[R] lm: RME vs. ML

[Peter Dalgaard]

JLucke at ria.buffalo.edu wrote:
> You need to give your criteria for "preferable".  For normal-linear 
> models, REML estimates of variances are unbiased, whereas ML estimates are 
> downwardly biased.  

I suspect that you can't actually say anything general about the
direction of the bias, except for the residual term. In the cases that
can be analyzed explicitly, variance estimates are complicated linear
combinations of sums of squares, and if those are not biased by the same
relative amount, the net result could conceivably be a positive bias. I
could be wrong though.

> My intuition is that the ML-induced bias would be 
> worse in small samples. I don't know about other distributions. Likewise I 
> don't know about MSE or other criterion for preference.
> 


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