Peter Dalgaard <[EMAIL PROTECTED]> 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?
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 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 ______________________________________________ R-devel@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-devel
