[Rd] proposal: allowing alternative variance estimators in glm/lm

[Thomas Lumley]

There has been recent discussion about alternatives to the model-based 
standard error estimators for lm. While some people like the sandwich 
estimator and others don't, it is clear that neither estimator dominates 
the other for any sane loss function.  It is also worth noting that the 
sandwich estimator is the default for t.test().

I think it would be useful for models using other variance estimators to 
be able to inherit from lm and use summary.lm and predict.lm (and 
similarly for glm).  The main step in making this possible would be
moving the variance-covariance matrix computation that is currently 
duplicated in summary.lm and predict.lm into vcov.lm, and then having 
summary.lm and predict.lm call vcov().

This allows a fitting function (whether lm() or another function) to 
produce objects that inherit usefully from lm and glm but have other 
standard error estimators, by supplying a new vcov method for the class. 
The initial discusssion was about heteroscedasticity-consistent sandwich 
estimators, but from my point of view autocorrelation-consistent 
estimators and estimators that handle sampling weights are more 
interesting.

OOP purists might point out that the relationship involved is not, 
strictly speaking, inheritance.  They would be quite right. However, 
unless someone wants to rewrite glm and lm for S4 classes I think that 
battle is lost.


     -thomas

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