[Rd] proposal: allowing alternative variance estimators in glm/lm
tlumley at u.washington.edu
Wed Dec 27 18:54:36 CET 2006
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
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 Lumley Assoc. Professor, Biostatistics
tlumley at u.washington.edu University of Washington, Seattle
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