I've been reading about performing exploratory factor analysis via principal axis factor extraction (PAF) and principal component analysis (PCA). I'm a bit confused about why the difference between the two methods is important, and the overarching question is why/when to use one method over the other?
Both methods use an eigen-decomposition of a matrix. In the PAF case, the input matrix is a reduced correlation matrix with communalities on the diagonal, whereas in PCA the input is just the correlation matrix
Why is it important that one method uses the reduced correlation matrix with communalities, and the other uses just the correlation matrix? How do the results differ, and how does that then change the interpretation of factor loadings?
Further reading states that PAF is a factor method, whereas PCA is a component method. I'm not sure why this distinction is important
The book states the following: "in component analysis, all of the variance in the variables, rather than just the common variance is analyzed. There is therefore no uniqueness term in the equation for component analysis". How does this relate to the use of communalities?