# Solved – correlations between factors in r- scores or loadings

I've conducted a factor analysis in r with three factors (function=fa {psych};rotation=promax ; method=GLS).

`` fa1 =fa(d,nfactors=3,rotate="promax",oblique.scores=TRUE,method="gls",missing=TRUE,scores=TRUE,impute="mean") ``

Now I would like to add a correlation matrix between the three factors. Which matrix will be better in defining the correlation between the factors? using the scores correlation?

``cor(fa1\$scores) ``

or the loadings correlation?

``cor(fa1\$loadings) ``
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#### Best Answer

The `psych` package's `fa` function should already provide you with the matrix of correlations between factors; there's no need for you to do this yourself. This information will be located in a section of your output labeled "With factor correlations of", just below the output pertaining the the proportion of variance explained by your factor solution. Though you could examine correlations between factor scores, this would introduce the problem of rotational indeterminacy–correlations between latent factors (what `fa` provides automatically), as opposed to observed factor scores, do not share this limitation. In practice though, both approaches will likely produce similar estimates of factor correlations. A matrix of the correlations between factor loadings, on the other hand, would not provide you with the kind of information you are seeking about the association between your factors.

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