared error". The author therefore aims to "encourage reevaluation of the uncritical preference for REML".
This makes me wonder; Why is the REML method of choice when it in fact increases the MSE, which is supposed to reflect the general quality of the estimator (i.e., low bias and low variability). Unbiasedness is a useful property, but in combination with large variability our estimate could still be located very far from the population value. From an applied researcher's perspective, wouldn't we prefer a slightly biased estimator, with lower variability?
I'd be happy with any intuitive explanations, as well as more detailed references to articles or books. Any reading material I've come across usually highlights the pros (i.e. how REML reduces bias), but the cons (e.g. MSE/variability) are hardly ever mentioned.
Thank you in advance!