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
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