title 'Factor analysis: estimation methods, artificial example';

data twofact(type=CORR);
  _type_='CORR';
  input _name_ $ Y1 Y2 Y3 Y4 Y5 Y6;
  datalines;
Y1  1.00  .20  .24  .00  .00  .00
Y2   .20  1.0  .30  .00  .00  .00
Y3   .24  .30  1.0  .00  .00  .00
Y4   .00  .00  .00  1.0  .56  .63
Y5   .00  .00  .00  .56  1.0  .72
Y6   .00  .00  .00  .63  .72  1.0
;

*-- A PCA will not recover the correct factor pattern;
proc factor data=twofact nfact=2;

*-- Using the true communalities will recover the factor pattern;
proc factor data=twofact nfact=2;
   priors .16  .25  .36  .49  .64  .81;

*-- Using SMC;
proc factor data=twofact nfact=2;
   priors smc;
   

*-- Using ML;
proc factor data=twofact nfact=2 method=ML;