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st: Calculating R2 for pweighted data.
From
Steve Samuels <[email protected]>
To
Judy Lee <[email protected]>, [email protected]
Subject
st: Calculating R2 for pweighted data.
Date
Wed, 28 Aug 2013 10:42:24 -0400
I'm forwarding a private question from Judy Lee, who referred to some
old posts of mine.
Dear Ms. Lee:
I didn't hand-calculate R2, just AdjR2 starting from R2.
********************************
sysuse auto,clear
reg mpg length trunk [pw=rep78]
di %15.10f e(r2)
di %15.10f e(r2_a) //adjusted r-square
di %15.10f 1 - (1- e(r2))*68/66 //by hand
*******************************
The latter is from the relation:
AdjR2 = 1 - (1 - R2)*(n-1)/(n - p -1),
where p = no. covariates
Please ask any further questions on Statalist, and be sure to read the
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Steven Samuels
> On Aug 26, 2013, at 6:07 PM, Judy Lee wrote:
>
> How do you hand calculate R^2? I cant seem to match with my regression from STATA
>
> Re: st: adjusted r-squared, regress with pweight
>
> From
>
> Steve Samuels <[email protected]>
> To
> [email protected]
> 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 <[email protected]> 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 <[email protected]> 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 <[email protected]> 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 <[email protected]> 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
>>>> [email protected]
>>>> 18 Cantine's Island
>>>> Saugerties NY 12477
>>>> USA
>>>> Voice: 845-246-0774
>>>> Fax: 206-202-4783
>>>>
>>>
>>>
>>>
>>> --
>>> Steven Samuels
>>> [email protected]
>>> 18 Cantine's Island
>>> Saugerties NY 12477
>>> USA
>>> Voice: 845-246-0774
>>> Fax: 206-202-4783
>>>
>>
>>
>>
>> --
>> Steven Samuels
>> [email protected]
>> 18 Cantine's Island
>> Saugerties NY 12477
>> USA
>> Voice: 845-246-0774
>> Fax: 206-202-4783
>>
>
>
>
> --
> Steven Samuels
> [email protected]
> 18 Cantine's Island
> Saugerties NY 12477
> USA
> Voice: 845-246-0774
> Fax: 206-202-4783
>
--
Steven Samuels
[email protected]
18 Cantine's Island
Saugerties NY 12477
USA
Voice: 845-246-0774
Fax: 206-202-4783
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• References:
• st: adjusted r-squared, regress with pweight
• From: David Kantor <[email protected]>
• Re: st: adjusted r-squared, regress with pweight
• From: Stas Kolenikov <[email protected]>
• Re: st: adjusted r-squared, regress with pweight
• From: Steve Samuels <[email protected]>
• Re: st: adjusted r-squared, regress with pweight
• From: Steve Samuels <[email protected]>
• Re: st: adjusted r-squared, regress with pweight
• From: Steve Samuels <[email protected]>
• Re: st: adjusted r-squared, regress with pweight
• From: Steve Samuels <[email protected]>
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