There's a lot of information on the forum about the differences between principal components analysis (PCA) and exploratory factor analysis (EFA) (for example here and here). I am new to both methods, but after looking through various answers to previous posts, I think that EFA is a better fit for my question, but I don't think it fits my data.
I have 6 observed variables which purport to measure the same construct. I want to contrast these 6 observed variables to hypothesis on whether they measure the same thing or if, in fact, they could be reflecting different constructs. This is very exploratory at this stage; I'm not interested in testing a hypothesis, but rather on coming up with one.
My first thought was to run a PCA and show how the variables cluster together in a biplot. However, I think most people would agree EFA is better for my question(?). The problem with EFA in my case is that 2 factors is the maximum I can choose to extract (as my number of observed variables is 6) and the EFA result indicates that I need more than 2 factors (I'm using the factanal function in R).
Could I simply use PCA and justify this on the grounds that more variables would be needed for a reliable EFA? (Note that I wouldn't be able to have many more variables as there aren't other ways of estimating the construct - this isn't an issue with the amount of data.)
If EFA is the only way to go, what could be done regarding the need for more factors vs. low number of variables?
