# Exploratory factor analysis using oblique and bifactor rotation : different pattern loadings

Meng Hu 07/08/2016. 0 answers, 72 views

When I try to compare oblique rotated factor analysis (promax, ML) with bifactor rotated analysis (ML), I get different pattern loadings. I don't know which solution should be retained; I am planning to use EFA to decide which pattern to be used for bifactor approach to MGFCA. Generally, when I read about bifactor solution, the pattern is identical to one produced by oblique rotated factor analysis in many, many examples.

MLFAwhite4<-factanal(datawhite3, factors=4, rotation="promax")
print(MLFAwhite4, digits=3, cutoff=.05)

Factor1 Factor2 Factor3 Factor4
spatrels   0.458   0.072
visaudit   0.566           0.058   0.051
verbcomp   0.261  -0.065   0.668
vismatch           0.520  -0.080   0.247
analsyn    0.637                   0.064
numrev            -0.099  -0.135   0.813
concform   0.758
picrecog   0.289   0.133
memwords          -0.152   0.114   0.606
geninfo                    0.885  -0.087
retrieve  -0.092   0.220   0.283   0.153
audatten           0.398   0.055   0.082
decisions          1.002          -0.167

BIFACTORwhite5ml<-fa(r=datawhite3, nfactors=5, max.iter=100, warnings=TRUE, rotate="bifactor", fm="ml")
print(BIFACTORwhite5ml, digits=3, cutoff=.05)

ML1    ML2    ML3    ML4    ML5    h2    u2  com
spatrels  0.423  0.057 -0.003  0.114  0.186 0.229 0.771 1.58
visaudit  0.604  0.004  0.063  0.103  0.262 0.448 0.552 1.45
verbcomp  0.672 -0.040  0.482  0.035  0.052 0.689 0.311 1.84
vismatch  0.513  0.427 -0.090 -0.046 -0.107 0.467 0.533 2.12
analsyn   0.621 -0.034 -0.016  0.289 -0.016 0.471 0.529 1.42
numrev    0.626 -0.036 -0.176 -0.239 -0.078 0.487 0.513 1.51
concform  0.691 -0.039  0.061  0.276  0.092 0.567 0.433 1.38
picrecog  0.298  0.110  0.030  0.007  0.293 0.188 0.812 2.29
memwords  0.553 -0.091  0.007 -0.269 -0.012 0.387 0.613 1.51
geninfo   0.585  0.003  0.616 -0.008 -0.019 0.722 0.278 2.00
retrieve  0.405  0.188  0.170 -0.045 -0.186 0.265 0.735 2.32
audatten  0.371  0.324  0.034 -0.080  0.069 0.255 0.745 2.16
decisions 0.402  0.761  0.004  0.016  0.019 0.742 0.258 1.52

The pattern here is generally different from an oblique rotated factor analysis. Maybe the syntax is incorrect ? If it's correct, then, what should I do (conclude) at this point, considering my final goal is to conduct CFA with bifactor approach ?

Thank you.

ttnphns 07/08/2016
It is the first time I've heard of "bifactor rotation" (shame on me). Can explain it or give a source where it is explained? Also, your first analysis seem to extract 4 factor and the second - 5 factors. And the programs are different (factanal vs fa) - did you make sure that they return the same results under all other conditions being equal?
Meng Hu 07/09/2016
If you don't like the term, let's just say it's an exploratory factor analysis using bifactor method. There is a reason why I added one factor in the bifactor method. The first factor, as you can see, is a general factor (on which all variables load), and all other factors are group/specific factors. And in the first method, which is a common approach to EFA, you get only specific factors, not the general factor. I generally also see authors do it like this. As for the difference between factanal and fa, there is none. You can do factanal or fa using fm=ml and you get exact same results.