[R] Robust standard errors in logistic regression

[Thomas Lumley]

On Wed, 5 Jul 2006, Martin Maechler wrote:
>>>>>> "Celso" == Celso Barros <celso.barros at gmail.com>
>>>>>>     on Wed, 5 Jul 2006 04:50:29 -0300 writes:
>
> [...............]
>    Celso> By the way, I was wondering if there is a way to use rlm (from MASS)
>    Celso> to estimate robust standard errors for logistic regression?
>
> rlm stands for 'robust lm'.  What you need here is  'robust glm'.
>
> I've already replied to a similar message by you,
> mentioning the (relatively) new package "robustbase".
> After installing it, you can
> use
> 	robustbase::glmrob()

We have a clash of terminology here.  The "robust standard errors" that 
"sandwich" and "robcov" give are almost completely unrelated to glmrob(). 
My guess is that Celso wants glmrob(), but I don't know for sure.

The Huber/White sandwich variance estimator for parameters in an ordinary 
generalized linear model gives an estimate of the variance that is 
consistent if the systematic part of the model is correctly specified and 
conservative otherwise.  It is a computationally cheap linear 
approximation to the bootstrap.  These variance estimators seem to usually 
be called "model-robust", though I prefer Nils Hjort's suggestion of 
"model-agnostic", which avoids confusion with "robust statistics". This is 
what sandwich and robcov() do.

glmrob() and rlm() give robust estimation of regression parameters. That 
is, if the data come from a model that is close to the exponential family 
model underlying glm, the estimates will be close to the parameters from 
that exponential family model.  This is a more common statistical sense of 
the term "robust".


I think the confusion has been increased by the fact that earlier S 
implementations of robust regression didn't provide standard errors, 
whereas rlm() and glmrob() do. This was partly a quality-of-implementation 
issue and partly because of theoretical difficulties with, eg, lms().


 	-thomas

Thomas Lumley			Assoc. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle