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RE: st: xtmixed with vce robust or cluster robust


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: xtmixed with vce robust or cluster robust
Date   Mon, 31 Aug 2009 22:34:21 +0100

Thanks, Stas, very insightful (as usual).  One thought below:

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Stas Kolenikov
> Sent: 31 August 2009 19:28
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: xtmixed with vce robust or cluster robust
> 
> On Mon, Aug 31, 2009 at 11:49 AM, Schaffer, Mark 
> E<M.E.Schaffer@hw.ac.uk> wrote:
> > If I'm estimating using -xtmixed- or -xtreg,mle-, it seems 
> natural to 
> > me that I'd want to be covered in the usual "robust" way: 
> the equation 
> > is misspecified enough to mess up the VCE but not enough to 
> make the 
> > coefficient estimates inconsistent, and by using a robust or 
> > cluster-robust VCE I can fix the former.
> >
> > Can you explain what's odd about this in terms that an applied 
> > econometrician can understand?
> 
> Mark,
> 
> your intuition is right: you have an M-estimation problem, 
> and there is nothing in the general theory of these that 
> precludes the sandwich estimator from working in this 
> instance. What I am GUESSING about mechanics of -_robust- 
> (and you probably know it better than I do after writing the 
> -ivreg2- stuff) is that it might be complicated to force 
> -_robust- to think about cluster-level scores only, as it is 
> used to operate on the observation level scores. This is kind 
> of wide-vs-long thing: the wide format with single line per 
> panel would be exactly what -_robust- looks for, but that's 
> not how Stata wants to think about every other panel data 
> estimation task -- way easier done with long data. May be I 
> am totally mistaken here; I never tried to dig into -_robust- 
> ado-file, so may be you could create a subsetting variable 
> -bysort cluster (id) : gen byte first = (_n==1)- and subset 
> the sample -if first- to force -_robust- to only use those 
> first observations.
> 
> A quick -viewsource xtmixed.ado- shows that it is written as 
> a -ml model d0- estimator. The likelihood is evaluated for 
> the model+data as a whole, and numeric derivatives are taken 
> by computing the likelihood at several points and taking the 
> required differences of those single numbers. See [ML] book 
> (Stata Corp. might consider distributing this as a part of 
> documentation... maybe?). So no kind of scores are produced 
> by -xtmixed- at all. I believe -xtreg- works by direct data 
> matrix manipulations, so it does not necessarily produce 
> scores, either.
> 
> So as a bottom line to the inner applied econometrician 
> sitting inside Mark is, "No theoretical obstacles; somebody 
> just needs to sit down and try to (1) get the appropriate 
> scores/estimating equations out of
> -xtreg- or -xtmixed-, and (2) code the sandwich estimator, 
> using or not using the official -_robust-". Given that Stata 
> Corp. did not have the resources to do this kind of coding 
> when these commands were released and updated, it may not be 
> as easy as it sounds.
> 
> John mentions -gllamm- where -cluster- and -robust- options 
> are available despite the data being in the long format. 
> -gllamm- is also implemented as -ml model d0- estimator. For 
> what I know, the sandwich estimator is hard coded in 
> -gllamm-; that is, Sophia R-H just re-wrote all the -_robust- 
> formulas... which might have been a relatively small 
> programming expense compared to numeric integration. So she 
> has done exactly what I said in the previous paragraph to be 
> "not as easy as it sounded".
> 
> Now, the meaning of -robust- standard errors after -xtmixed- 
> might be a somewhat of a mystery.

Is this analogous to the use of -robust- in a probit estimation?  I
remember reading a discussion by Dixit somewhere (I think it was in the
book he did for the World Bank about 10 years ago) about how allowing
for heteroskedasticity in a probit model makes no sense, because if the
variance isn't constant, a probit is not estimating anything
consistently (I think this is what the argument was ... several layers
of brain dust are getting in the way).  But estimating a probit model
with cluster-robust *does* make sense, because within-group correlation
or other failures of independence doesn't imply a probit is useless,
does mess up the usual classical SEs, and doesn't mess up cluster-robust
SEs (with enough assumptions etc. etc.)

Does this carry over here?  I.e.,

> With -regress-, the 
> -robust- option is correcting for heteroskedasticity: you 
> believe you modeled the first moments right, but not sure 
> about higher order moments (the second moments, in this 
> case). That's what Mark said: the model is bad, but not as 
> bad as to kill the point estimates. If you have 
> heteroskedasticity, your -xtmixed- model is likely wrong in 
> its variance part, and the variance parameters may not 
> necessarily correspond to well-defined population parameters.
> If so, what does the inference on these point estimates do? 

if I have, say, within-group correlation that the -xtmixed- model
doesn't model properly, does cluster-robust help?  For example, say my
-xtmixed- model is a lot better than nothing (in efficiency terms) but
there is still within-group dependence that is not properly modelled,
and I suspect this.  Would this be a reasonable rationale to want to use
cluster-robust?

I hope this makes sense - I am afraid my inner applied econometrician
might be starting to babble at this late hour....

--Mark

> Sandwich standard errors might have a role if you have 
> correctly modeled the first two moments in your -xtmixed-, 
> but unsure about higher moments, which I believe to be a 
> relatively peculiar situation for mixed models (although 
> pretty common to SEM world with Satorra-Bentler corrections).
> 
> Same interpretation comment applies to -gllamm-; frankly I 
> don't think I've ever tried to run it with -robust- option, 
> so I never had to bother explaining the meaning of sandwich 
> standard errors for -gllamm- :)).
> 
> I am just thinking aloud there; you are welcome to join me if 
> you like, but I cannot put my finger on anything other than 
> Huber's (1967) article 
> (http://www.citeulike.org/user/ctacmo/article/553268).
> 
> --
> Stas Kolenikov, also found at http://stas.kolenikov.name 
> Small print: I use this email account for mailing lists only.
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