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Re: st: xtgee robust standard errors


From   Roger Newson <roger.newson@kcl.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: xtgee robust standard errors
Date   Fri, 16 Aug 2002 16:03:20 +0100

At 09:27 16/08/02 -0500, Roberto G. Gutierrez wrote:
Bo Cutter <wcutter@ucla.edu> asks:

> I am using the xtgee command to get robust standard error estimates for a
> random-effects panel data model. (i.e. xtgee..., family(gauss) link(ident)
> robust). p.446 of manual S-Z (last sentence, first paragaph) has a sentence
> that implies these robust standard errors are correct even if the
> panel-specific effect is correlated with the regressors. Can anyone tell me
> if I am interpreting this statement correctly ? And do you know what the
> reference behind this statement is ?

Yes, this statement is true. In general, the robust standard errors are a
true indicator of the sample-to-sample variability of your parameter estimates
even in mis-specified models.

As for a reference, try

Domowitz & White (1982). Misspecified models with dependent observations.
Journal of Econometrics, 20, 35-58.
Strictly speaking, it depends what you mean by "misspecified". According to -[R] xtgee-, the "robust" variances provided by -xtgee- are "semi-robust", or "semi-Huber" in the terminology of Newson (2000) and Hardin and Hilbe (2001). This means that, in general, they are asymptotically robust to mis-specification of the covariance structure, but not asymptotically robust to mis-specification of the conditional mean Y given X. However, if the link function is the canonical link for the variance function (or family), then the semi-Huber variance is also the full Huber variance, which is robust to mis-specification both of the covariance and of the conditional mean. The identity link is canonical for the Gaussian family, the inverse link is canonical for the gamma family, the inverse square link is canonical for the inverse Gaussian family, the logit link is canonical for the binomial family, and the log link is canonical for the Poisson family.

I hope this helps.

Roger

References

Hardin J, Hilbe J. Generalized linear models and extensions. College Station, TX: Stata Press; 2001.

Newson R. rglm: Robust variance estimates for generalized linear models. In Stata Technical Bulletin Reprints 2000; 181-190. College Station, TX: Stata Press; 2000.



--
Roger Newson
Lecturer in Medical Statistics
Department of Public Health Sciences
King's College London
5th Floor, Capital House
42 Weston Street
London SE1 3QD
United Kingdom

Tel: 020 7848 6648 International +44 20 7848 6648
Fax: 020 7848 6620 International +44 20 7848 6620
or 020 7848 6605 International +44 20 7848 6605
Email: roger.newson@kcl.ac.uk

Opinions expressed are those of the author, not the institution.

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