st: Adjusted generalized r-squared, anyone?

["Clive Nicholas" <clivelists@googlemail.com>]

Is it legitimate to substitute Nagelkerke (1991) r-squared, thus

\bar{R}^{2}_{G}=1-\left( \frac{L(0)}{L(\hat{\theta})} \right)^{2/n}

in the equation for adjusted ('normal') r-squared, thus

\bar{R}^{2} = 1-(1-R^{2})\frac{n-1}{n-k-1}

?

I'd like to say the answer to this is obvious, but it isn't to me.
Google searching turned up nothing, and although there is a correction
for Ns in Nagelkerke r-squared, it doesn't appear to be the full df
correction that we see in adjusted r-squared.

Moreover, my lack of statistical sophistication daren't suggest

\bar{R}^{2}_{G}=1-\left( \frac{L(0)}{L(\hat{\theta})} \right)^{2/{n-1}{n-k-1}}

Or could it? Has it been already? Thoughts?

-- 
Clive Nicholas

[Please DO NOT mail me personally here, but at
<clivenicholas@hotmail.com>. Please respond to contributions I make in
a list thread here. Thanks!]

"My colleagues in the social sciences talk a great deal about
methodology. I prefer to call it style." -- Freeman J. Dyson.
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