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From |
Mark Schaffer <M.E.Schaffer@hw.ac.uk> |

To |
statalist@hsphsun2.harvard.edu, Constantine Daskalakis <c_daskalakis@entwhistle.jci.tju.edu> |

Subject |
Re: st: Robust variances |

Date |
Sat, 24 May 2003 00:44:22 +0100 (BST) |

Constantine, Quoting Constantine Daskalakis <c_daskalakis@entwhistle.jci.tju.edu>: > At 04:48 PM 5/23/03, Mark Schaffer wrote: > >Hi everybody. With respect to clustering, > > > >Personally, I think this problem is VERY easy to stumble into > [decoded = > >I've done it myself] and could do with much more highlighting in > the > >manuals, and in the on-line help and error messages. > > > >--Mark > > I am confused. > > Consider the simplest case where I compute a robust variance from > all the > data (ie, a single cluster). Are you saying that I get information > equivalent to an observation of 1? If you have a single cluster and you treat each observation within the cluster as independent, then the Omega_hat matrix used in the matrix product 1/N * X' * Omega_hat * X has a diagonal of squared residuals. Each observation contributes a different residual. This would be the standard Eicker-Huber-White-"sandwich" robust (but not cluster-robust) covariance estimator. No problem here. This isn't what Stata does for cluster-robust SEs. The point of using cluster-robust SEs is to relax the independence assumption: the estimate of the var-cov matrix is robust to arbitrary intra-cluster correlation. Observations within a cluster can be correlated (or not) in any fashion, it doesn't matter so long as you assume that observations across clusters are independent. To get the cluster-robust SEs, Stata aggregates clusters to get the "super-observations" to which I referred in my previous email. The Omega_hat matrix in this case is block diagonal - each block consists of the "super-observation" contributed by a cluster, and the off-diagonal blocks are zeros because of the independence-across-clusters-assumption. Now if you have a single cluster, you aggregate and you get a single super- observation. The rank of the cluster-robust var-cov matrix will be one (see help j_robustsingular from within Stata for more on this) and of course inference will be impossible. It makes sense if you think about it. Standard errors that are robust to arbitrary intra-cluster correlation means that *any* correlation between observations within a cluster is OK, and the SEs will still be consistent. No scheme for estimating the variance-covariance matrix will get you this if you have only one cluster! This is equivalent to asking for consistent SEs without imposing any structure on the variance-covariance matrix at all. You have N observations, but N*(N-1)/2 correlations and there's no way you can get an estimate of that. Minor point in passing - the Stata manuals refer to Rogers (1993) as the source for the cluster-robust approach (I think he used to work at Stata Corp) but as far as I can tell, Hal White should get the credit - it's described in his 1984 book Asymptotic Theory for Econometricians. --Mark > That is certainly not the case. > Only if > the actual correlation is 1, I will get an "effective" N of 1. If > the > actual correlation is 0, I will get an "effective" N similar to my > original > observations. In this simple case, are you then saying that the > robust > variance is nonsense? The Liang and Zeger GEE approach does exactly > that > and it's been shown to be consistent in lots of situations, so your > point > must be different. > > Maybe you're arguing that, with a single cluster, the robust > variance is > fine, but when you sum across clusters, then you have to have a > "large > number" of clusters? > > Any comments/direction from the good Stata people on this? > > cd > > > > > > The documents accompanying this transmission may contain > confidential > health or business information. This information is intended for the > use of > the individual or entity named above. If you have received this > information > in error, please notify the sender immediately and arrange for the > return > or destruction of these documents. > ________________________________________________________________ > > Constantine Daskalakis, ScD > Assistant Professor, > Biostatistics Section, Thomas Jefferson University, > 125 S. 9th St. #402, Philadelphia, PA 19107 > Tel: 215-955-5695 > Fax: 215-503-3804 > Email: c_daskalakis@mail.jci.tju.edu > Webpage: > http://www.kcc.tju.edu/Science/SharedFacilities/Biostatistics > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > Prof. Mark Schaffer Director, CERT Department of Economics School of Management & Languages Heriot-Watt University, Edinburgh EH14 4AS tel +44-131-451-3494 / fax +44-131-451-3008 email: m.e.schaffer@hw.ac.uk web: http://www.sml.hw.ac.uk/ecomes ________________________________________________________________ DISCLAIMER: This e-mail and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom it is addressed. If you are not the intended recipient you are prohibited from using any of the information contained in this e-mail. In such a case, please destroy all copies in your possession and notify the sender by reply e-mail. Heriot Watt University does not accept liability or responsibility for changes made to this e-mail after it was sent, or for viruses transmitted through this e-mail. Opinions, comments, conclusions and other information in this e-mail that do not relate to the official business of Heriot Watt University are not endorsed by it. ________________________________________________________________ * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Robust variances***From:*"Scott Merryman" <smerryman@kc.rr.com>

**References**:**Re: st: Mantel-Haenszel vs. clustered logistic - please help***From:*Constantine Daskalakis <c_daskalakis@entwhistle.jci.tju.edu>

**st: Mantel-Haenszel vs. clustered logistic - please help***From:*Ricardo Ovaldia <ovaldia@yahoo.com>

**Re: Re: st: Stata crashes using test after***From:*Ricardo Ovaldia <ovaldia@yahoo.com>

**st: Robust variances***From:*Constantine Daskalakis <c_daskalakis@entwhistle.jci.tju.edu>

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