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

From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>
Date: Sat 18 Jun 2005 - 08:42:43 EST

James Salsman <james@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.

-- 
   O__  ---- Peter Dalgaard             ุster Farimagsgade 5, Entr.B
  c/ /'_ --- Dept. of Biostatistics     PO Box 2099, 1014 Cph. K
 (*) \(*) -- University of Copenhagen   Denmark          Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk)                  FAX: (+45) 35327907

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Received on Sat Jun 18 08:51:50 2005

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