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st: Factors correlated after -predict-... What is going wrong?


From   Trevor Zink <tzink@bren.ucsb.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Factors correlated after -predict-... What is going wrong?
Date   Wed, 11 Dec 2013 10:55:33 -0800

Hi Statalist,

I am using -factor- to develop three factors, rotating them using -rotate, varimax- and then produce variables from the factors using -predict-. Varimax is orthogonal rotation so should produce factors with zero correlation. Testing the factors' correlation after rotation with -estat common- produces the expected result, that correlation is 0. However, after I produce variables from the factors using -predict-, these new variables are correlated. How? Why? I tried replicating the steps using the example dataset from the manual (/r12/sp2), and in that case the predicted variables also have zero correlation. So, I guess it's something unique to my dataset, but I have no idea what. Any ideas?

Thanks,
Trevor Zink

Here's a code/out snippet:

. factor q3b q3c q3d q3e q3f q3g q3h q3l q3m, factor(3)
(obs=112)

Factor analysis/correlation Number of obs = 112 Method: principal factors Retained factors = 3 Rotation: (unrotated) Number of params = 24

--------------------------------------------------------------------------
         Factor  |   Eigenvalue   Difference Proportion   Cumulative
-------------+------------------------------------------------------------
        Factor1  |      2.05668      0.64145 0.5745       0.5745
        Factor2  |      1.41523      0.84971 0.3953       0.9698
        Factor3  |      0.56551      0.28624 0.1580       1.1278
        Factor4  |      0.27927      0.17225 0.0780       1.2058
        Factor5  |      0.10702      0.24115 0.0299       1.2357
        Factor6  |     -0.13413      0.07784 -0.0375       1.1982
        Factor7  |     -0.21198      0.02515 -0.0592       1.1390
        Factor8  |     -0.23712      0.02337 -0.0662       1.0728
        Factor9  |     -0.26049            . -0.0728       1.0000
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(36) = 290.70 Prob>chi2 = 0.0000

Factor loadings (pattern matrix) and unique variances

-----------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3 | Uniqueness
-------------+------------------------------+--------------
             q3b |   0.5642    0.2899   -0.2814 | 0.5184
             q3c |   0.4128    0.5956   -0.1803 | 0.4424
             q3d |   0.1122    0.5641   -0.1312 | 0.6520
             q3e |   0.2152    0.3567    0.0335 | 0.8253
             q3f |   0.4873   -0.2166    0.0502 | 0.7131
             q3g |   0.7222   -0.3959   -0.0625 | 0.3179
             q3h |   0.7545   -0.4174   -0.0195 | 0.2561
             q3l |   0.2966    0.3510    0.3937 | 0.6339
             q3m |   0.3045    0.1735    0.5232 | 0.6034
-----------------------------------------------------------

. rotate, varimax blanks(.3) factor(3)

Factor analysis/correlation Number of obs = 112 Method: principal factors Retained factors = 3 Rotation: orthogonal varimax (Kaiser off) Number of params = 24

--------------------------------------------------------------------------
         Factor  |     Variance   Difference Proportion   Cumulative
-------------+------------------------------------------------------------
        Factor1  |      1.86726      0.46529 0.5216       0.5216
        Factor2  |      1.40196      0.63377 0.3916       0.9132
        Factor3  |      0.76820            . 0.2146       1.1278
--------------------------------------------------------------------------
LR test: independent vs. saturated: chi2(36) = 290.70 Prob>chi2 = 0.0000

Rotated factor loadings (pattern matrix) and unique variances

-----------------------------------------------------------
        Variable |  Factor1   Factor2   Factor3 | Uniqueness
-------------+------------------------------+--------------
             q3b |   0.3402    0.6048           | 0.5184
             q3c |             0.7316           | 0.4424
             q3d |             0.5478           | 0.6520
             q3e |             0.3641           | 0.8253
             q3f |   0.5230                     | 0.7131
             q3g |   0.8243                     | 0.3179
             q3h |   0.8601                     | 0.2561
             q3l |                       0.5516 | 0.6339
             q3m |                       0.6139 | 0.6034
-----------------------------------------------------------
    (blanks represent abs(loading)<.3)

Factor rotation matrix

    -----------------------------------------
                 | Factor1  Factor2  Factor3
    -------------+---------------------------
         Factor1 |  0.8431   0.4610   0.2769
         Factor2 | -0.5334   0.7820   0.3224
         Factor3 | -0.0680  -0.4195   0.9052
    -----------------------------------------

. estat common

Correlation matrix of the varimax rotated common factors

    --------------------------------------------
         Factors |  Factor1   Factor2   Factor3
    -------------+------------------------------
         Factor1 |        1
         Factor2 |        0         1
         Factor3 |        0         0         1
    --------------------------------------------

. predict FUTURE DYNAMISM DIVERSITY
(regression scoring assumed)

Scoring coefficients (method = regression; based on varimax rotated factors)

    --------------------------------------------
        Variable |  Factor1   Factor2   Factor3
    -------------+------------------------------
             q3b |  0.07582   0.31198  -0.12150
             q3c |  0.00770   0.42358   0.01669
             q3d | -0.10003   0.24865   0.00936
             q3e | -0.02314   0.12156   0.08707
             q3f |  0.13150  -0.02809   0.05570
             q3g |  0.36793   0.01214  -0.05684
             q3h |  0.47400  -0.04866   0.02340
             q3l | -0.00905   0.02469   0.36526
             q3m | -0.00374  -0.04271   0.42293
    --------------------------------------------


. pwcorr FUTURE DYNAMISM DIVERSITY

             |   FUTURE DYNAMISM DIVERS~Y
-------------+---------------------------
      FUTURE |   1.0000
    DYNAMISM |   0.0301   1.0000
   DIVERSITY |   0.0418   0.1544   1.0000

.
end of do-file




--
Trevor Zink, MBA, MA
Ph.D. Candidate
UC Regents Special Fellow
Bren School of Environmental Science and Management
University of California, Santa Barbara
tzink@bren.ucsb.edu <mailto:tzink@bren.ucsb.edu>
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