I am struggling with understanding the relationship (or rather, the interaction) between different factor rotation algorithms and score extraction methods in Exploratory Factor Analysis. As far as I understand, oblique rotations (like direct oblimin) allow for correlations between the extracted factors, while orthogonal rotations do not. This much is clear. What I don't understand is how the choice of score extraction method (Anderson-Rubin, Bartlett or Regression) interacts with the choice of rotation. From what I understand, the Anderson-Rubin method ensures that the factor scores will be orthogonal while the Bartlett method allows the factors to correlate. Does this mean that the Anderson-Rubin method should not be used following an oblique rotation? Or do the two things apply to completely separate things and there is something I'm sorely missing?
On a related note: Am I correct in assuming that if one plans to regress the score of one factor on the other factors, only the oblique-Bartlett combination should be used?
Please, try to keep the explanation relatively simple, as I don't have an extensive mathematical background.