[R] extend summary.lm for hccm?

Charles C. Berry cberry at tajo.ucsd.edu
Tue Dec 26 18:24:04 CET 2006


On Mon, 25 Dec 2006, Achim Zeileis wrote:

> On Sun, 24 Dec 2006, John Fox wrote:
>
>> If I remember Freedman's recent paper correctly, he argues that sandwich
>> variance estimator, though problematic in general, is not problematic in the
>> case that White described -- an otherwise correctly specified linear model
>> with heteroscedasticity estimated by least-squares.
>
> More generally, sandwich-type estimators are valid (i.e., estimate
> the right quantity, although not necessarily precisely, as Frank pointed
> out) in situations where the estimating functions are correctly specified
> but remaining aspets of the likelihood (not captured in the estimating
> functions) are potentially not.

Not exactly. The asymptotic properites are good, but in samples of 
moderate size the properties (including both biasedness and variance) can 
be surprisingly bad. And if you are trying to calculate a p-value, getting 
a too-small variance estimate gives you spuriously small p-values. FWIW, 
I've seen a case in which the nominal size of a test based on the sandwich 
estimator was several orders of magnitude smaller than a test with correct 
nominal size.

There is a modest literature on this. Some refs:

Background Papers:

Drum M, McCullagh P. Comment. Statistical Science 1993; 8:300-301.

Freedman DA. On the So-Called "Huber Sandwich Estimator" and "Robust"
Standard Errors. The American Statistician, Volume 60, Number 4, 
November 2006, pp. 299-302(4)

-----

Some Proposed Corrections:

Fay MP and Graubard BI. Small-Sample Adjustments for
Walt-Type Tests Using Sandwich Estimators. Biometrics 2001; 57:
1198-1206.

Guo X, Pan W, Connett JE, Hannan PJ and French SA.  Small-sample
performance of the robust score test and its modifications in
generalized estimating equations Statistics in Medicine 2005;
24:3479-3495

Mancl LA and DeRouen TA, A Covariance Estimator for GEE with Improved
Small-Sample Properties. Biometrics 2001; 57:126-134.

Morel JG, Bokossa MC, and Neerchal NK.  Small Sample Correction for
the Variance of GEE Estimators Biometrical Journal 2003; 45(4):
395-409.

Pan W and Wall MM. Small-sample adjustments in using the
sandwich variance estimator in generalized estimating
equations. Statistics in Medicine  2002; 21:1429-1441.


HTH,

Chuck

>
> In linear models, it is easy to see what this means: the mean function has
> to be correctly specified (i.e., the errors have zero mean) but the
> correlation structure of the errors (i.e., their (co-)variances) might
> differ from the usual assumptions. In GLMs, in particular logistic
> regression, it is much more difficult to see against which types of
> misspecification sandwich-based inference is robust.
>
> Freedman's paper stresses the point that many model misspecifications also
> imply misspecified estimating functions (and in his example this is rather
> obvious) so that consequently the sandwich-type estimators estimate the
> wrong quantity.
>
> Best wishes,
> Z
>
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Charles C. Berry                        (858) 534-2098
                                          Dept of Family/Preventive Medicine
E mailto:cberry at tajo.ucsd.edu	         UC San Diego
http://biostat.ucsd.edu/~cberry/         La Jolla, San Diego 92093-0717



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