[R] adjusted R^2 vs. ordinary R^2

[Peter Dalgaard]

James Salsman <james at bovik.org> writes:

> I thought the point of adjusting the R^2 for degrees of
> freedom is to allow comparisons about goodness of fit between
> similar models with different numbers of data points.  Someone
> has suggested to me off-list that this might not be the case.
> 
> Is an ADJUSTED R^2 for a four-parameter, five-point model
> reliably comparable to the adjusted R^2 of a four-parameter,
> 100-point model?  If such values can't be reliably compared
> with one another, then what is the reasoning behind adjusting
> R^2 for degrees of freedom?


Well, the adjusted R^2 is the percent variance explained by
covariates. So it compares the conditional variance (given covariates)
to the marginal variance. This is less sensitive to DF issues than the
usual R^2, but it does still require that both quantities make sense.
This is not a given, and in particular the R^2 (either one) is quite
dubious when the covariates are chosen by design.

 
> What are the good published authorities on this topic?

Dunno. Common sense should really suffice in this matter.


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