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


From   Stas Kolenikov <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: deriving a bootstrap estimate of a difference between two weighted regressions
Date   Tue, 3 Aug 2010 14:37:51 -0500

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.

-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.

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