Good Literature about Problems with R squared A question from a newbie. Recently, I was told that R squared or adjusted R squared can not used as a criteria to select a good regression model (model selection) due to, for example, overfitting . I have been searching for literature about this issue. Anyone can point me to to some good literature or empirical evidence which can be used as references. Thanks in advance.
 A: There is a huge discussion, lasting for years, on which model selection is "better" or "best" and there is not a definite answer on that. It depends on your data, models you compare, your definition of "best" model (i.e. "the simplest one" or "the best fitting one"). There's also lots of different methods: AIC, BIC, TIC, Deviance, WAIC, $R^2$, Mallow’s $C_p$ etc. Also, for linear regression AIC and $R^2$ have much in common (e.g. check this discussion). In most cases you can find arguments for and against each of this methods and in practice you use a combination of those and not single method alone.
On the literature you could check Wikipedia on $R^2$ (and the references quoted there), the article by Burnham & Anderson (2004), or their book. You can find nice chapters on model selection also on this two books. Googling could lead you to some more papers and books or Monte Carlo simulation papers but you won't find a definite answer on which method is "best" and "appropriate".
AIC is more general and could be applied for a greater variety of models, but, on another hand, $R^2$ has some nice properties - e.g. it could be understood (or sometimes misunderstood) as "variance explained" and has always the same [0, 1] range, so you can apply it to compare models computed on different datasets etc., so there there are approaches to generalize this method e.g. for GLM or LMM.
