[R] generalized inverse using matinv (Design)

[Frank Paetzold]

thank you all.

i have deliberately chosen matinv (although obviously 
an outdated version) because it uses the sweep operator.
i know of other methods to calculate generalized inverses.
however, it is also true that the sweep operator is capable of 
computing g2 generalized inverses. 

The ginv returns the Moore-Penrose inverse, which has nicer 
numerical properties if computed by svd, but it is just not 
what i want.
(besides, svd is very slow and should not be applied to the normal 
equations anyway)

so lets explain my peculiar interest in matinv:
i am trying get my head around the type III SS that 
SAS popularized. i know that those hypotheses are 
hated in the R community but they are the standard 
hypothesis given by all other statistics software.
i know how to compute type III SS and how to translate them 
to meaningful hypothesis of the cell means model.
but i do not have an intuitive understanding why 
they are computed as they are.

so i came across my matinv problem when i tried to 
to compute the generating matrix
              _  
H = (X'X)  X'X

used for the construction of estimable functions.
if the g2-inverse is used, then H has canonical form
which simpifies the interpretion. 
i just wanted to check if it is invariant to cell frequencies.

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