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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 10:39:54 -0400 |

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 * * 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>

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

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