Statalist The Stata Listserver


[Date Prev][Date Next][Thread Prev][Thread Next][Date index][Thread index]

Re: st: Re: adjusted r square


From   Richard Williams <Richard.A.Williams.5@ND.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Re: adjusted r square
Date   Tue, 20 Feb 2007 19:29:26 -0500

At 10:34 AM 2/20/2007, Ulrich Kohler wrote:
However, as an aside: I do not find the arguments for the adjusted R2 very
convincing. It is sometimes said that you have to be punished for including
additional variables in a model. But why? Because the R2 increases? Why do I
need to be punished for this? It is just a simple fact that I can explain
more variance with an additional variable. Punishment and especially the
I don't think "punishment" is the original rationale for adjusted R^2, although that is often cited as one of its benefits. Rather, R^2 is biased upwards, especially in small samples. Adjusted R^2 corrects for that.

McClendon discusses this in "Multiple Regression and Causal Analysis", 1994, pp. 81-82.

Basically he says that sampling error will always cause R^2 to be greater than zero, i.e. even if no variable has an effect R^2 will be positive in a sample. When there are no effects, across multiple samples you will see estimated coefficients sometimes positive, sometimes negative, but either way you are going to get a non-zero positive R^2. Further, when there are many Xs for a given sample size, there is more opportunity for R^2 to increase by chance.

So, adjusted R^2 wasn't primarily designed to "punish" you for mindlessly including extraneous variables (although it has that effect), it was just meant to correct for the inherent upward bias in regular R^2.


-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
OFFICE: (574)631-6668, (574)631-6463
FAX: (574)288-4373
HOME: (574)289-5227
EMAIL: Richard.A.Williams.5@ND.Edu
WWW (personal): http://www.nd.edu/~rwilliam
WWW (department): http://www.nd.edu/~soc
*
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/




© Copyright 1996–2014 StataCorp LP   |   Terms of use   |   Privacy   |   Contact us   |   What's new   |   Site index