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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 10:55:02 -0400 |

I couldn't leave it for long, and I've managed to hand calculate the adjusted r-square e(r2_a) 0.6188088229 reported by -reg [pw]- . My conclusion stands: adjusted r-square from a pweighted regression is an estimate of the one that would be obtained from OLS on a SRS of the same size. Steve On Thu, May 13, 2010 at 10:39 AM, Steve Samuels <sjsamuels@gmail.com> wrote: > Well, e(r2_a) was 0.6188, not 0.6218, my revised hand calculation, so > I still have not figured it out! I'll have to leave this for another > time, > > Steve > > On Thu, May 13, 2010 at 10:14 AM, Steve Samuels <sjsamuels@gmail.com> wrote: >> 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 >> > > > > -- > 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/

**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>

**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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