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Hi again all: Quick question regarding Mplus output for oblique rotations. Are the loadings in the output pattern coefficients (v. structure coefficients)? I believe I read somewhere (Tim Brown) this was the case, but just wanted to be sure it still is. Also, in comparing a 2 factor solution with results from SPSS using Oblimin, I find that the coefficients for some indicators are quite different (model fit about the same of course). Why might this be the case? I did notice that the Promax rotated coefficients were closer to what SPSS generated for Oblimin, but this puzzles me. I don't think it is because of FIML in Mplus (vs. listwise in SPSS b/c as noted the Promax coefficients were in the ballpark). Also, somewhat relatedly, what determines the given sign (+/) of a given loading...for example, in some cases between the two runs (SPSS/Mplus) the absolute values were on the mark, but the signs were different. Thanks in advance for any insight. 


Yes, the factor loadings are pattern coefficients. The Mplus V6 UG, page 539 mentions a gamma parameter for Oblimin. The default value for this may be chosen differently between the programs. Change of signs in a column of the factor loading matrix is inconsequential. It merely represents a different rotation that is trivially related to the one with all opposite signs. An example is an ability factor turned into an inability factor. 


Thanks Dr. Muthen. One conceptual question I am currently grappling with: Does one have to have an a priori logic laid out for choosing the type of orthogonal rotation they decide upon? Let's say hypothetically your pattern coefficients aren't interpretable with Oblimin (i.e., < .4 for most) then you run Promax and the factor structure is more clear and you get loadings that you generally originally expected (i.e., in the direction and degree expected). Is this fishing or simply working through the different angles of rotation for oblique to maximize the loadings and foster the substantive interpretation? In my reading of the literature, at least in Psych, Endo etc. nobody seems to lay out their arguments for choosing rotation beyond whether orthogonal or oblique. 


I think when you are doing EFA, you are in an exploratory stage and therefore investigating different kinds of rotations is perfectly ok. One needs to be aware of EFA not being able to decide on correlated or uncorrelated factors because the solutions are equivalent in terms of the reproduced correlation matrix  and choose whichever equivalent representation that gives the most useful interpretation. 

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