* FILE: factor.nmt.matrix.sas
* Illustrations of how various factor 
* rotation strategies give the same "predicted"
* corelation matrix. Data are from the national merit
* twins data set.
* Data are the scores on the National Merit 
* Scholarship Qualifying Exam. See file factor.nmt.sas
* for the code that generated these matrices
* ;
proc iml;
* matrix ufp in the unrotated principal components
  factor pattern matrix;
ufp = {0.84052  -0.08465,
       0.80421   0.47742,
       0.87832  -0.25013,
       0.83376   0.25885,
       0.86387  -0.35760};
rhat = ufp * ufp`;
print rhat (|format=6.3|) 'Rhat from unrotated principal components';

vrfp = {0.69134   0.48548,
        0.29637   0.88704,
        0.82813   0.38498,
        0.46164   0.74098,
        0.88746   0.29422};
rhat = vrfp * vrfp `;
print rhat (|format=6.3|) 'Rhat from varimax rotated factor pattern';

prfp =  {0.63264   0.28790,
        -0.02118   0.94850,
         0.84247   0.10599,
         0.24295   0.69877,
         0.95380  -0.03024};
rf = { 1.00000   0.63280,
       0.63280   1.00000};
rhat = prfp * rf * prfp`;
print rhat (|format=6.3|) 'Rhat from promax rotated factor pattern';
quit;