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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. > * > * 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/ > -- Heriot-Watt University is a Scottish charity registered under charity number SC000278. * * 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/

**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>

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

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