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# Re: st: adjusted r-squared, regress with pweight

 From Steve Samuels 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

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