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

[Steve Samuels <sjsamuels@gmail.com>]

My formula for the weighted mean above was wrong,  because I based it
on the wrong  weights for the average treatment effects. I can fix the
formula, but since you must bootstrap anyway,  I recommend Stas's
approach.

Steve

On Tue, Aug 3, 2010 at 3:37 PM, Stas Kolenikov <skolenik@gmail.com> wrote:
> 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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-- 
Steven Samuels
sjsamuels@gmail.com
18 Cantine's Island
Saugerties NY 12477
USA
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