[R] generalized inverse using matinv (Design)

[Frank Paetzold]

i am trying to use matinv from the Design package
to compute the generalized inverse of the normal equations 
of a 3x3 design via the sweep operator.

That is, for the linear model 
y = µ + x1 + x2 + x1*x2 
where x1, x2 are 3-level factors and dummy coding is being used

the matrix to be inverted is

X'X =

9 3 3 3 3 3 3 1 1 1 1 1 1 1 1 1
3 3 0 0 1 1 1 1 0 0 1 0 0 1 0 0
3 0 3 0 1 1 1 0 1 0 0 1 0 0 1 0
3 0 0 3 1 1 1 0 0 1 0 0 1 0 0 1
3 1 1 1 3 0 0 1 1 1 0 0 0 0 0 0
3 1 1 1 0 3 0 0 0 0 1 1 1 0 0 0
3 1 1 1 0 0 3 0 0 0 0 0 0 1 1 1
1 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0
1 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0
1 0 0 1 1 0 0 0 0 1 0 0 0 0 0 0
1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0
1 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
1 0 0 1 0 1 0 0 0 0 0 0 1 0 0 0
1 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0
1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 0
1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1

this matrix has rank=9

however, matinv(X'X) falsely returns rank=4, 
no matter what the tolerance threshold eps is set to.

also the defining property of the 
generalized inverse 
             _ 
X'X %*% (X'X)  %*% X'X = X'X

is not satisfied.

if i use qr (from the base package) the rank is 
correctly determined as 9.

any ideas?

thank you

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