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

Meng Hu 07/08/2016. 0 answers, 72 views
factor-analysis factor-rotation

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.

Here's my syntax, and an example of pattern loadings :

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

Loadings:
          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)

Standardized loadings (pattern matrix) based upon correlation matrix
            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.

2 Comments
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.

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