From: Peter Dalgaard <p.dalgaard_at_biostat.ku.dk>

Date: Tue 01 Mar 2005 - 09:46:47 EST

Date: Tue 01 Mar 2005 - 09:46:47 EST

Peter Dalgaard <p.dalgaard@biostat.ku.dk> writes:

> Where I would have expected

*>
**> > (20*5*0.6917-2)/(5*(19-5*.6917))
**> [1] 0.8643953
**>
**> Does anyone have a clue as to what is going on here? Is mighty SAS
**> simply doing the wrong thing? The G-G epsilon depends only on the
**> eigenvalues of the observed covariance matrix, so surely the H-F
**> correction should depend only on the dimension and the DF for the
**> empirical covariance matrix?
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Just in case anyone was wondering, I think I now know what SAS is doing, and yes, it is a bug.

The HF correction is

HFeps = (n * (k-1) * GGeps - 2) / ((k-1) * ((n-1) - (k-1) * GG.eps))

for the simple two-way layout, where the residual SSD matrix has (n-1) degrees of freedom. For the case with covariates, it looks like (to 4 significant digits) SAS is generalizing the above to

HFeps = (n * (k-1) * GGeps - 2) / ((k-1) * (f - (k-1) * GG.eps))

where f is the degrees of freedom for the SSD. However, the first n also needs adjustment; the correctly generalized formula should read

HFeps = ((f+1) * (k-1) * GGeps - 2) / ((k-1) * (f - (k-1) * GG.eps))

(The G-G epsilon is essentially the squared mean of the eigenvalues of a suitably transformed SSD divided by the mean of the squares of the eigenvalues. This is less than one unless all eigenvalues are identical. H-F replaces numerator and denominator with bias-corrected variants. However, since everything is a function of the SSD matrix, sthe formula can only depend on n via the degrees of freedom.)

-- O__ ---- Peter Dalgaard Blegdamsvej 3 c/ /'_ --- Dept. of Biostatistics 2200 Cph. N (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - (p.dalgaard@biostat.ku.dk) FAX: (+45) 35327907 ______________________________________________ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-develReceived on Tue Mar 01 09:55:12 2005

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