There is an option in syntax of FACTOR (factor analysis) command to just read a loading matrix and perform a rotation (e.g., varimax) of the factors. It is ordered like
FACTOR /MATRIX= IN(FAC=*)
/CRITERIA ITERATE(50) RCONVERGE(.0001)
/ROTATION VARIMAX.
I was surprised with that if I suggest a loading matrix with m (number of factors) > p (number of variables), FACTOR would take in and rotate only the square p x p portion of the matrix. The "surplus" factors are simply unnoticed.
I don't think it is correct behaviour, because a rotation operation (such as varimax, quartimax, etc.) itself does not require m<p. It is the factor extraction which will demand m<p or m<=p.
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Kirill Orlov
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