RE: R-square statistic
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RE: R-square statistic

>Percent variance accounted for is an exactly analogous calculation, but
>based on mean squares.   Still, there is a problem in that the expected
>value of MS(Total) is influenced not only by the extent to which the model
>explains variation in the response variable, but also by the design of the
>experiment, for instance the number of replications of each level of a
>treatment factor.   I think the Genstat people would say that for this
>reason it is better to compare variance components.   Which is all very well
>for random effects, but what do you do with fixed effects...?
>Nick Galwey

Wouldn't the smallest var(e) not be the better criterion for best model?
(definitely much better than R2, for reasons just described by Nick)

A R2 type criterion (in the lines of what Nick described) could be 
1-(var(e)/var(E)) where var(E) is the residual variance
under a model with just fitting mu and var(e) the resid. variance under the 
current/best model.
This criterion is just as valid for fixed as for mixed models, and can be 
easily calculated with asreml.


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