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RE: st: Unbalanced panel data + Adjusted R-square


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Unbalanced panel data + Adjusted R-square
Date   Tue, 10 Feb 2004 14:31:06 -0000

An overlapping set of prejudices on R-square can be found at 
http://www.stata.com/support/faqs/stat/rsquared.html

The spirit of adjusted R-sq is to penalise
for using up df. Sensible! yet unfortunately, the literature 
on AIC, BIC, etc., etc. shows that there are lots 
of ways of collapsing 

{goodness of fit, parsimony} 

on to a single number encapsulating 

{model virtue}

-- all highly defensible and yet all highly objectionable. 

Nick 
n.j.cox@durham.ac.uk 

Stas Kolenikov

> > How can I transform the R-square into an adjusted R-square?
> >
> > Is it correct to use the transformation for OLS models 
> (i.e.  adj. R-
> > square = 1-(1-R-square)*(n-1)/(n-k); where n=number of 
> observations and
> > k=number of parameters; see Gujarati (2002), p. 218)?
> 
> My two cents: I would tend to think that R2 only makes sense 
> for iid data.
> What most people tend to think about it is that it is "the 
> proportion of
> explained variance" -- is that the sense you want to put into it, too?
> Well, so what is the "variance", in your case? If you have any sort of
> heteroskedasticity, then the very concept of the disturbance 
> variance is
> not well defined: the variance of epsilon varies from one 
> observation to
> another, so there is no single number to quantify that. In the panel
> setting, you would want to think of the between panel and within panel
> terms (as -xtreg- does), even if you don't assume any 
> heteroskedasticity.

... 
 
> So the bottom line is, the R2, adjusted or not, does not 
> sound to me as a
> very interesting thing to look at in the panel setting. I 
> might be wrong
> though -- maybe there's something special that you need your 
> R2adj for?

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