As it was already pointed out by others, you used different methods
(principal components in SAS vs. factor analysis in R). When you use the
same method (+ varimax rotation) in both programs, there may still be a
*small* difference: this comes from (possibly) different stopping criteria.
In R, the default stopping criterion in varimax is eps = 1e-5; I've once set
it to 1e-12 to make the results *almost* identical with the output of
another program (Statistica).

Kenn

On Tue, Mar 31, 2009 at 3:17 PM, John Fox <jfox@mcmaster.ca> wrote:

> Dear TY,
>
> Considering that you used different methods -- maximum-likelihood factor
> analysis in R and principal components analysis in SAS -- the results are
> quite similar (although the three rotated factors/components come out in
> different orders).
>
> I hope this helps,
>  John
>
> > -----Original Message-----
> > From: r-help-bounces@r-project.org [mailto:r-help-bounces@r-project.org]
> On
> > Behalf Of Tae-Young Heo
> > Sent: March-31-09 7:07 AM
> > To: r-help@r-project.org
> > Subject: [R] Factor Analysis Output from R and SAS
> >
> > Dear Users,
> >
> > I ran factor analysis using R and SAS. However, I had different outputs
> from
> > R and SAS.
> > Why they provide different outputs? Especially, the factor loadings are
> > different.
> > I did real dataset(n=264), however, I had an extremely different from R
> and
> > SAS.
> > Why this things happened? Which software is correct on?
> >
> > Thanks in advance,
> >
> > - TY
> >
> > #R code with example data
> >
> >  # A little demonstration, v2 is just v1 with noise,
> >  # and same for v4 vs. v3 and v6 vs. v5
> >  # Last four cases are there to add noise
> >  # and introduce a positive manifold (g factor)
> >  v1 <- c(1,1,1,1,1,1,1,1,1,1,3,3,3,3,3,4,5,6)
> >  v2 <- c(1,2,1,1,1,1,2,1,2,1,3,4,3,3,3,4,6,5)
> >  v3 <- c(3,3,3,3,3,1,1,1,1,1,1,1,1,1,1,5,4,6)
> >  v4 <- c(3,3,4,3,3,1,1,2,1,1,1,1,2,1,1,5,6,4)
> >  v5 <- c(1,1,1,1,1,3,3,3,3,3,1,1,1,1,1,6,4,5)
> >  v6 <- c(1,1,1,2,1,3,3,3,4,3,1,1,1,2,1,6,5,4)
> >  m1 <- cbind(v1,v2,v3,v4,v5,v6)
> >  cor(m1)
> > #          v1        v2        v3        v4        v5        v6
> > #v1 1.0000000 0.9393083 0.5128866 0.4320310 0.4664948 0.4086076
> > #v2 0.9393083 1.0000000 0.4124441 0.4084281 0.4363925 0.4326113
> > #v3 0.5128866 0.4124441 1.0000000 0.8770750 0.5128866 0.4320310
> > #v4 0.4320310 0.4084281 0.8770750 1.0000000 0.4320310 0.4323259
> > #v5 0.4664948 0.4363925 0.5128866 0.4320310 1.0000000 0.9473451
> > #v6 0.4086076 0.4326113 0.4320310 0.4323259 0.9473451 1.0000000
> >
> > factanal(m1, factors=3) # varimax is the default
> >
> >
> > # Output from R
> >
> > #Call:
> > #factanal(x = m1, factors = 3)
> >
> > #Uniquenesses:
> > #   v1    v2    v3    v4    v5    v6
> > #0.005 0.101 0.005 0.224 0.084 0.005
> >
> > #Loadings:
> > #   Factor1 Factor2 Factor3
> > #v1 0.944   0.182   0.267
> > #v2 0.905   0.235   0.159
> > #v3 0.236   0.210   0.946
> > #v4 0.180   0.242   0.828
> > #v5 0.242   0.881   0.286
> > #v6 0.193   0.959   0.196
> >
> > #               Factor1 Factor2 Factor3
> > #SS loadings      1.893   1.886   1.797
> > #Proportion Var   0.316   0.314   0.300
> > #Cumulative Var   0.316   0.630   0.929
> >
> > #The degrees of freedom for the model is 0 and the fit was 0.4755
> >
> > /* SAS code with example data*/
> >
> > data fact;
> > input v1-v6;
> > datalines;
> > 1  1  3  3  1  1
> > 1  2  3  3  1  1
> > 1  1  3  4  1  1
> > 1  1  3  3  1  2
> > 1  1  3  3  1  1
> > 1  1  1  1  3  3
> > 1  2  1  1  3  3
> > 1  1  1  2  3  3
> > 1  2  1  1  3  4
> > 1  1  1  1  3  3
> > 3  3  1  1  1  1
> > 3  4  1  1  1  1
> > 3  3  1  2  1  1
> > 3  3  1  1  1  2
> > 3  3  1  1  1  1
> > 4  4  5  5  6  6
> > 5  6  4  6  4  5
> > 6  5  6  4  5  4
> > ;
> > run;
> >
> > proc factor data=fact rotate=varimax method=p nfactors=3;
> > var v1-v6;
> > run;
> >
> > /* Output  from SAS*/
> >
> >                                                          The FACTOR
> > Procedure
> >                                           Initial Factor Method:
> Principal
> > Components
> >
> >                                              Prior Communality Estimates:
> > ONE
> >
> >
> >
> >                                  Eigenvalues of the Correlation Matrix:
> > Total = 6  Average = 1
> >
> >                                          Eigenvalue    Difference
> > Proportion    Cumulative
> >
> >                                     1    3.69603077    2.62291629
> > 0.6160        0.6160
> >                                     2    1.07311448    0.07234039
> > 0.1789        0.7949
> >                                     3    1.00077409    0.83977061
> > 0.1668        0.9617
> >                                     4    0.16100348    0.12004232
> > 0.0268        0.9885
> >                                     5    0.04096116    0.01284515
> > 0.0068        0.9953
> >                                     6    0.02811601
> > 0.0047        1.0000
> >
> >                                      3 factors will be retained by the
> > NFACTOR criterion.
> >
> >
> >
> >                                                         Factor Pattern
> >
> >                                                  Factor1
> > Factor2         Factor3
> >
> >                                       v1         0.79880
> > 0.54995        -0.17614
> >                                       v2         0.77036
> > 0.56171        -0.24862
> >                                       v3         0.79475
> > -0.07685         0.54982
> >                                       v4         0.75757
> > -0.08736         0.59785
> >                                       v5         0.80878
> > -0.45610        -0.33437
> >                                       v6         0.77771
> > -0.48331        -0.36933
> >
> >
> >                                                Variance Explained by Each
> > Factor
> >
> >                                              Factor1         Factor2
> > Factor3
> >
> >                                            3.6960308       1.0731145
> > 1.0007741
> >
> >
> >                                          Final Communality Estimates:
> Total
> > = 5.769919
> >
> >                           v1              v2              v3
> > v4              v5              v6
> >                   0.97154741      0.97078498      0.93983835
> > 0.93897798      0.97394719      0.97482345
> >
> >
> >
> >                                                    The FACTOR Procedure
> >                                                    Rotation Method:
> Varimax
> >
> >                                                Orthogonal Transformation
> > Matrix
> >
> >                                                           1
> > 2               3
> >
> >                                           1         0.58233
> > 0.57714         0.57254
> >                                           2        -0.64183
> > 0.75864        -0.11193
> >                                           3        -0.49895
> > -0.30229         0.81220
> >
> >
> >                                                     Rotated Factor
> Pattern
> >
> >                                                  Factor1
> > Factor2         Factor3
> >
> >                                       v1         0.20008
> > 0.93148         0.25272
> >                                       v2         0.21213
> > 0.94590         0.17626
> >                                       v3         0.23781
> > 0.23418         0.91019
> >                                       v4         0.19893
> > 0.19023         0.92909
> >                                       v5         0.93054
> > 0.22185         0.24253
> >                                       v6         0.94736
> > 0.19384         0.19939
> >
> >
> >                                                Variance Explained by Each
> > Factor
> >
> >                                              Factor1         Factor2
> > Factor3
> >
> >                                            1.9445607       1.9401828
> > 1.8851759
> >
> >
> >                                          Final Communality Estimates:
> Total
> > = 5.769919
> >
> >                           v1              v2              v3
> > v4              v5              v6
> >
> >                   0.97154741      0.97078498      0.93983835
> > 0.93897798      0.97394719      0.97482345
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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