Poisson regression: computation of linear combination of coefficients. Should one use the scaled var-cov matrix?

windows XP
R 2.10

When computing the variance of a linear combination of the

coefficients from a Poisson regression (i.e. glm with log link and
offset) should one use the scaled or unscaled covariance matrix? For a
simple linear regression (i.e. lm), I believe we use the unscaled
matrix; for Poisson regression I believe we use the scaled matrix.

Questions: (1) Am I correct about the use of the scaled matrix for
the

Poisson regression?

(2) What is the difference between the scaled and unscaled matrices?
Thanks,
John

The scaled covariance matrix is the unscaled one multiplied by the 
dispersion, which is 1 for the Poisson and binomial families. I.e. they 
are one and the same in this case. For the Gaussian case, the dispersion 
is obtained from the the residual SS. In either case, the scaled version 
  is the one to use, although you might use it unscaled in Poisson.

One little mystery is why vcov.glm (which you might as well have used), 
does this:

{
     so <- summary.glm(object, corr = FALSE, ...)
     so$dispersion * so$cov.unscaled
}

rather than just return cov.scaled? (Historical reasons, I suspect).

John David Sorkin M.D., Ph.D.
Chief, Biostatistics and Informatics
University of Maryland School of Medicine Division of Gerontology
Baltimore VA Medical Center
10 North Greene Street
GRECC (BT/18/GR)
Baltimore, MD 21201-1524
(Phone) 410-605-7119
(Fax) 410-605-7913 (Please call phone number above prior to faxing)

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