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Can anyone explain what the differences are between $R^2$ vs. Adj$R^2$ in MuMIn function dredge?

The help file says only The character strings "$R^2$" and "adj$R^2$" are treated in a special way, and will add a likelihood-ratio based $R^2$ and modified-$R^2$ respectively to the result. Specifically, for a set of OLS linear regressions, am I correct to use $R^2$, not adj $R^2$?

From reading elsewhere, it appears the adj $R^2$ may be for non-linear models, though I at first thought it may the multiple $R^2$ for use with >1 predictor variable in the regression.

Ferdi
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ecologist1234
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  • It is not common at Crossvalidated to answer your own questions within less than an hour. Please don't do it again. – Ferdi Feb 02 '17 at 08:00
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    @Ferdi, I don't see a problem with that. Raising interesting problems and answering by yourself is even encouraged (I think it is mentioned on "the tour" of the site). (Whether this was an interesting problem is another question.) – Richard Hardy Feb 02 '17 at 12:16
  • @RichardHardy Thank you. I thought that this rather implies to when you find the answer to a question you had some months ago. – Ferdi Feb 02 '17 at 12:53
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    @Ferdi, The way I understood it was that time does not matter. If you know the answer even before posting the question but think this can be helpful for someone else in this wide world (e.g. you have spent a lot of time and effort finding the answer, and you think you might not be the only one to ever look for it), then you can post it, IMHO. E.g. [this](http://stats.stackexchange.com/questions/55929/what-is-an-unbiased-estimate-of-population-r-square) old thread is like that (answer posted an hour after the question). – Richard Hardy Feb 02 '17 at 13:31

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Adj $R^2$ provides Nagelkerke's modification of $R^2$ to correct for cases (esp. logistic regression) where the likelihood-ratio based $R^2$ MuMIn calculates would not otherwise have a maximum value of 1.

Found this in help file for function r.squaredLR.

Ferdi
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ecologist1234
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