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


From   Stas Kolenikov <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Cluster-correlated robust variance estimator for M regression
Date   Tue, 13 Oct 2009 12:49:32 -0500

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.

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