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From |
Stas Kolenikov <skolenik@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: xtmixed with vce robust or cluster robust |

Date |
Mon, 31 Aug 2009 13:27:51 -0500 |

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. 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? 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. * * 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/

**Follow-Ups**:**RE: st: xtmixed with vce robust or cluster robust***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**References**:**st: xtivreg2 Random Effects and Durbin Wu Hausman***From:*"Yong, Sook (yong)" <s.yong@lancaster.ac.uk>

**st: xtmixed with vce robust or cluster robust***From:*John Antonakis <john.antonakis@unil.ch>

**Re: st: xtmixed with vce robust or cluster robust***From:*Stas Kolenikov <skolenik@gmail.com>

**RE: st: xtmixed with vce robust or cluster robust***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

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