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From |
Richard Williams <[email protected]> |

To |
[email protected] |

Subject |
Re: st: R-SQUARED AND XTGEE |

Date |
Tue, 28 Oct 2003 21:35:23 -0500 |

At 01:46 AM 10/29/2003 +0000, Clive Nicholas wrote:

I'm not sure I understand (a)(i) -- Two Xs could be perfectly correlated with each other, and yet both could have zero correlation with Y. Can you elaborate or give an example?(a) Whatever is judged to be the 'best' measure of R^2, one *must* keep in mind that (i) high levels of intercorrelation between X-variables inflate R^2 to artifically-high levels; and (ii) models deploying aggregate-level data with large spatial units of analysis inevitably have knock-on (upward) effects on R^2, regardless of its measurement;

I agree that I would certainly be suspicious of a perfect R^2. But, there may not be anything else to explain -- it could just be that some percentage of what happens in the world is due to random, chance factors. Also, while you are correct in saying that in practice there will always be more to explain, an implication of that is that our models inevitably suffer from omitted variable bias -- which probably means that, not only have we failed to consider the effects of variables not included in the model, we have likely mis-estimated the effects of the variables we do have. So, I think an ideal goal is to make R^2 as high as it should be, but no higher, i.e. get a perfectly specified model, and if that produces an R^2 of .10 then so be it. If by some wild chance I ever did explain all the variability in a variable, I'm sure I could find some new variable to move on to, so I wouldn't be too worried about running out of challenges!(b) Why should *anybody* attempt to build a regression model that hopes to produce an R^2 of 100%? Anybody with half a brain on these matters will tell you that if your model has yielded a 'perfect' R^2, something is wrong (probably multicollinearity among two or three X-variables). When will people learn to love *low* levels of R^2? Low levels means there is more to explain, and thus stretches our academic imaginations by providing us with more challenges as to what the missing key factors might be.

I agree with that. The goal is correct model specification and R^2 may tell you little about how well you have met that goal. But if you do all these things you may find that a nice large R^2 comes along as an added bonus.If only social scientists, psychologists and economists alike simply focused on the theoretical and empirical validity and reliability of their variables and modelled social reality as accurately as possible in order to test theories about human behaviour, then this will tell us more than what R^2 tells us about *anything!* :-)

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Richard Williams, Associate Professor

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**Follow-Ups**:**st: MULTICOLLINEARITY & R-SQUARED***From:*"Clive Nicholas" <[email protected]>

**References**:**st: R-SQUARED AND XTGEE***From:*"Clive Nicholas" <[email protected]>

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