Admissible Values of γ in Direct Oblimin Rotation

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Abstract
It is shown that for nonpositive values of the parameter γ in the oblimin criterion, the criterion achieves a minimum on the manifold of all possible oblique rotations of any given full rank initial loading matrix A. For every positive value of γ, on the other hand, it is shown that there exists a full rank initial loading matrix A for which the oblimin criterion does not achieve a minimum over the manifold of all oblique rotations of A. These results help explain the sometimes divergent behavior that results from using direct oblimin algorithms with γ set to a positive value.

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