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Re: st: deriving a bootstrap estimate of a difference between two weighted regressions


From   "Ariel Linden, DrPH" <ariel.linden@gmail.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   Re: st: deriving a bootstrap estimate of a difference between two weighted regressions
Date   Wed, 4 Aug 2010 10:07:59 -0700

Thank you, Stas. I will take your suggestions under advisement!



Date: Tue, 3 Aug 2010 14:37:51 -0500
From: Stas Kolenikov <skolenik@gmail.com>
Subject: Re: st: deriving a bootstrap estimate of a difference between two
weighted regressions

On Tue, Aug 3, 2010 at 1:20 PM, Ariel Linden, DrPH <ariel.linden@gmail.com>
wrote:
> Thank you Stas and Steve for your comments!
>
> When I stated that the first model's weight would be ATT and the next 
> ATC, it was already after running the propensity score model and 
> establishing
the
> weights for each subject:
> ATT = cond(treatvar, 1, propvar/(1- propvar)), and ATC = 
> cond(treatvar, (1-propvar)/propvar, 1)
>
> Under these conditions, there should be no negative weights, so that 
> is
not
> a concern.

The negative weights would come out of Steve's suggestion to entertain the
difference in weights (as that's what your procedure boils down to).

> I am thinking that the code would look something like this, but I 
> would appreciate your input:
>
> 1. bootstrap _b[treatvar] from first regression with [pw=ATT] 2. save 
> 10,000 samples to file (or tempfile) 3. bootstrap _b[treatvar] from 
> second regression with [pw=ATC] 4. save 10,000 samples to file (or 
> tempfile) 5. gen difference = treatvar1-treatvar2 6. bootstrap 
> r(mean): sum  difference, to get bootstrapped CIs
>
> Does this make sense?

1-2 will produce something very similar to the _se[treatvar] in your basic
regression with ATT weights (probably with -robust- option), and
3-4 will produce something very similar to _se[treatvar] in the regression
with ATC weights. I outlined the code for you in the previous message -- you
need to bootstrap the whole estimation procedure = { the propensity
regression (leading to the weights) + two main regressions with two sets of
weights }. In other words, for each bootstrap sample, you would need to run
everything in the curly brackets to produce your "difference" estimate.

I cannot comment on the scientific validity of this procedure; other people
more knowledgeable in treatment effect estimation could do that.



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