At 8:17 AM -0400 3/31/09, John Fox 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
As John pointed out, PCA is not the same as FA. Unfortunately, SAS labeled the PCA as a factor analysis, when it is not. And, when one does a principal components and extracts just the first three components (as you did), the unrotated solution is identical:
package(psych) pc3 <- principal(x,3,rotate="none") print(pc3,digits=5,cut=0)
V PC1 PC2 PC3
V1 1 0.79880 0.549948 -0.17614
V2 2 0.77036 0.561712 -0.24862
V3 3 0.79475 -0.076853 0.54982
V4 4 0.75757 -0.087363 0.59785
V5 5 0.80878 -0.456096 -0.33437
V6 6 0.77771 -0.483310 -0.36933
PC1 PC2 PC3
SS loadings 3.69603 1.07311 1.00077
Proportion Var 0.61601 0.17885 0.16680
Cumulative Var 0.61601 0.79486 0.96165
Test of the hypothesis that 3 factors are sufficient.
The degrees of freedom for the model is 0 and the fit was 1.57483
The number of observations was 18 with Chi Square = 19.16046 with
prob < NA
When you then rotate these components using Varimax, the solutions differ at the fourth decimal place
pc3 <- principal(x,3) print(pc3,cut=0,digits=5)
V PC1 PC2 PC3
V1 1 0.19991 0.93168 0.25210
V2 2 0.21193 0.94606 0.17562
V3 3 0.23805 0.23479 0.90997
V4 4 0.19920 0.19084 0.92891
V5 5 0.93057 0.22225 0.24208
V6 6 0.94738 0.19422 0.19896
PC1 PC2 PC3
SS loadings 1.94470 1.94172 1.88350
Proportion Var 0.32412 0.32362 0.31392
Cumulative Var 0.32412 0.64774 0.96165
Bill
-----Original Message----- From: r-help-boun...@r-project.org [mailto:r-help-boun...@r-project.org]OnBehalf 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 outputsfromR 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 RandSAS. 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:VarimaxOrthogonal 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 0.92909v5 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 v60.97154741 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 guidehttp://www.R-project.org/posting-guide.htmland 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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