Can I do parallel analysis with any type of exploratory factor analysis/principal component analysis? I wish to perform parallel analysis to determine how many factors I should extract from my maximum likelihood exploratory factor analysis. I have been referred to a program that calculates the eigenvalues for random data using Monte Carlo for principal component analysis.  I am not doing principal component analysis, however. I am doing maximum likelihood exploratory factor analysis. I have been told that you can do it for any type of EFA, but I am uncertain. For example, a few of the macros I have seen require that you identify if you are using PCA or PAF. This clearly means that it matters to some extent. 
Note that I have tried doing parallel analysis for PAF using the engine at http://ires.ku.edu/~smishra/parallelengine.htm. Unfortunately, the results did not make much sense. Every eigenvalue in my data was greater than the eigenvalue from the website, which I believe meant I should extra 100+ factors. 
Questions:


*

*Can I use the parallel analysis results designed to be used with PCA to determine how many factors I should extract from my maximum likelihood factor analysis?

*If not (I expect the answer to the above question is "no"), how can I do a parallel analysis to determine how many factors I should extract from my maximum likelihood exploratory factor analysis? 
 A: I do not have an original source, but it appears this topic is actually quite debated. Some argue that you can do parallel analysis from PCA eigenvalues when doing PAF/maximum likelihood EFA, while others suggest this is inappropriate. 
B. P. O'Connor wrote the following in his macro for parallel analysis for PCA/PAF (people.ok.ubc.ca/brioconn/nfactors/nfactors.html):

Principal components eigenvalues are often used to determine the number of common factors. This is the default in most statistical software packages, and it is the primary practice in the literature. It is also the method used by many factor analysis experts, including Cattell, who often examined principal components eigenvalues in his scree plots to determine the number of common factors. But others believe this common practice is wrong. Principal components eigenvalues are based on all of the variance in correlation matrices, including both the variance that is shared among variables and the variances that are unique to the variables. In contrast, principal axis eigenvalues are based solely on the shared variance among the variables. The two procedures are qualitatively different. Some therefore claim that the eigenvalues from one extraction method should not be used to determine the number of factors for the other extraction method. The issue remains neglected and unsettled.

A: Check out the fa.parallel() function in R's psych package by William Revelle since it does this with various extraction methods, one of which can be by ML (the default I believe is 'minres'). Hope that helps.
