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From |
Steve Samuels <sjsamuels@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: adjusted r-squared, regress with pweight |

Date |
Thu, 13 May 2010 10:14:23 -0400 |

Okay, I think that I've figured it out, and I apologize for the confusion. The adjusted R-square computed by -reg [pw] - corrects the weighted estimates of the MSE and population variance by the same corrections that would be appropriate for OLS regression on a sample of the same size. For the auto example with two covariates and one intercept, , n = 69, and the corrections to MSE and variance are (69/66) and (69/68), respectively. With these correction, adjusted R-square = 0.6218, the value given in e(r2_a). These can be interpreted as follows: The unadjusted and adjusted R-squared are estimates of those that would have been reported if one had done OLS on a SRS of n = 69. Adjusted R-squared is not, contrary to my original belief, a "population" estimate of anything. Steve On Thu, May 13, 2010 at 9:33 AM, Steve Samuels <sjsamuels@gmail.com> wrote: > I'm going to withdraw my conclusion that the adjusted R-square from > reg [pw] is incorrect, until I can figure out how Stata calculates > it.. I think that my hand calculation may be incorrect because the > population definition of "mean square error' is not as clear to me as > it was some months ago when I did it. This just reinforces Stas's > conclusion that these concepts are not too meaningful in a complex > survey setting. > > Steve > > > On Thu, May 13, 2010 at 8:59 AM, Steve Samuels <sjsamuels@gmail.com> wrote: >> I think that the adjusted r-square reported after -reg- with [pweight] >> is in error and that the displayed R-square is, in fact, adjusted >> R-square. I ran three weighted regressions (code below) >> >> I also directly calculated the adjusted r-square from svy: reg from >> the weighted estimates of mean square error Ve and population variance >> V: adjusted R-square = 1- Ve/V. ( agree with Stas that this has >> little practical value when data are heteroskedastic and clustered--it >> refers to >> >> The results were: >> Displayed R-square Adjusted r-square: >> reg [pw] 0.6300 0.6188 (e(r2_a) >> reg [fw] 0.6300 0.6268 (displayed) >> svy: reg 0.6300 0.6300 (direct) >> >> ************CODE***************** >> sysuse auto,clear >> reg mpg length trunk [pw=rep78] >> di e(r2_a) //adjusted r-square >> reg mpg length trunk [fw=rep78] >> >> svyset _n [pweight=rep78] >> svy: reg mpg length trunk >> ********************************** >> >> Steve >> >> --Stas Kolenikov to statalist >> Yes, David, it was asked before a number of times :)). Sum of squares >> and all that ANOVA stuff assumes the normal regression model (i.e., >> the regression errors follow N(0,sigma^2) distribution). pweights >> imply a probability sampling design, under which no distributional >> assumptions are made, so the ANOVA table is inappropriate. You can >> still compute all the sums of squares, of course, but they may not >> have readily available population analogues; and the distributional >> results for F-tests do not have the exact finite sample interpretation >> anymore (although you'd still be able to get asymptotic Wald tests, I >> imagine). >> >> Likewise, you should not expect these things to show up when you >> specify -robust- or -cluster- standard errors -- you know your data >> are heteroskedastic, so why on earth would you ask for some sort of >> averaged variance? >> Steven Samuels >> sjsamuels@gmail.com >> 18 Cantine's Island >> Saugerties NY 12477 >> USA >> Voice: 845-246-0774 >> Fax: 206-202-4783 >> > > > > -- > Steven Samuels > sjsamuels@gmail.com > 18 Cantine's Island > Saugerties NY 12477 > USA > Voice: 845-246-0774 > Fax: 206-202-4783 > -- Steven Samuels sjsamuels@gmail.com 18 Cantine's Island Saugerties NY 12477 USA Voice: 845-246-0774 Fax: 206-202-4783 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: adjusted r-squared, regress with pweight***From:*Steve Samuels <sjsamuels@gmail.com>

**References**:**st: adjusted r-squared, regress with pweight***From:*David Kantor <kantor.d@att.net>

**Re: st: adjusted r-squared, regress with pweight***From:*Stas Kolenikov <skolenik@gmail.com>

**Re: st: adjusted r-squared, regress with pweight***From:*Steve Samuels <sjsamuels@gmail.com>

**Re: st: adjusted r-squared, regress with pweight***From:*Steve Samuels <sjsamuels@gmail.com>

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