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Stata FAQ
Using fautil

The fautil package contains six factor analysis utilities:

• facom is used to display the communalities after using the factor command.
• faform is used to transform the factor loadings to canonical form after using factor with the ml option.
• favar computes variance of rotated factors.
• fapara computes parallel analysis for eigenvalues comparing the eigenvalues of the factor analysis with eigenvalues of randomly generated variables to assist in determining the number of factors.

We will demonstrate their use with the hsb6 dataset containing 600 observations from the High School and Beyond survey. You can download this family of programs written by ATS by typing findit fautil (see How can I use the findit command to search for programs and get additional help? for more information about using findit).

use http://www.ats.ucla.edu/stat/stata/faq/hsb6, clear

factor locus concept mot read write math sci ss, pf
(obs=600)

            (principal factors; 3 factors retained)
  Factor     Eigenvalue     Difference    Proportion    Cumulative
------------------------------------------------------------------
     1        3.26431         2.81286      1.0136         1.0136
     2        0.45145         0.38003      0.1402         1.1538
     3        0.07142         0.12435      0.0222         1.1760
     4       -0.05293         0.00925     -0.0164         1.1596
     5       -0.06218         0.04246     -0.0193         1.1403
     6       -0.10464         0.02665     -0.0325         1.1078
     7       -0.13129         0.08446     -0.0408         1.0670
     8       -0.21575               .     -0.0670         1.0000

               Factor Loadings
    Variable |      1          2          3    Uniqueness
-------------+-------------------------------------------
       locus |   0.45240    0.23874    0.02028    0.73793
     concept |   0.10452    0.42593    0.08342    0.80070
         mot |   0.28873    0.42664   -0.06357    0.73057
        read |   0.83028   -0.06557    0.05675    0.30312
       write |   0.76978   -0.02423   -0.13154    0.38955
        math |   0.79117   -0.07648    0.04239    0.36640
         sci |   0.76408   -0.12571    0.14442    0.37952
          ss |   0.68823   -0.06691   -0.12974    0.50503

facom

         communalities
  locus         0.2621
concept         0.1993
    mot         0.2694
   read         0.6969
  write         0.6104
   math         0.6336
    sci         0.6205
     ss         0.4950

fapara, seed(123456789)
(obs=600)

Parallel Analysis for Eigenvalues

      Eigen   Random      Dif
c1   3.2643   0.1713   3.0930
c2   0.4515   0.1351   0.3164
c3   0.0714   0.0809  -0.0095
c4  -0.0529   0.0358  -0.0888
c5  -0.0622  -0.0331  -0.0291
c6  -0.1046  -0.0352  -0.0694
c7  -0.1313  -0.1204  -0.0109
c8  -0.2157  -0.1423  -0.0735

faplot 1 2 ld



rotate, promax(4) fac(2)

            (promax rotation)
               Rotated Factor Loadings
    Variable |      1          2    Uniqueness
-------------+--------------------------------
       locus |   0.28686    0.31079    0.73793
     concept |  -0.15801    0.48900    0.80070
         mot |   0.01717    0.50696    0.73057
        read |   0.83119    0.00359    0.30312
       write |   0.74850    0.04447    0.38955
        math |   0.80051   -0.01233    0.36640
         sci |   0.80447   -0.07025    0.37952
          ss |   0.69659   -0.01116    0.50503

favar

     fac1    fac2    fac3
   3.1319  0.5999  0.0714

factor locus concept mot read write math sci ss, ml

(obs=600)
number of factors adjusted to 4
Iteration 0:   log likelihood = -44.498916
Iteration 1:   log likelihood = -12.948465
Iteration 2:   log likelihood = -7.1820399
Iteration 3:   log likelihood =  -.5545783
Iteration 4:   log likelihood =  -.4870617
Iteration 5:   log likelihood = -.43017792
Iteration 6:   log likelihood = -.43001638
Iteration 7:   log likelihood = -.43000977

            (maximum likelihood factors; 4 factors retained)
  Factor     Variance       Difference    Proportion    Cumulative
------------------------------------------------------------------
     1        2.65567         1.52252      0.5770         0.5770
     2        1.13315         0.45423      0.2462         0.8232
     3        0.67892         0.54423      0.1475         0.9707
     4        0.13470               .      0.0293         1.0000

Test:  4 vs. no   factors.  Chi2(  32) = 1820.21, Prob > chi2 =  0.0000
Test:  4 vs. more factors.  Chi2(   2) =    0.85, Prob > chi2 =  0.6534

               Factor Loadings
    Variable |      1          2          3          4    Uniqueness
-------------+------------------------------------------------------
       locus |   0.35888    0.24486    0.24389    0.00936    0.75168
     concept |   0.01945    0.12649    0.55691   -0.20927    0.62960
         mot |   0.25425    0.07879    0.54745    0.15110    0.60664
        read |   0.62857    0.58298   -0.01051    0.10096    0.25465
       write |   1.00000   -0.00000   -0.00000   -0.00000    0.00000
        math |   0.63267    0.47960   -0.02118    0.01493    0.36905
         sci |   0.56916    0.60055   -0.09418   -0.16371    0.27975
          ss |   0.58527    0.34705   -0.01263    0.17541    0.50614

faform

Factor Loadings in Canonical Form

           1         2         3         4
r1   0.44850   0.21540   0.02576   0.01052
r2   0.10975   0.56299   0.11882  -0.16491
r3   0.30008   0.51942  -0.10106   0.15272
r4   0.83637  -0.06503   0.17560   0.10347
r5   0.86330  -0.06744  -0.48482  -0.12294
r6   0.78471  -0.07021   0.10123   0.00349
r7   0.77946  -0.13073   0.27029  -0.15024
r8   0.68355  -0.06534  -0.01858   0.14851

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