[R] extend summary.lm for hccm?

[Achim Zeileis]

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.

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