What issues, if any, might there be in rotating factors in order to obtain factor/component loadings of binary data? Is it acceptable to rotate the factors when doing a traditional PCA? (Assuming I’m using a polychoric correlation matrix.)
I am not a statistician, but an applied educational researcher making sure my approach is appropriate to the problem at hand.
My doubt comes from a note in the SAS support site that advises to use
PROC PRINCOMP or
PROC CORRESP instead of
PROC FACTOR (in all cases to be careful to factor a tetrachoric correlation matrix). One important difference between these two procedures and
PROC FACTOR is that the former do not implement factor rotation, even though a PCA can be specified within
PROC FACTOR, and would otherwise seem to be preferable for exploratory analysis. It occurred to me that perhaps rotation of factors is inappropriate for binary data, but I cannot find a discussion of this in literature or stat forums.
The problem, in case you care to know the context: We have data from several hundred colleges around the U.S. regarding what programmatic/curricular elements they implement in certain kinds of cohort educational programs. 24 variables, all dichotomous. We are looking to find patterns of how those elements tend to group together (in addition to a separate latent class analysis or cluster analysis to categorize the programs). Factor analysis is not appropriate since there is not a theoretical underlying latent structure that these elements are “measuring”.