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The best tool to resolve (multi-) collinearity is in my view the Cholesky-decomposition of the correlation/covariance matrix.
If the correlation-matrix, say R, is positive definite, then all entries on the diagonal of the cholesky-factor, say L, are non-zero (aka machine-epsilon). Btw, to use this tool for the collinearity-detection it must be implemented as to allow zero-eigenvalues, don't know, whether, for instance, you can use SPSS for this.
The number of on-zero entries in the diagonal indicate the actual rank of the correlation-matrix. And because of the triangular structure of the L-matrix the variables above the first occuring diagonal zero form a partial set of variables which is of reduced-rank. However, there may be some variables in that block, which do not belong to that set, so to find the crucial subset which contains only the multicollinearity you do several recomputations of the cholesky-decomposition, where you reorder the variables such that you find the smallest possible subset, which shows rank-reduction - so this is an iterative procedure. (If needed, I'll show an example where I use my MatMate-program for the script, later).