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Re: st: Cluster-correlated robust variance estimator for M regression


From   James Shaw <shawjw@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Cluster-correlated robust variance estimator for M regression
Date   Tue, 13 Oct 2009 13:05:35 -0500

Thanks for the prompt response.  I suspected that the estimated
weights might factor into generating the scores, though I was not sure
how to implement them.  So, should I interpret the "scale" in your
code to be the derivative of the objective function with respect to
the parameters of interest?

I generally agree with your concerns about the jackknife, though it
seems to yield estimates that are similar to those provided by the
bootstrap in this case.  I am not a huge fan of M estimation.  The
only benefit it provides over quantile regression is efficiency, and
the resulting estimates lack the interpretability of quantile
regression estimates.  I am in need of a robust estimator for
longitudinal data that will not entail resampling for variance
estimation since I am resampling at another stage in my code.
Unfortunately, my options are limited.

--
Jim





On Tue, Oct 13, 2009 at 12:49 PM, Stas Kolenikov <skolenik@gmail.com> wrote:
> If you are familiar with the theory of M-estimates, you could write
> the scores functions from -rreg-. Fiddle with the rreg.ado code a
> little bit, it's a pretty cute program. After everything is converged,
> but before everything is dropped, you would need to add a line like
>
> gen _score = `res'/`scale'*`weight'
>
> (of course you would need to figure out what the derivative of the
> objective function with respect to the parameter is exactly, and what
> all these internals of -rreg- mean). Then feed these scores into
> -_robust- (you might have to change some of the dated -estimates-
> command, which are now -ereturn- commands, to make -_robust-
> understand what's going on). I don't think there's a better way of
> doing that. In fact, I won't be sure that -jackknife- will even be
> consistent for this, as it may have difficulty with the not-so-smooth
> objective functions used in -rreg-.
>
> I am personally not very convinced by the idea of running -rreg- on
> longitudinal data. My thinking is: "-rreg- is a maximum likelihood
> estimator for the distribution of the errors that has a smooth
> normal-like density near zero, and exponentially decaying Laplace-like
> density in the tails. And as the maximum likelihood estimator, it
> assumes the data to be i.i.d. When you have a random effect working on
> top of it, you will likely lose efficiency quite a bit by
> misspecifying the (quasi-)likelihood to be that of i.i.d. data". But
> that's a complicated argument, you know your model is most likely
> wrong, anyway :)).
>
> On Tue, Oct 13, 2009 at 10:40 AM, James Shaw <shawjw@gmail.com> wrote:
>> Dear Statalist Members:
>>
>> I am interested in fitting a regression model using the M estimator
>> (-rreg- in Stata) to longitudinal data.  I would like to apply the
>> cluster-robust variance estimator to account for arbitrary
>> intraclass/intracluster correlation.  Is there any way to derive
>> cluster-robust
>> variance estimates for M estimates short of using the jackknife or
>> bootstrap?  I'd like to avoid resampling procedures if possible.
>> -rreg- does not allow for the prediction of scores.  Otherwise, I
>> would use _robust or -suest- or do the necessary programming myself.
>>
>> Thank you for your assistance.
>>
>> Regards,
>>
>> James W. Shaw, Ph.D., Pharm.D., M.P.H.
>> Assistant Professor
>> Department of Pharmacy Administration
>> College of Pharmacy
>> University of Illinois at Chicago
>> 833 South Wood Street, M/C 871, Room 252
>> Chicago, IL 60612
>> *
>> *   For searches and help try:
>> *   http://www.stata.com/help.cgi?search
>> *   http://www.stata.com/support/statalist/faq
>> *   http://www.ats.ucla.edu/stat/stata/
>>
>
>
>
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name
> Small print: I use this email account for mailing lists only.
>
> *
> *   For searches and help try:
> *   http://www.stata.com/help.cgi?search
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/
>



-- 
James W. Shaw, Ph.D., Pharm.D., M.P.H.
Assistant Professor
Department of Pharmacy Administration
College of Pharmacy
University of Illinois at Chicago
833 South Wood Street, M/C 871, Room 252
Chicago, IL 60612

*
*   For searches and help try:
*   http://www.stata.com/help.cgi?search
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



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